instrumentation and control of electromagnetic - Repositories

A MULTI-STAGE DISTRIBUTED ENERGY PLASMA ARC RAILGUN

by

RYAN KARHI, B.S.E.E., M.S.E.E.

A DISSERTATION

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

DOCTORATE OF PHILOSOPHY

IN

ELECTRICAL ENGINEERING

Prof. John Mankowski

Chairperson of the Committee

Prof. Michael Giesselmann

Co-Chairperson of the Committee

Prof. Stephen Bayne

Prof. Jahan Rasty

Dr. Ian McNab

Dr. David Wetz

Ralph Ferguson

Dean of the Graduate School

December, 2010

Texas Tech University, Ryan William Karhi, December 2010

ii

Copyright 2010, RyanKarhi


iii

ACKNOWLEDGMENTS

First and foremost I would like to thank my family for their unconditional love

and encouragement throughout my studies. A special thanks goes to the Air Force Office

of Scientific Research (AFOSR), whom without, these projects would not be possible.

Thank you for your continued support and trust towards the Center for Pulsed Power and

Power Electronics (P3E) at Texas Tech University. I want to also thank the Institute for

Advanced Technology (IAT) at the University of Texas, especially Ian McNab and David

Wetz, for their generous donations and collaboration on the Multidisciplinary University

Research Initiative (MURI) railgun project. To my advisors, Prof. Mankowski and Prof.

Giesselmann, your guidance and support throughout this project led to its success. Thank

you for taking me under your wing and sharing your knowledge. I also wish to

acknowledge Dr. Hemmert, who provided me with my first railgun project and an

introduction to electromagnetic launch technology. I would like to give credit to Jeff

Diehl, Patrick Kelly, and Ian El-Dana who aided in the fabrication and assembly of

numerous components. To my pulsed power colleagues, thank you for your advice and

motivation. Special thanks goes towards the technicians and machinists of the P3E lab,

Danny, Dino, Elmer, Shannon, Lee, and Joel for their valued assistance and broad

expertise. Finally, I want to acknowledge a positive camaraderie within the P3E

laboratory and I am grateful for the wisdom and experience gained.


iv

TABLE OF CONTENTS

ACKNOWLEDGMENTS ................................................................................................. iii

ABSTRACT ..................................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

INTRODUCTION .............................................................................................................. 1

1.1 Railgun Background ......................................................................................... 2

1.2 Distributed Energy Store Background .............................................................. 5

1.3 Plasma Armature Background .......................................................................... 9

1.4 Synchronous Theory........................................................................................ 12

1.5 Motivation ....................................................................................................... 14

PRELIMINARY PLASMA ARC RAILGUN EXPERIMENTS ..................................... 16

2.1 Introduction..................................................................................................... 16

2.2 Switching Schemes .......................................................................................... 17

2.3 Experimental Results ...................................................................................... 19

2.3.1 Breech-fed Railgun Data ......................................................................... 19

2.3.2 Asynchronous DES Railgun Data ............................................................ 23

2.3.3 Pseudo-synchronous DES Railgun Data .................................................. 27

2.4 Conclusion ...................................................................................................... 29

PLASMA ARC SPLITTING ............................................................................................ 31

3.1 Introduction..................................................................................................... 31

3.2 Arc Splitting Theory ........................................................................................ 31

3.3 Arc Splitting Data ........................................................................................... 33


v

3.4 Arc Splitting Prevention .................................................................................. 38

PLASMA ARC LENGTH ................................................................................................ 40

4.1 Introduction..................................................................................................... 40

4.2 Experimental Setup ......................................................................................... 40


4.4 Conclusion ...................................................................................................... 46

DEVELOPMENT OF A NEW SYSTEM PROTOTYPE ................................................ 48

5.1 Introduction..................................................................................................... 48

5.2 Free-Arc DES Railgun Simulation .................................................................. 49

5.2.1 Introduction .............................................................................................. 49

5.2.2 Implemented Simulation Equations ......................................................... 50

5.2.3 Simulation Parameters and Results.......................................................... 54

5.2.4 Conclusion ............................................................................................... 58


5.3.1 Rails and Containment Structure ............................................................. 59

5.3.2 Energy Modules ....................................................................................... 62

5.3.3 Diagnostics ............................................................................................... 65

5.3.4 Plasma Injector ........................................................................................ 66

5.3.5 Control System ........................................................................................ 67

5.3.6 Support Structure and Built System......................................................... 68


5.5 Conclusion ...................................................................................................... 73

A 40-STAGE DES PLASMA ARC RAILGUN .............................................................. 76


vi

6.1 Introduction..................................................................................................... 76


6.2.1 Containment Structure and Rails ............................................................. 77

6.2.2 Energy Module Modification ................................................................... 78

6.2.3 Printed Circuit Board Diagnostics ........................................................... 80

6.2.4 Data Acquisition System ......................................................................... 83

6.2.5 Built System ............................................................................................. 85

6.3 Control System ................................................................................................ 87

6.3.1 Introduction .............................................................................................. 87

6.3.2 Hardware .................................................................................................. 87

6.3.3 Software ................................................................................................... 89


6.4.1 Asynchronous Energy Scheme ................................................................ 91

6.4.2 Synchronous Energy Scheme .................................................................. 93

6.5 Conclusion ...................................................................................................... 95

SUMMARY AND CONCLUSION ................................................................................. 97

REFERENCES ............................................................................................................... 102

APPENDIX A ................................................................................................................. 103

MULTI-STAGE DES FREE-ARC SIMULATION ........................................... 103

APPENDIX B ................................................................................................................. 112

CONTROL SYSTEM CODE ............................................................................. 112

B.1 Control Program for Stages 1-24 ............................................................. 112

B.2 Control Program for Stages 25-40 ........................................................... 121


vii

APPENDIX C ................................................................................................................. 124

RAILGUN SYSTEM OPERATION MANUAL................................................ 124


viii

ABSTRACT

The development process pertaining to the design, fabrication, coding, and testing

of multi-stage distributed energy plasma arc railguns are presented. In collaboration on

an Air Force Office of Scientific Research (AFOSR) funded Multidisciplinary University

Research Initiative (MURI) project, the Center for Pulsed Power and Power Electronics

(P3E) at Texas Tech University is responsible for developing and investigating a

functional scale model of a multi-stage distributed energy store (DES) railgun to analyze

its effectiveness to suppress a restrike phenomenon and increase plasma armature railgun

performance 1. The term “restrike” denotes the formation of an electrical breakdown in

the railgun bore some distance behind a traveling plasma armature. The formation of this

secondary arc reduces the driving force on the primary armature and has led to a velocity

ceiling of approximately 6 km/s on all breech-fed plasma armature railguns. Numerous

solutions have been theorized as viable methods of restrike prevention but lack

experimental verification. The primary objective of our research team within the MURI

effort is to experimentally test Dr. Jerry Parker’s theoretical restrike suppression

technique 2 that was developed at Los Alamos National Laboratory in the 1980’s. The

project tasks are organized to identify potential problematic issues and verify theoretical

concepts before implementation of a full scale system.


ix

LIST OF FIGURES

Fig. 1.1: Schematic of Ampere’s Law ................................................................................ 3

Fig. 1.2: Railgun Force Schematic ...................................................................................... 4

Fig. 1.3: Breech-fed Energy Scheme .................................................................................. 6

Fig. 1.4: Distributed Energy Store Scheme ........................................................................ 7

Fig. 1.5. Illustration of the Electric Field Profile for a Breech-Fed Scheme and a DES

Scheme. ............................................................................................................................... 8

Fig. 1.6: Schematic of a Free-Arc Traveling Below Mach 10. ......................................... 10

Fig. 1.7: Schematic of a Free-Arc Traveling Above Mach 10. ......................................... 11

Fig. 2.1. Circuit Diagrams of the 3 Types of Switching Schemes. (a) Breech-Fed (b)

Asynchronous and (c) Pseudo-Synchronous. ................................................................... 18

Fig. 2.2. Plasma Velocity Comparison. ........................................................................... 20

Fig. 2.3. Breech-Fed System Data Using the Alumina Bore Insulators. ......................... 21

Fig. 2.4. Breech-Fed System Data Using the G-10 Bore Insulators. ............................... 22

Fig. 2.5. Arc Erosion Photographs. (a) Breech Region and (b) Middle Region. ............. 23

Fig. 2.6. Asynchronous DES Railgun Data Using G-10 Bore Insulators. ....................... 24

Fig. 2.7. Asynchronous DES Railgun Data Using Alumina Bore Insulators. ................. 26

Fig. 2.8. Pseudo-Synchronous DES Railgun Data Using G-10 Bore Insulators. ............ 28

Fig. 2.9. Pseudo-Synchronous DES Railgun Data Using Alumina Bore Insulators........ 29

Fig. 3.1. Distributed Energy Current Waveforms. ........................................................... 34

Fig. 3.2. Armature B-dot Probe Signals from Shot 1....................................................... 36



x


Fig. 4.1. Schematic of Photodiode Reverse Voltage Circuit11

. ........................................ 41

Fig. 4.2. A Drawing of the DES Railgun and Optical Diagnostics. ................................ 41

Fig. 4.3. Illustration of the Fiber Line Mounting. ............................................................ 42

Fig. 4.4. A Picture of the Five Optical Fiber Couplers. ................................................... 43

Fig. 4.5. Photodiode Waveforms with Corresponding Armature Current. ...................... 44

Fig. 4.6. Arc Length Calculations vs. Pressure and Location. ......................................... 45

Fig. 4.7. Arc Velocity Calculations vs. Pressure and Location. ...................................... 46

Fig. 5.1. Schematic of a Stage in which the Plasma Arc has Passed Through2. .............. 51

Fig. 5.2. Schematic of a Stage that Contains the Plasma Arc2. ....................................... 51

Fig. 5.3. Simulated Current Waveforms for a 40-Stage System. Top: Current Waveforms

for Stages 1-20. Bottom: Current Waveforms for Stages 21-40. ...................................... 56

Fig. 5.4. Simulated Armature Current. ............................................................................ 57

Fig 5.5. Simulated Arc Velocity. ..................................................................................... 58

Fig. 5.6. Cross-Sectional View of the Railgun Prototype. ................................................ 60

Fig. 5.7. Interior View of the Containment Structure. ...................................................... 61

Fig. 5.8. Partially Disassembled Railgun View. ............................................................... 61

Fig. 5.9. CAD Drawing of the Distributed Energy Module.............................................. 63

Fig. 5.10. Variable Self-Inductance Scheme. ................................................................... 64

Fig. 5.11. Rail B-dot Probe Orientation. ........................................................................... 66

Fig. 5.13. Control System Hardware. ............................................................................... 68

Fig. 5.14. Photographs of the 7-Stage Prototype System. (a) View of Switch and Diode

side. (b) View of Capacitor Bank Side. ............................................................................ 70


xi

Fig. 5.16. B-dot Measurements from the Prototype System. ............................................ 72

Fig. 6.1. CAD Drawing of a 40-Stage DES Railgun. ....................................................... 76

Fig. 6.2. Photograph of the Containment Structures. ........................................................ 77

Fig. 6.3. Photograph of the Lap Joint Rail (Top-Back View, Bottom-Front View). ........ 78

Fig. 6.4. CAD Drawing of the Distributed Energy Module.............................................. 79

Fig. 6.5. Photograph of the PCB B-dot Probe and Plot of the Integrated and Calibrated

Data. .................................................................................................................................. 81

Fig. 6.6. Photograph of the PCB Rogowski Coil and Plot of the Integrated and Calibrated

Data. .................................................................................................................................. 82

Fig. 6.7. PCB Armature B-dot Probes. (a) 2-Turn Design. (b) 14-Turn Design. (c) 28-

Turn Design. ..................................................................................................................... 83

Fig. 6.8. National Instruments DAQ System. ................................................................... 85

Fig. 6.9. Photograph of the 40-Stage DES Railgun (Top/Side View). ............................. 86

Fig. 6.10. Photograph of the 40-stage DES Railgun (Isometric View). ........................... 86

Fig. 6.11. Control System Hardware. ............................................................................... 88

Fig. 6.12. Flow Chart of the Control Program. ................................................................. 90

Fig. 6.13. Current Waveforms from a 40-Stage asynchronous DES Railgun. ................. 92

Fig. 6.14. Armature B-dot Waveforms from a 40-Stage asynchronous DES Railgun. .... 93

Fig. 6.15. Current Waveforms from a 40-Stage Synchronous DES Railgun. .................. 94

Fig. 6.16. Armature B-dot Waveforms from a 40-Stage Synchronous DES Railgun. ..... 95

Fig. B.1. LabVIEW Control Program for Stages 1-24 with Red Zoom Box Labels. ..... 112

Fig. B.2. 3 Second Wait Function (Z1). .......................................................................... 113

Fig. B.3. Set Line Direction for Digital Input/Output Modules (Z2). ............................ 114


xii

Fig. B.4. Check Digital Input/Output Modules Status (Z3). ........................................... 114

Fig. B.5. Trigger Sequence for DAQ, Plasma Generation, and Stage 1 (Z4). ................ 115

Fig. B.11. LabVIEW Control Program for Stages 25-40 with Red Zoom Box Labels. . 121

Fig. B.12. 1 Second Wait Function (Z9). ........................................................................ 122

Fig. B.13. Trigger Loop to Start Reading the B-dot Probes (Z10). ................................ 123


1

CHAPTER Ι

INTRODUCTION

The Air Force’s interest in electromagnetic launch technology is driven by the

search for an economical means to launch large numbers of micro-satellites into orbit.

The current costly method involves burning millions of pounds of fuel and is growing

obsolete. Recent plasma railgun development alongside the development of smaller and

lighter satellites has brought new hope back to the electromagnetic launcher. Rapidly

advancing integrated circuit (IC) technology has opened the door for an inrush of micro

devices. These devices include satellites weighing a mere 20 pounds that are capable of

withstanding the large G-forces associated with fast acceleration up to the escape velocity

of approximately 11.2 km per second.

Achieving the escape velocity using a solid metal armature is an unlikely

scenario. An extremely large magnitude of current (Mega-Amperes) is required to

accelerate the satellite launch package to velocities in excess of 10 km per second. Heat

flux generated by Mega-Ampere currents flowing through the armature for hundreds of

milliseconds to seconds will melt the solid structure and eventually transition into

plasma. Reducing this current magnitude to kilo-Amperes and slowly accelerating the

armature is a solution; however, this requires a launcher length in excess of a few

kilometers and would be difficult to maintain electrical contact due to armature erosion or

degradation as it travels down the long rail length. In addition, solid metal armatures will

gouge the rails at hypervelocities, resulting in a short rail lifetime. Therefore, a plasma

armature is presently the only solution to achieve hypervelocities using a railgun.


2

Challenges still exist to successfully launch any payload to a hypervelocity using

a plasma armature railgun. These obstacles include: thermal management, structural

failure, pre-injection, plasma puffing and/or blow-by, plasma bifurcation, and restrike

suppression. The latter is the most misunderstood problem to resolve in order to achieve

the hypervelocity regime. Restrike refers to secondary arcs that form behind a primary

plasma armature and prove to be detrimental to achieving the theoretical velocity of

electromagnetic launchers. Further explanation of this effect is covered in the plasma

armature background, Section 1.3. Numerous solutions have been theorized as viable

methods of restrike prevention but lack experimental verification. Our research team is

tasked to analyze a theory involving a multi-stage DES railgun system. This concept was

first proposed by Marshall3 in an asynchronous scheme and later by Parker

2

synchronously. This paper will investigate the design and performance of small scale

DES railgun systems, with future motivation towards a full scale product.

1.1 Railgun Background

The laws of physics that govern the operation of a railgun are not new to the

scientific community. A power source supplies a large magnitude of current, kA to MA,

through the conductive rails and armature. From Ampere’s law, a mathematical

consequence of the Biot-Savart law, this current produces a large magnitude magnetic

flux density. This magnetic flux circulates the rails in accordance to the right hand rule

shown in Fig. 1.1.


3

Fig. 1.1: Schematic of Ampere’s Law

The interaction of this current (moving charged particles) in a magnetic field leads

to an interesting effect. A Dutch theoretical physicist, Hendrik Lorentz, discovered in

1896 that electric and magnetic fields interact with charged particles4. This causes a

force called the Lorentz force and we concentrate our attention on the Lorentz magnetic

force, equation 1.1. This equation describes the main driving force behind

electromagnetic projectile acceleration. The cross product of current density and a

magnetic field results in a magnetic force given by

(1.1)

where is the current density vector [A/m2] and is the magnetic field vector [T].

This force can be much stronger than the pull of Earth’s gravity and has attracted

the attention of scientists for a variety of applications. In the application of a railgun, this

force is applied to a metallic conductor or conducting plasma, known as the armature. An

equivalent form of the Lorentz magnetic force in relation to a railgun is given by

(1.2)


4

where I is the current through the armature [A] and dL/dx is known as the inductance

gradient [L/m] which is a function of the rail geometry. The force applied to the

armature must overcome a frictional drag FD associated with contact with the rails.

The breech-fed railgun concept and forces are shown schematically in Fig. 1.2.

The armature completes the electrical circuit between the rails and allows current to flow

provided by an energy source. The cross product of the current density through the

armature and the magnetic field rotating around the rails and coupling into the armature

produces, in accordance with the Lorentz magnetic force, a force vector parallel to the

rails and directed away from the breech end. Since the rails are also present in this

magnetic field and have current flowing through them, additional Lorentz forces acts to

push the rails away from each other. Therefore, the rails must be contained in an

enclosure to oppose these forces and retain the electrical connection between the

armature and rails.

Fig. 1.2: Railgun Force Schematic


5

1.2 Distributed Energy Store Background

Two main energy schemes are discussed in this dissertation and it is worthwhile

to explain their differences. One is the breech-fed energy scheme and the other is the

distributed energy store (DES) scheme. An explanation of the breech-fed energy scheme

is addressed first since it is the simpler of the two.

In a breech-fed energy scheme, Fig. 1.3, electrical energy is applied to the breech

end of the rails using a single energy source. The input current flows in a loop through

both rails and the armature. For maximum energy efficiency, all of the electrical energy

would be converted into kinetic energy to drive the armature. In reality, there are many

loss mechanisms associated with the presented configuration. However, we will focus on

the two dominate mechanisms. One is the joule heating resistive losses in the rails and

armature. Rail conductivity and geometry determine this resistance. As the armature

travels further away from the breech, the current must flow through an increasing length

of rail. The result is a larger resistance and in effect, larger power losses. The second

dominating loss mechanism is associated with the rail inductance. About half of the

input energy is converted into magnetic energy where it is stored in the rails. As the

current flows through an increasing rail length, more of the electrical input energy is

converted and stored magnetically. The combination of these loss mechanisms results in

poor energy efficiency for systems with long rail lengths.


6

Fig. 1.3: Breech-fed Energy Scheme

To reduce the described energy losses, Marshall3 proposed a new railgun

configuration in 1980 known as the distributed energy store (DES) scheme, Fig. 1.4. For

the breech-fed scheme, a single current loop exists that grows in length with the armature

motion, all the way down to the muzzle. The DES scheme maintains continuous rails but

creates multiple current loops that flow through reduced rail distances. This is

accomplished by replacing the large breech-fed energy source with many smaller

independent energy sources known as distributed energy stores, which are electrically

connected to the rails at different locations along the rail length. The combination of a

single DES and the length of rail between it and the subsequent DES is known as a

“stage” within the system. Each of these stages produces short current pulses behind the

armature to maintain a Lorentz driving force. The short current pulses sourced from each

of the stages flows through a small portion of the rail length which reduces the inductive

and resistive energy losses. Additional advantages to this energy scheme include:

improved current waveform control, reduce switch current carrying requirements, and a

reduced electric field several bore diameters behind the armature.


7

Fig. 1.4: Distributed Energy Store Scheme

In 1989, Parker1 theorized an additional advantage of the DES scheme. During

his research analyzing the formation of restrike arcs within plasma armature railguns, he

concluded that restrike is an electrical breakdown that requires an electric field across the

rails. His experiments also discovered that these restrike arcs developed many bore

diameters behind the primary plasma armature. He postulated multiple solutions to

suppress restrike, including the DES scheme. The DES scheme is theorized to suppress

restrike arc formation because the electric field, Fig. 1.5, associated with the back EMF

voltage is localized to active stage regions. This reduces the probability of an electrical

breakdown in the dense ablated gas trailing behind the armature. Due to an end of

plasma armature railgun research in the 1980’s, this theory was never experimentally

tested for legitimacy.


8

Fig. 1.5. Illustration of the Electric Field Profile for a Breech-Fed Scheme and a DES

Scheme.

Although energy efficiency is improved in the DES scheme, electrical complexity

increases with the number of stages implemented. If energy is released by a stage ahead

of the armature, the effect is the creation of a Lorentz force opposing the desired muzzle

oriented motion. This result is detrimental to achieve the target velocity and must be

prevented at all costs. Since a number of DES railguns are examined in this paper, issues

associated with timing control are addressed by implementing control systems for

accurate and reliable railgun operation.


9

1.3 Plasma Armature Background

Plasma armature railguns have been the subject of active research and

development since the Rashleigh and Marshall paper5 was published in 1978. This paper

stated the theoretical possibility of accelerating plasma armatures to a significant fraction

of the speed of light with velocity limitations realized by projectile-bore interactions. A

decade later, experimental research identified the true velocity limiting factor, known as

plasma restrike. The processes contributing to the generation of these secondary arcs are

presented below. For a more in depth description refer to the following papers1,6

.

The experiments in this paper accelerate a different type of armature known as a

“free-arc”. Unlike solid metal armatures, this armature is essentially a super heated gas

in a plasma state. The plasma typically has a temperature ranging from 20,000 to 30,000

Kelvin, similar to the surface temperature of the Sun. The reason it is referred to as a

free-arc is because no physical load exists for the plasma to push, with exception of the

bore fill gas. In a conventional plasma armature railgun, the plasma is accelerated

electromagnetically by the Lorentz force and contained and compressed by the magnetic

pressure. When a nonconductive payload is placed ahead of the plasma, the plasma

pressure pushes or accelerates the payload to a target velocity. For the MURI project this

payload is a 20 lb micro-satellite with a target velocity equal to the escape velocity. To

relieve the financial burden of a large energy storage facility required to accelerate a

launch package, a free-arc railgun is an adequate substitution to physically emulate in-

bore plasma dynamics at hypervelocities. It is imperative to understand the in-bore

physical interactions involving a free-arc to analyze the data presented in this paper.


10

This section will give the reader a basic understanding of the underlying free-arc

physical processes. A small amount of plasma is generated inside of the bore at the

breech end. This conductive plasma is accelerated by the Lorentz magnetic force. In our

experiments, the bore is filled with air at pressures varying from 5 to 50 Torr. In this low

pressure environment the plasma rapidly accelerates to a velocity much greater than 0.34

km/s, the speed of sound in air. This effect results in the formation of a shock front as the

radiating plasma sweeps up the air ahead of it, seen in Fig. 1.6.

Fig. 1.6: Schematic of a Free-Arc Traveling Below Mach 10.

When the plasma velocity exceeds Mach 10, the shocked gas begins to ionize and

becomes part of the moving plasma6. Therefore, two well defined regions exist inside of

the bore; the accelerating plasma arc and the unshocked gas ahead of it, displayed in Fig.

1.7.


11

Fig. 1.7: Schematic of a Free-Arc Traveling Above Mach 10.

Assuming no ablation, the plasma arc’s velocity can be calculated6 by

(1.3)

where =dL/dx is the inductance gradient, is the ratio of specific heat, is the initial

gas density, I is the armature current, is the rail separation distance, is the distance the

shock front has moved, and is a scale length describing the viscous forces.

The illustration, shown in Fig. 1.7, depicts a free-arc traveling above mach 10 in a

quasi-equilibrium state after having moved a substantial distance down the rail length.

The extreme heat radiating from the plasma ablates material from the walls. This ablated

material becomes ionized which allows magnetic forces to accelerate it. A small portion

of this ionized material joins the main plasma arc while most experiences viscous

boundary forces and is swept backwards to form the plasma tail region. In this region the

ionized particles mix with neutral gas that reduces the conductivity. The weakly ionized

particles lose much of their acceleration and fall even further back into what is known as

the neutral region, where no current flows. The gas in this region is highly energetic and

both heat and momentum continue to ablate material from the walls. The high gas


12

density and weak ionization contribute to quench conductivity. However, the presence of

a high electric field will cause run-away ionization and the resulting Paschen breakdown

will establish a secondary arc that is known as restrike. According to Paschen’s Law,

electrical breakdown is a function of the gas composition, the pressure, and the electric

field across a constant gap distance. The electric field that causes restrike is generated by

the moving magnetic field emanating from the rails1, given by

(1.4)

where =dL/dx is the inductance gradient, is the armature current, is the plasma

armature velocity, is the gas velocity behind the armature, is the armature voltage,

and is the rail separation distance. The first term in the equation is known as the back

electromotive force (EMF) voltage. This induced voltage is a consequence of changing

magnetic flux and is a function of the armature velocity. Therefore, an armature traveling

at a hypervelocity can generate a back EMF voltage large enough to exceed the

breakdown voltage across the rail gap.

1.4 Synchronous Theory

This paper will discuss two different current waveform profiles implemented on a

DES scheme. The first is known as “synchronous” and the second is “asynchronous”.

Synchronous refers to the speed of an electromagnetic wave in the LC transmission line

formed by the rails and capacitors being matched to the velocity of the armature. A

synchronous distributed energy system is theorized to prevent restrike by reducing the

breech voltage, a function of arc velocity, to a magnitude below the high voltage


13

breakdown threshold. The electric field associated with this breech voltage is generated

by the moving magnetic field emanating from the rails, Eq. 1.4. Examining this equation,

the armature current can be carefully chosen such that the rail current in critical sections

of the railgun can be near zero. This is accomplished by underdamping the DESs to

source negative current. An asynchronous DES scheme does not match the armature and

phase velocities and in addition, does not allow current reversal to take place on any of

the energy banks.

The two schemes are similar in that both implement the technique of distributed

energy to increase efficiency and reduce the trailing electric field. However, according to

the electric field equation, Eq. 1.4, the synchronous scheme will be more effective.

Current reversal is utilized on a synchronous scheme to effectively cancel residual

positive current remaining in regions many bore diameters behind the main plasma arc.

Elimination of this current does not fully quench the E-field, but reduces the magnitude

to prevent restrike.


14

1.5 Motivation

The Center for Pulsed Power and Power Electronics (P3E) at Texas Tech University

continues to develop and investigate distributed energy source (DES) schemes applicable

to hypervelocity electromagnetic launch systems. The goal is to identify potential

problematic issues and verify theoretical concepts before implementation onto a full scale

system. A distributed energy scheme is attractive for a number of reasons:

(1) Theoretically predicted to suppress restrike arc formation

(2) Proven to increase energy conversion efficiency vs. breech-fed configuration7

(3) Ability to tailor the projectile acceleration (soft launch and constant acceleration)

(4) Multiple stages reduce the switch current carrying requirements

Although Marshall3 is credited with the DES railgun concept, the theoretical analysis

and mathematical background of (1) was developed at Los Alamos National Laboratory

in the 1980’s by Parker2. The primary objective of our research team within the

Multidisciplinary University Research Initiative (MURI) effort is to examine Parker’s

theoretical concept through basic research. Although all DES railguns have the potential

to suppress restrike, Parker’s theory2 maximizes the energy efficiency while minimizing

the current in the bore behind the armature. This is accomplished by two main principles.

The first is to operate in a “synchronous” mode where the plasma velocity is matched to

the gun’s intrinsic velocity, or phase velocity. This is accomplished by adjustment of the

pressure and current so the arc transits a stage in about the half cycle time of the DES

discharge current. The second principle involves under-damped DES current waveforms

that provide negative current to cancel out residual positive current that is trailing behind


15

the armature. This promotes an enhanced isolation of the electric flux in the bore behind

the armature.

The second discussed benefit (2) becomes important when launcher lengths exceed a

few meters. Since the projected satellite payload will inherently contain electronics

prone to failure by excessive acceleration forces, a launcher of considerable length

becomes a critical requirement to reduce or “soften” the acceleration loads. For

applications where railgun lengths greater that ten meters are required (as in our case),

sustaining energy store simulations show energy conversion efficiencies in excess of 60

percent can be achieved8.


16

CHAPTER ΙΙ

PRELIMINARY PLASMA ARC RAILGUN EXPERIMENTS

2.1 Introduction

This chapter reiterates restrike data obtained from a breech-fed railgun and brings

closure to past DES railgun experiments at Texas Tech University. The experimental

setups and control systems are described in the thesis9; therefore, these topics will not be

discussed in this paper.

Experimental results from three preliminary railgun configurations are presented.

These include a breech-fed railgun, a 4-stage asynchronous DES railgun, and a 4-stage

pseudo-synchronous DES railgun. The latter DES railgun does not meet all of Parker’s

requirements for synchronous operation and is therefore referred to as “pseudo-

synchronous.” The two DES systems are simply a first step approach to analyze

distributed energy schemes and identify possible problem areas undetected by theory and

simulations. Acquired data from the breech-fed system determined the amount of energy

and current magnitude required for restrike in the railgun bore. These conditions were

applied to the distributed energy schemes to determine if the preliminary systems could

prevent restrike before movement to a truly synchronous system.


17

2.2 Switching Schemes

Three different switching schemes are employed. They are breech-fed, asynchronous,

and pseudo-synchronous. The circuit diagram for each configuration is shown in Fig.

2.1. The breech-fed scheme, shown in Fig. 2.1(a), is the most conventional switching

scheme. Each of the capacitor banks are connected to the breech side of the railgun.

Switching of each of the banks is staggered in order to generate a “trapezoidal” type

current pulse. The asynchronous switching scheme, shown in Fig. 2.1(b), employs a

distributed energy feed. Each of the capacitor banks delivers current upon arrival of the

armature at the respective feed point to the railgun. Since the SCRs only conduct current

in one direction, only positive current is fed to the railgun. The pseudo-synchronous

switching scheme, shown in Fig. 2.1(c), is similar to the asynchronous type with the only

variation in the first stage switching. An SDD303KT rectifier diode is placed in anti-

parallel with the thyristor to act like a triac switch and allow both positive and negative

current flow. The diode has a peak hold-off voltage of 6 kV and a non-repetitive peak

surge current of 60 kA for 8.3 ms. The magnitude of the negative current was controlled

using a carbon resistor in series with the diode. Pseudo-synchronous switching

experiments utilizing the alumina inserts were preformed for two cases: the first without

this resistance and the second with a 120 m resistor.


18

(a)

(b)

(c)

Fig. 2.1. Circuit Diagrams of the 3 Types of Switching Schemes. (a) Breech-Fed (b)

Asynchronous and (c) Pseudo-Synchronous.


19

2.3 Experimental Results

2.3.1 Breech-fed Railgun Data

The control system was not integrated onto the breech-fed system. Rather, fixed trigger

timing was applied to the three stages sequentially at 1, 160, and 190 s. The graph in

Fig. 2.2 displays the effects of ablation on the arc’s velocity for the breech-fed system.

The experimental data is an average of two shots per pressure using alumina and G-10 as

the ablated material. As expected, experimentation using the alumina inserts resulted in

higher arc velocities. Heavy ablation with the G-10 resulted in an increase of arc mass

and therefore an arc velocity reduction. A noticeable reduction is observed at pressures

of 5-10 Torr where the effect of ablation on the arc’s velocity is more profound.

Increasing pressure slowed down the arc for both cases because there are more initial gas

molecules to be swept up and added to the plasma mass. Accompanying the two velocity

waveforms is a third velocity waveform calculated from Eq. 1.3.

This equation is a function describing the plasma velocity assuming no ablation.

Calculations made using Eq. 1.3 at each pressure correspond reasonably to experiments

using the low ablating alumina.


20

Fig. 2.2. Plasma Velocity Comparison.

The collected data in Fig. 2.3 used the alumina bore insulators, a chamber pressure of 5

Torr, and a charging voltage of 3 kV. The current contribution from all three stages is

shown alongside four rail B-dot probe signals. The four probes were located 18.5, 96.7,

174.8, 241.3 cm, respectively, from the breech. Each B-dot measures the derivative of

the rail current at different sections of the railgun. The raw voltage signals (not shown)

have been integrated to analyze the current through the rails at each probe location. A

Rogowski coil measured a 40 kA, approximately trapezoidal, current pulse 500 s in

width. This waveform shape maintained a constant driving force on the plasma arc for

the majority of propagation through the bore. The rail current waveforms in this figure

show no indication of restrike. The current seen at B-dot 2 appears to exceed the input

current. This effect can be attributed to calibration error and was later corrected. The

occurrence of restrike was absent from all experimental tests utilizing the alumina


21

insulators in the breech-fed system. If the current magnitude was incrementally

increased, eventually restrike would be observed.

Fig. 2.3. Breech-Fed System Data Using the Alumina Bore Insulators.

An example of restrike is shown in Fig. 2.4 for the breech-fed system. This particular

shot used G-10 bore insulators, a chamber pressure of 10 Torr, and a charging voltage of

3.5 kV. Collected data from a number of shots (not shown) indicated repeated

development of restrike arcs using the G-10 bore insulators. By observing the rail

currents seen at rail B-dots 4-7, it is apparent that the rail current at these locations does

not match the sourced current magnitudes from the capacitor banks. A portion of the

current must therefore be flowing elsewhere, demonstrating a classical example of

restrike. The data suggest that a secondary arc formed sometime after 130 s.


22

Fig. 2.4. Breech-Fed System Data Using the G-10 Bore Insulators.

Figures 2.5(a) and (b) show different erosion patterns on the copper rails after

approximately 15 shots. Figure 2.5(a) is a picture taken at the breech end of the rails.

The plasma arc formation appears to be a highly dynamic process. The “chicken scratch”

erosion traces produced by the plasma are streamer-like with no defined structure. As the

plasma travels a distance of many bore diameters, the magnetic pressures within the bore

confine the plasma to the center of the rails. Figure 2.5(b) shows the rail erosion at a

location between the breech and the muzzle. Here, the erosion trace is only present at the

center of the rail surface, suggesting a narrow arc profile. Light sanding refinished the

surface and allowed the rails to be used repeatedly.


23

(a) (b)

Fig. 2.5. Arc Erosion Photographs. (a) Breech Region and (b) Middle Region.

2.3.2 Asynchronous DES Railgun Data

The experimental results obtained from a 15 kJ, 4-stage asynchronous DES plasma arc

railgun are presented. The railgun was divided into four equal distant stage lengths

measuring 58 cm. Replication of the breech-fed system current waveform was achieved

to close approximation. This allows for direct comparison of ablation and restrike data

between the two systems. Experimental results using the two in-bore materials, alumina

and G-10, are discussed.

The collected data in Fig. 2.6 used the G-10 bore insulators, a chamber pressure of 10

Torr, and a charging voltage of 2.7 kV. The current distribution from all four stages is

shown alongside five rail B-dot probe signals. The five probes were located 18.5, 96.7,

135.7, 194.3, 322.6 cm, respectively, from the breech. To analyze a distributed system

properly, the current contribution from all stages prior to the probe location must be

compared to the probe’s signal. The stage 1 probe analysis shows no observable restrike.

The probe’s signal shows the current rise up to the full current magnitude and then

follows the current waveform throughout 450 s. From 450 to 500 s, the probe

indicates a negative 6 kA magnitude flowing toward the breech. This current is sourced


24

from the energy released in stage 4 and is the time when a secondary arc arrives at the

probe.

Fig. 2.6. Asynchronous DES Railgun Data Using G-10 Bore Insulators.

A clear indication of current flowing toward the breech is observed in the remaining

three stages. In stage 2 probe analysis, the negative current waveform (observed between

250-500 s) mirrors the waveform produced from the last two stages with a reduced

magnitude. This indicates that not all of the current released by stages 2, 3, and 4 is

flowing toward the primary arc.

The plasma arc has an approximate length of 5-15 bore diameters neglecting ablation

and increases linearly throughout its bore travel6. Calculation of the upper limit of this

approximation results in a plasma arc 25.5 cm in length, nearly half the stage length. The


25

upper limit is appropriate with the high ablating G-10 bore insulators. Analysis of the

control system trigger timing indicates stage firing when the head of the arc has traveled

less than half the length of the respective stage. Since the full arc length is not ahead of

the input current location, a portion of the distributed current will be diverted to the

trailing plasma tail. This tail region is composed of highly ionized ablated material swept

back from viscous boundary forces. Compared to the arc head, this plasma region lacks

the density required for stability and is vulnerable to bifurcation from the arc head by

magnetic pressure gradients sourced from a distributed current feed. These presented

data confirm the discovery of a new type of secondary arc formation within a plasma arc

railgun, referred to as “plasma arc splitting.” By definition of the Lorentz force, the

portion of the plasma in front of the input current location continues to accelerate toward

the muzzle while the portion behind is accelerated toward the breech. In these data, this

process is observed when the second stage is triggered. Since the arc traveling toward the

muzzle is now significantly reduced in length, plasma arc splitting will not occur when

the last two stages fire. The rate at which the plasma tail grows during this time interval

is reduced as a consequence of the high arc velocity ablating less material. A velocity

calculation using Eq. 1.3 with the current magnitude flowing toward the breech suggests

that the secondary arc arrives at the stage 1 probe at 450 s (in agreement with the data

presented in Fig. 2.6) if it starts from the second stage position. Chapter III describes this

plasma arc splitting process in greater detail.

The collected data in Fig. 2.7 used the alumina bore insulators, a chamber pressure of

10 Torr, and a charging voltage of 2.7 kV. The four probes were located 18.5, 96.7,

135.7, 322.6 cm, respectively, from the breech. The total rail current magnitude has


26

increased and the pulse width has decreased in direct comparison to the data presented in

Fig. 2.6. These effects are realized by an increase of the arc velocity due to the low

ablation characteristic of the Alumina. In other words, the increased velocity caused the

latter stages to trigger earlier due to the active control system.

With comparable energy to the breech-fed system using the alumina bore insulators,

Fig. 2.3, secondary arc formation by restrike should not occur. Analysis of the data

proves the existence of a secondary arc within the bore which can be associated with

plasma arc splitting. In these data sets, the stage 1 probe analysis shows no current

diversion or negative current. Current diversion is first observed in the stage 3 probe

signal.

Fig. 2.7. Asynchronous DES Railgun Data Using Alumina Bore Insulators.


27

The low ablating alumina and higher arc velocity allow the full arc length to pass the

second stage input current location before it is triggered. Therefore, plasma arc splitting

does not occur at the second stage. When the arc arrives at the third stage, the arc length

has increased and its velocity has been reduced. The velocity reduction is attributed to

the growing arc mass while it sweeps up ablated material from the bore walls and the fill

gas ahead of it. Thus, the probability of plasma arc splitting increases and occurs when

stage 3 fires. The secondary arc is accelerated past the stage 2 probe but lacks the

velocity required to reach the stage 1 probe before the system energy has expired.

2.3.3 Pseudo-synchronous DES Railgun Data

The experimental results obtained from the 15 kJ, 4-stage pseudo-synchronous DES

plasma arc railgun are presented. The stage lengths remain identical to the asynchronous

energy scheme, 58 cm. Equal stage lengths were chosen for analysis of the constant

energy model2. Both alumina and G-10 were experimentally tested and the results are

compared to the previous systems.

The collected data in Fig. 2.8 used the G-10 bore insulators, a chamber pressure of 10

Torr, and a charging voltage of 2.5 kV on the first stage and 2.9 kV on the last three

stages. This allowed for a more constant total rail current waveform. The five probes

were located 18.5, 96.7, 135.7, 194.3, 322.6 cm, respectively, from the breech. A

resistance of 120 m placed in series with the diode, Fig. 2.1(c), limited the stage 1

negative current flow to a maximum 11 kA.


28

Fig. 2.8. Pseudo-Synchronous DES Railgun Data Using G-10 Bore Insulators.

Once again, plasma arc splitting is observed when stage 2 is fired. No conclusion

can be made pertaining to the pseudo-synchronous energy scheme’s ability to suppress

restrike. Since the secondary arc that formed by the bifurcation is accelerated towards

the breech, the breech voltage attributed to back EMF is reduced. This voltage reduction

prevents a restrike arc formation.

The collected data in Fig. 2.9 used the alumina bore insulators, a chamber pressure of

10 Torr, and a charging voltage of 2.5 kV on the first stage and 2.9 kV on the last three

stages. The four probes were located 18.5, 96.7, 135.7, 322.6 cm, respectively, from the

breech. No series resistance is added to the diode, allowing a negative current flow of 24

kA.


29

Neither plasma arc splitting nor restrike is observed in these data sets. All of the

integrated probe signals follow their respective current waveforms. The stage 2 probe

analysis shows a discrepancy between the probe signal and the expected current;

however, this is most likely due to a calibration error. Velocity calculations using Eq. 1.3

provide reassurance that no current is being diverted from the primary arc.

Fig. 2.9. Pseudo-Synchronous DES Railgun Data Using Alumina Bore Insulators.

2.4 Conclusion

Three different energy schemes were built, tested, and analyzed for secondary arc

formation. Two types of secondary arcs were observed, restrike and plasma arc splitting.

The latter proved dominate in the distributed energy schemes. The suppression of such

arcs is essential to maintain acceleration on the payload. All three systems used a plasma


30

arc which allowed for velocities up to 11 km/s with 15 kJ of energy. The arc length is

believed to be in excess of 20 bore diameters, especially when the G-10 bore insulators

are implemented. An accurate calculation of the arc length was not possible with data

obtained from the rail B-dot probes. Further investigation of the arc length is discussed

in Chapter IV.

Similar energy and current waveforms provided direct comparison between the

schemes when analyzing ablation effects and analysis of secondary arc formation. Rail

B-dot probes measured the rail current at different locations along the rail to provide a

means to detect these secondary arcs and provide in-bore velocity measurements. A real

time feedback control system was integrated into the distributed systems for a precise

release of energy upon the armature’s arrival to a later stage.

The breech-fed system did not require a feedback control system; instead, it used fixed

trigger timing. Restrike was detected using the G-10 bore insulators after a period of 130

s with an average current magnitude of 40 kA. Experimentation under similar

conditions using the alumina bore insulators showed no indication of restrike and an arc

velocity matching closely to a calculated velocity (assuming no ablation). This provides

evidence to suggest ablation as one contributing factor to restrike.

The asynchronous and pseudo-synchronous DES railguns both experienced plasma arc

splitting which prevented an accurate restrike prevention analysis. Interestingly, the

pseudo-synchronous shot using the alumina bore insulators did suppress both types of

secondary arc formation. Plasma arc splitting must be prevented to provide an accurate

assessment of restrike suppression by distributed energy railguns.


31

CHAPTER ΙΙΙ

PLASMA ARC SPLITTING

3.1 Introduction

Analysis of rail B-dot data presented in Chapter II revealed current diversion

away from the primary arc. The cause of this effect was initially believed to be restrike,

where a secondary arc forms near the breech and draws current from active distributed

stages. However, the conditions required for such a restrike event to occur were not met

using the alumina bore insulators. To improve the analysis and determine the cause of

this current diversion, alternative diagnostics (armature B-dot probes) were implemented

to provide real-time measurement of the location, velocity, and direction of secondary

plasma arcs. The experiments using this railgun diagnostic provided evidence to

discredit the restrike phenomenon as the cause of the observed current diversion. These

presented data confirm the discovery of a new type of secondary arc formation within a

free-arc railgun, referred to as “plasma arc splitting.” This chapter investigates the

splitting methodology and provides a viable method of prevention.

3.2 Arc Splitting Theory

Plasma arc splitting occurs at the distributed energy input locations along a free-

arc DES railgun bore and is believed to be a product of opposing magnetic pressures

perturbing the plasma arc. According to basic railgun theory, magnetic pressure

magnitudes are dominated by the current and exist on both the rails and the armature, or


32

in our case, a plasma arc. The magnetic pressure on the arc is equal to the Lorentz force

acting on the arc per area,

(3.1)

where is the inductance gradient [H/m], I is the current through the arc [A], h is the

rail separation distance [m], and w is the bore width [m]. Additional variables that may

contribute to the splitting process include the plasma’s ion density and electron density.

For traditional breech-fed railguns, this arc magnetic pressure is always confined

to the rear or downstream region of the arc. For the distributed energy railgun, this is not

always the case. Let’s examine a situation where a distributed feed is triggered to release

its energy into the tail of a long plasma arc. When the energy is released, some of the

current will flow into the primary current carrying region of the arc, now ahead of the

feed location, while some will flow through the ionized plasma tail. This ionized

material provides a low resistance path which will eventually lead to a breakdown

formation across the rails. Since current conduction is now located both ahead of and

directly at the feed location, the opposing magnetic pressures will perturb the plasma and

split the primary arc into two separate current carrying bodies. This effectively generates

a secondary arc within the railgun bore. According to the Lorentz force, the arc ahead of

the distributed feed will continue to be accelerated toward the muzzle and the arc behind

the feed will be accelerated toward the breech.


33

3.3 Arc Splitting Data

The rail B-dot probes used in past experiments10

detects the flow of current

through a rail at a specific rail location. This diagnostic proved useful in the detection of

diverting current, but the measurement of the number of current carrying arcs, their

positions in the bore, and their propagation directions yields too complex to extract from

the rail probe data. To overcome this problem, armature B-dot probes are employed.

The armature B-dot probe functions to detect the changing magnetic field of current

carrying arcs in the railgun bore. This allows for the detection of multiple arcs, if

present, and their propagation direction.

Four independent armature B-dot probes were integrated into the system. The

four probes were located 30.5, 47.0, 63.5, 78.7 cm respectively from the breech. Data

collected from the four armature B-dot probes are analyzed for three separate railgun

shots to investigate the dynamic arcs behaviors. All of the experimental shots presented

utilize a 2-stage asynchronous plasma arc DES railgun. The first stage has 1660 F of

capacitance and a 1 H power conditioning inductor. The second stage, which is

distributed, utilizes three series RLC circuits comprised of an 830 F capacitor and a 2

H inductor. These three circuits have independent switches which are closed by a hard

coded timing scheme to produce relatively constant current. The distributed feed is

located 58 cm from the railgun breech. The charging voltage is 2.7 kV with an air

background gas pressure of 10 Torr. The first and second shot contain a 1 s delay of the

second stage trigger upon arrival of the armature, while the third shot has a delay of 25

s. The current waveforms of each stage are displayed in Fig. 3.1. These waveforms are

integrated Rogowski coil data collected from the first experimental shot discussed. The


34

second shot produced nearly identical current waveforms, due to similar initial

conditions; however, the waveforms of the third and final experiment varied slightly

because of a longer delay of the second stage trigger.

Fig. 3.1. Distributed Energy Current Waveforms.

These collected data in Fig. 3.2 shows the armature B-dot voltage signals from the

first discussed shot. No calibration procedure was performed on the sensors. A post

processed offset along the voltage axis allows for a clear view of their magnitudes

throughout the presented time interval. The main armature arrives at the first probe at 70

s, indicated by a positive voltage spike. Arrival to the second, third, and fourth probe is

clearly evident by the first positive voltage spike in each observable trace. By measuring

the time between the maximums of these preliminary spikes, the velocity from the breech

to the first probe is 4 km/s, 7 km/s from the first to second and second to third, and 8

km/s from the third to fourth probe. It is important to note that the location of the second

stage distributed energy feed resides between the second and third probes, 58 cm from

the breech. The second stage is triggered at 110 s upon the arc arrival to the distributed


35

feed location. Beginning 37 s after this release of energy, the second probe detects time

varying magnetic fields emanating from an unknown source. These oscillations are

observed until the first stage shuts off at 214 s, indicated by a positive spike in voltage.

A corresponding spike occurs in the first probe signal but is absent from the last two. A

pair of negative voltage spikes at 243 s and 268 s is also visible along the first two

probe signals.

These data suggest that a secondary arc is formed by the plasma arc splitting

phenomenon. The magnetic pressure created by the second stage sourced current is

imparted on the plasma and believed to cause perturbations which lead to its division into

two separate current carrying arcs. At this time, nearly all of the current released from

the breech is diverted to the secondary arc because it is the path of least resistance and

inductance. This breech current produces a Lorentz force that should drive the secondary

arc toward the muzzle. However, a second Lorentz force is acting in opposition that

restricts its movement. This additional Lorentz force is a product of current flow to the

secondary arc sourced by the distributed feed. Because current flowing from the

distributed feed is shared between both arcs, the primary arc continues acceleration

toward the muzzle as indicated by the third and fourth armature B-dot signals. The

opposing magnetic pressures on the secondary arc confine it to remain between the

distributed current feed and the position of the first B-dot probe. This event is identified

in these data of the second B-dot probe from 147 s to 183 s, which corresponds to the

unknown source of voltage oscillations discussed earlier. The breech current continues to

decay over time and stops flowing at 214 s. This is indicated by the pair of positive

voltage spikes (induced voltage by an opening switch) observed in the first and second


36

probe signals. Since these spikes only appear on the first two probe signals, the position

of the secondary arc has to be between the second and third probe locations. After this

time the secondary arc has a magnetic pressure component solely in the breech direction.

The arc now moves past the second probe position at 243 s and past the first probe at

268 s, indicated by negative voltage spikes because the magnetic flux enters from the

opposite face of the B-dot loop.

Fig. 3.2. Armature B-dot Probe Signals from Shot 1.

The collected data in Fig. 3.3 shows the armature B-dot voltage signals from the

second discussed shot. Initial conditions are identical to the first shot, but the results are

slightly different. Once again, a secondary arc is believed to develop as a direct result of

plasma arc splitting due to the distributed feed. Similar voltage oscillations are observed

from 156 s to 176 s at the time the when the current magnitude sourced from the

second stage equals and surpasses the first stage current magnitude. The first observable

difference is an absent voltage spike at 215 s on the second probe signal. This implies

that the secondary arc is located in a region between the first and second probe at the time


37

the first stage turns off. Further evidence to support this statement is seen by a missing

negative voltage spike in the second probe signal after the breech-fed current falls to

zero. As the secondary arc is accelerated toward the breech a strong negative voltage

spike at 250 s signifies its propagation past the first probe location.


The conclusion after examining these data of the first two shots leads our team to

believe that plasma arc splitting is a real phenomenon. If multiple secondary arcs are

formed behind the distributed feed through plasma perturbations, the opposing magnetic

pressures from the breech current and distributed feed current most likely cause the arcs

to collapse together into a single entity. Although no restrike was observed with the DES

railgun system of Chapter II, a new form of secondary arc formation has been discovered

which threatens plasma armature performance.


38

3.4 Arc Splitting Prevention

Plasma arc splitting develops from the flow of current into the ionized tail or

body of the plasma arc. This can be prevented by waiting until the full length of the arc

is ahead of the distributed feed location before the release of energy. This allows the

arc’s magnetic pressure to exist only at the tail end region. The triggering delay time in

the control system was lengthened to 25 s, allowing adequate time for the arc length to

pass the distributed feed position. All other initial conditions remain identical to the first

two shots.

The collected data in Fig. 3.4 shows the armature B-dot voltage signals from the

third shot. There is no observable secondary arc detection from any of the B-dot probe

signals. The primary arc movement is detected by each sensor and is traveling towards

the muzzle. It is also evident that a small positive voltage spike appears in all four

waveforms at 220 s. As discussed in the first two shots this is an induced voltage

caused by turn off of the first stage switch. Because this effect is now seen in all four

probe waveforms, the current sourced from the breech is flowing past each probe location

and through the primary arc. Thus, plasma arc splitting can be prevented by maintaining

the arc magnetic pressure to the back of the plasma arc.


39



40

CHAPTER ΙV

PLASMA ARC LENGTH

4.1 Introduction

Since secondary arc formation from plasma arc splitting can be suppressed by

precise timing of the release of distributed energy, insight into the length of the arc is

critical. Optical diagnostics were originally integrated into the railgun in effort to analyze

plasma density and composition by the use of spectroscopy (not discussed in this

dissertation). A simple replacement of the spectrograph with photodiodes provided an

accurate arc length measurement device. It is possible to extract the arc length from data

obtained by B-dot probes, but luminosity profiling does not require complex post

processing techniques. These experiments utilize the same 2-stage asynchronous plasma

arc DES railgun discussed in Chapter III.

4.2 Experimental Setup

The optical diagnostics selected are Hamamatsu S1336-18BK photodiodes. The

photodiodes have a spectral response range of 320 nm to 1100 nm and a rise time of 0.1

s. To improve the frequency response and linearity, a reverse voltage of 4.5 V was

applied across the diode. A schematic diagram of the circuit is shown below in Fig. 4.1.


41

Fig. 4.1. Schematic of Photodiode Reverse Voltage Circuit

11.

The values of R and C in the schematic are 10 k and 0.1 F, as recommended

by Hamamatsu. Five of these photodiodes are utilized to provide light detection at five

different in-bore locations, Fig. 4.2. The photodiodes cannot be directly exposed to the

bore due to the intense heat radiated by the plasma arc. Instead, optical fibers coupled the

light signals to the detectors at a safe distance away.

Fig. 4.2. A Drawing of the DES Railgun and Optical Diagnostics.

The optical fiber selected was available in-house and is manufactured by

Fiberguide Industries, item# SFS200/220 N. It is made of pure fused silica for efficient

light coupling and high quality transmission. In order to expose the optical fiber to the

inside of the bore, 1.0 mm holes were drilled into the middle of the alumina tiles. The

hole diameter was kept to a minimum because it encourages plasma leakage. Additional

holes, 1.3 cm in diameter, are drilled into the adjacent G-10 support structure to allow for


42

internal access to the alumina tile holes. The actual optical fiber mounting location along

the length of the gun is not accurate in Fig. 4.3, but the picture shows an exposed bore to

illustrate how the fibers are oriented. The optical fibers are drawn in blue and the black

boxes represent the coupling of two fiber lines.

Fig. 4.3. Illustration of the Fiber Line Mounting.

The coupling fasteners of the five optical fibers are shown in Fig. 4.4. They are

spaced 7.6 cm apart and are symmetrically positioned at the distributed feed location with

the third fiber located directly at the distributed feed point. This allowed plasma length

data to be collected before, after, and directly at the secondary stage. Foreshadowing

thermal damage to the exposed fiber tips, optical couplers were used to provide a 5 cm

replaceable fiber lead extending into the alumina.


43

Fig. 4.4. A Picture of the Five Optical Fiber Couplers.


As previously mentioned, these experiments utilize the same 2-stage

asynchronous plasma arc DES railgun discussed in Chapter III. The charging voltage

remained at 2.7 kV; however, the in-bore background gas pressure was varied from 5 to

30 Torr. The five induced voltage signals from the photodiodes are displayed in Fig. 4.5

for a bore pressure of 20 Torr. The plasma arc current waveform is plotted on a

secondary y-axis for correlation. Traditional techniques to calibrate the sensors were

abandoned due to fiber polish degradation during repeated experimental testing.

Therefore, a comparison of the arc current magnitude to light intensity is neglected with a

focus on the waveform shape and pulse width. All of the photodiode waveforms more or

less exhibit a similar shape. There is an exponential rise of voltage on the leading pulse

edge followed by a linear transition extending to the point of maximum amplitude. As

expected, there appears to be a larger current density through the arc head than through

the body. The brief exponential rise indicates a short, compact plasma arc head and the


44

linear region is indicative of a long plasma body. The long body is unique to the free-

running arc since it is only bound by viscous drag and the in-bore gas pressure, not a

solid projectile. Current distribution is difficult to determine in the body region. Highly

ionized ablation products present in this region due to viscous drag continue to emit

radiation. Thus, the voltage induced luminosity is not directly correlated with a current

carrying region. The falling edges of the waveforms appear to decay exponentially, with

the longest fall time observed on the fourth photodiode waveform. This delayed decay is

associated with a long tail region.

Fig. 4.5. Photodiode Waveforms with Corresponding Armature Current.

The plasma arc length is measured from the photodiode data and presented in Fig.

4.6. The length is calculated by multiplying the photodiode waveform pulse width with a

calculated arc velocity derived from the rise times. A length calculation is provided for

each fiber location for varying gas pressures between 5 and 30 Torr. A monotonically

increasing function of arc length for both position and pressure would be expected from a

breech-fed energy scheme. While the distributed energy scheme proves to agree with the


45

latter, the arc length traces are not monotonic in relation to position. A trend in shape

does exist however and will be explained with a focus on a single curve.

Analyzing the 5 Torr trace, the arc length is initially 17.7 cm as it moves past the

first fiber location. This length is reduced to 8.9 cm at the second fiber position. As

discussed in Chapter III, the opposing magnetic pressures sourced from the distributed

feed can perturb the plasma. These perturbations allow the plasma to expand from 13.5 –

19.5 cm as it propagates past the third and fourth fiber locations. Interestingly, when the

arc reaches the fifth fiber location, the length is reduced once again to a value of 9.4 cm.

This can be explained by a return of the magnetic pressure to the tail end of the plasma

arc. These experiments found the arc length to be as long as 37 cm (30 Torr air pressure)

and conversely as short as 8 cm (5 Torr air pressure). These data shed insight into the

complex and highly dynamic interactions of multiple magnetic pressure vectors acting

near the distributed feed. The arc length calculations presented were beneficial to the

suppression of plasma arc splitting during future experiments.

Fig. 4.6. Arc Length Calculations vs. Pressure and Location.


46

Fig. 4.7 is a plot of the calculated arc velocity as a function of position for various

pressures. A decrease in velocity is observed on all of the traces at the second fiber

location. This further supports the hypothesis that an opposing Lorentz force is acting on

the plasma sourced from the distributed feed. Velocity calculations from the third

through fifth fiber locations indicate slight increases and decreases of velocity. It is

postulated that this could be a direct consequence of either a variable plasma mass or

variable magnetic pressure. The perturbations could alter the plasma mass through

bifurcation while a variable magnetic pressure corresponds to a changing driving force.

The derivatives of these velocities (accelerations) could have a significant impact on the

payload.

Fig. 4.7. Arc Velocity Calculations vs. Pressure and Location.

4.4 Conclusion

This chapter described an experiment to measure the plasma arc length in effort to

determine the appropriate firing times of distributed energy modules to prevent plasma

arc splitting. The arc length was measured using five equally spaced optical diagnostics

(photodiodes) positioned before, after, and directly at a distributed current feed. Optical


47

fibers exposed to the bore coupled the light signals to the photodiode detectors to prevent

thermal damage radiating from the plasma. The same 2-stage asynchronous plasma arc

DES railgun discussed in Chapter III was implemented in these experiments. The light

intensity profiles indicated a short, compact plasma arc head and long plasma body and

tail region. The plasma length was calculated for each fiber location for varying air

pressures between 5 and 30 Torr. As expected, the arc length increased with rising air

pressure because the higher pressures provided more available fill gas molecules

vulnerable to ionization by the plasma. These experiments found the arc length to be as

long as 37 cm (30 Torr air pressure) and conversely as short as 8 cm (5 Torr air pressure).

Further, the investigation found the arc length to be dynamic near the distributed current

feed. This result was not foreshadowed and is believed to be a product of gradient

magnetic pressures perturbing the plasma arc. In addition, these perturbations affected

the arc velocity which could impart significant changes of acceleration on the payload.


48

CHAPTER V

DEVELOPMENT OF A NEW SYSTEM PROTOTYPE

5.1 Introduction

The knowledge acquired from experiments described in Chapters II-IV is utilized to

design and test a fully synchronous DES railgun. Since a large stage number is required

to achieve synchronous operation, our team decided to build a DES railgun with 40

stages. This number was selected based on a theoretical synchronous system2 described

by Parker. The complexity of a DES railgun increases with stage number, so after

completion of the full system design, it was agreed to first build a prototype that mimics

the design and operation of the first few stages. This chapter will discuss the

development of a synchronous DES railgun simulation, as well as the design,

construction, and testing of a 7-stage DES railgun prototype. The objectives of the

prototype are to design, built, and test:

a) A 7-stage DES railgun with successful arc propagation towards the

muzzle.

b) A containment structure capable of maintaining low pressures (mTorr range).

c) A bore compression technique to suppress plasma leakage.

d) A flange to couple multiple containment structures together while maintaining

vacuum and bore compression.

e) Compact distributed energy modules capable of sourcing the necessary energy.

f) Precision diagnostics including B-dot probes and Rogowski coils.


49

5.2 Free-Arc DES Railgun Simulation

5.2.1 Introduction

The overall Texas Tech objective is to characterize a fully synchronous

distributed energy railgun. To this point only a 4-stage pseudo-synchronous DES railgun

has been built and tested. Although not fully synchronous, discoveries made with the

initial system highlighted critical design issues advantageous for the new system in

development. A necessary phase of the design called for a computer simulation to

characterize component values and ultimately determine economic feasibility. Both

simulation results and practical system components are discussed. The simulation is

designed to achieve an arc velocity greater than 8 km/s with 40 stages contributing to

provide 50 kA of nearly constant current. The circuit equations implemented are

characterized by a lumped circuit element model2. These design equations are coded and

calculated using the MATLAB® environment. Complex plasma armature dynamics are

neglected due to their irrelevance for the design information sought. The energy stored

within each stage and its length will remain constant; however, variations of these

constants are analyzed for optimization of a realistic design. Values obtained from the

simulation allow for the selection of realizable system components such as: capacitors,

switches, and power conditioning devices.


50

5.2.2 Implemented Simulation Equations

The code was developed in accordance to derived circuit equations for a distributed

energy model2. The code implements the derivation of two loop equations from a

lumped circuit element model describing the capacitive energy store stages. The first

loop equation characterizes the electrical system for the case when the arc has passed

through a respective stage. The simulation equation yields

(5.1)

where i represents the stage number, in coulombs is the charge on capacitor [C],

is the stage resistance [ ], is the stage inductance [H], is the stage rail resistance

[ /m], is the stage length [m], and =dL/dx is the inductance gradient [H/m]. A

thorough derivation is presented2, including dimensionless variables and equations. The

schematic from which equation (5.1) was derived is shown in Fig. 5.1.


51

Fig. 5.1. Schematic of a Stage in which the Plasma Arc has Passed Through2.

The second loop equation characterizes the electrical system for the case when the arc

is contained within a respective stage. Here, N refers to the stage number and the second

order differential equation used in the simulation yields

– (5.2)

where is the arc velocity [m/s], and is the arc distance from the beginning of stage N

in meters. The schematic from which Eq. 5.2 was derived is shown in Fig. 5.2 below.

Fig. 5.2. Schematic of a Stage that Contains the Plasma Arc

2.

If the arc is at a distance from the railgun breech, the relationship between and

can be described as

(3)

The second order differential equations of (5.1) and (5.2) are solved using a

MATLAB® routine ode45 with syntax of


52

[t,Y] = ode45(odefun, tspan, y0, options)

where odefun is a function that evaluates the right side of the differential equations, tspan

is a vector specifying the interval of integration, y0 is a vector of initial conditions, and

options is a function to adjust the integration parameters which was useful for the

calculation or equivalently the dI/dt calculation. The algorithm used for the ode45

routine is based on an explicit Runge-Kutta formula known as the Dormand-Prince pair12

.

The terms presented in equations (5.1)-(5.3) are all straight forward with the exception

of the arc velocity term. The simulation uses a derived plasma velocity equation (1.3)

which assumes no in-bore wall ablation and has the form

(4)

where =dL/dx is the inductance gradient [H/m], is the ratio of specific heat [unit

less], is the initial gas density [kg/m3], I is the armature current [A], is the rail

separation distance [m], is the distance the shock front has moved [m], and is a scale

length as a consequence of viscous forces [m]. The equation for the scale length is

characterized by

(5)

where is the drag coefficient [unitless].

The location of the shock front, the ratio of specific heat, the scale length, and the drag

coefficient are all difficult to determine by neglecting complex physics. The values used

in the simulation were determined using experimental data with comparable parameters10

.


53

For strong ionizing shocks, the ratio of specific heat has a strong dependence on the

degree of dissociation and ionization6. A common value of 1.2 under this condition is

used in the simulation. The scale length is calculated by setting the drag coefficient to a

constant value of 0.0049, which was calculated from the comparable experiment. By

analyzing Eq. 5.4 it can be observed that the arc velocity is now a function of only two

temporal variables, the current through the arc and the shock front distance. Since the

current is a user defined variable, the remaining dependent variable to be determined is

the location of the shock front. This is not an intuitive calculation and drastically affects

the arc velocity in the simulation. An attempt was made to approximate the shock front

movement by setting it equal to the arc movement. Since the current is essentially

constant, this produced a linear decrease of the velocity as the arc traveled down the rails.

The velocity measurement of a past experiment10

confirms a velocity reduction with arc

distance, but to a lesser degree than what Eq. 5.4 predicts. An advanced code6 also had

difficulty matching theory to experimental data and concluded that there must be a linear

dependence on the drag coefficient for the hypervelocity regime. Taking this into

consideration, a compromise was made by making the shock front distance constant

while maintaining a constant drag coefficient. Therefore, the time varying velocity is

solely proportional to the arc current. When the shock front distance is set to the rail

length, reasonable values of velocity are obtained by comparison to experimental

measurements found in literature10

.


54

5.2.3 Simulation Parameters and Results

This section describes the selected parameters and results for the simulation using a

“constant energy” model. A “constant energy” model refers to equal stage lengths,

constant efficiency, and constant electrical energy stored in each stage which allows each

stage to deliver an equal amount of energy to the arc2. The specified model was selected

because of its simplicity and practicality to build and maintain a real world system. With

the exception of the first stage, the latter 39 stages share a constant amount of stored

energy to be released upon the plasma arc’s arrival to a respective stage. The first stage

requires more energy than latter stages to rapidly accelerate the arc to a velocity near the

target velocity. This velocity is then maintained by the following stages.

The first stage contains the following parameter values:

Capacitance: 830 F

Voltage: 1500 V

Resistance: 5 m

Inductance: 1 H

Stages 2-40 that follow the “constant energy” model contain the following parameter

values:

Capacitance: 750 F

Voltage: 750 V

Resistance: 5 m

Inductance: 1.5 H

The simulated railgun contains 40 stages with each stage measuring 15.24 cm

providing a total rail length of 6 meters. The rails are assumed to be copper with a

resistance of 100 /m and are spaced 10 mm apart. An inductance gradient of 0.45

H/m was calculated13

with respect to rectangular copper rails of dimension 0.64 cm x

3.18 cm. The physical interactions of gas molecules and atomic physics are neglected;


55

however, the initial gas density is needed for the velocity calculation. Rapid acceleration

of the arc requires a low pressure environment with the given current magnitude. Air at a

pressure of 10 Torr was used to solve for the initial gas density. The negative current

associated with each stage was additionally attenuated with a resistance of 100 m for

pulse shaping

The current waveforms simulated for all 40 energy stages are shown in Fig. 5.3. A

time step of 1 s was used for a total duration of 1 ms. The current magnitude of the first

stage is nearly three times the current magnitude of all remaining stages. As previously

stated, this is done to hastily accelerate the arc. By observation of the figure, the current

magnitudes of stages 2-40 are not equivalent as would be expected by following a

“constant energy” model. This is believed to be associated with the varying arc velocity,

which is proportional to the current in the computer simulation. The current released by a

stage flows through both the rails and through the arc. The rail resistance is therefore a

time varying parameter that depends on the arc velocity. In other words, as the arc

velocity increases, the arc distance increases between time steps, and the rail resistance is

a function of this distance which obviously affects the current flow. An additional

frequency dependant parameter can alter the rail resistance and is known as the skin

depth or penetration depth of current into the rail, but is not addressed in the present

simulation.


56

Fig. 5.3. Simulated Current Waveforms for a 40-Stage System. Top: Current Waveforms

for Stages 1-20. Bottom: Current Waveforms for Stages 21-40.

The total current contribution by all of the stages is displayed in Fig. 5.4. An

average value of 50 kA flows through the arc which meets the criterion of the simulation.

After an abrupt jump in magnitude attributed by the first stage, the current slowly rises,

nearly becomes constant, and then sharply decreases at the arrival to the railgun muzzle.


57

Negative current observed to flow after 0.6 ms is an effect of the release of energy

contained within the remaining stages.

Fig. 5.4. Simulated Armature Current.

A plot of the arc velocity is displayed in Fig. 5.5. The velocity waveform is

virtually identical to the total current waveform, which is expected because of the

velocity equation used in this computer simulation. The initial spike in velocity peaking

at 10 km/s corresponds to just over 40 kA of current. This velocity compares reasonably

well to an experimental velocity measurement from an analogous system10

. The

maximum plasma arc velocity is approximately 13 km/s, exceeding the minimum

velocity requirement by 5 km/s.


58

Fig 5.5. Simulated Arc Velocity.

5.2.4 Conclusion

A computer simulation of a 40-stage synchronous plasma arc DES railgun was

discussed. The simulation provides insight into the actual design and development of

both systems discussed in Chapters V and VI. The simulation results are in agreement

with the physical system requirements. The average current contribution was simulated

to be 50 kA providing a maximum arc velocity of 13 km/s. Values used in the simulation

for capacitors, switches, and power conditioning devices prove to be both realistic and

within the project budget. The experimental results will obviously not exactly match the

computer simulation so component values and parameters will require slight adjustments

for optimization.


59


This section will discuss the design and construction of a 7-stage DES railgun

prototype. The rationale of the prototype is to test all of the components designed for the

40-stage railgun.

5.3.1 Rails and Containment Structure

The assembled prototype is 1.2 m long with a 1.0 cm x 1.0 cm square bore cross

section. A cross-sectional view of the railgun is shown by a 2D computer-aided design

(CAD) assembly in Fig. 5.6. The railgun core utilizes rails made of UNS C11000 ETP

copper with a shoulder machined at both edges to seat the bore insulators and set the rail-

to-rail spacing. On the back sides of the rails, 1/4’’-28 holes provide an electrical

connection for brass all-thread distributed current feeds. The distance between the first

and second feed points is 20 cm and each additional feed is spaced 15.24 cm apart. The

containment structure is machined from 10.16 cm x 10.16 cm G-10 blocks and serves to


60

Fig. 5.6. Cross-Sectional View of the Railgun Prototype.

compress the core, resist the rail repulsive force, and maintain a low pressure air

environment. O-ring seals are encircled by a bolt pattern at each end to couple

flanges/faceplates to the structure. While the bottom of the containment remains solid, an

opening machined on the top aids the assembly process and provides a potential in-bore

window option to view the plasma armature. The latter is executed by replacing opaque

components with ones possessing translucent properties. During assembly, the railgun

core is seated at the bottom of a U-shaped channel cut along the length of the casing.

One side-wall of this channel is 90 degrees with respect to the channel floor while the

other has a 3 degree taper. This taper allows for the placement of shims, Fig. 5.7, to

compress the core horizontally. Vertical compression is achieved by positioning a 3.8 cm

x 3.2 cm G-10 block on top of the core and fastening top and bottom 15.24 cm x 1.9 cm

G-10 lids with an array of 3/4’’-10 fiberglass all-thread rods.


61

Fig. 5.7. Interior View of the Containment Structure.

A custom oval shaped o-ring, Fig. 5.8, seals the opening on the upper containment in

order to maintain vacuum. Additional locations vulnerable to vacuum leakage remain at

all of the distributed current feed access points. To prevent such leaks, NPT Nylon tube

fittings equipped with o-ring seals are mounted to the containment exterior.

Fig. 5.8. Partially Disassembled Railgun View.


62

The vacuum line and plasma injector are mounted at two access ports located on the

bottom of the containment. Plasma injection occurs in the breech region, 5 cm in front of

the breech current feed. This creates a small volume of magnetic pressure behind the

armature, encouraging muzzle oriented propagation. The same tube fitting implemented

for the distributed current feeds is used to seal around the plasma source. Vacuum is

drawn at the railgun muzzle to distance the bulky fittings and pressure sensors from

electrical components.

A G-10 flange, Fig. 5.7, couples two 61 cm containment structures together. The

7.62 cm long flange contains a 6.35 cm diameter thru hole which houses the railgun core.

Due to the rectangular geometry of the core, compression is maintained with semicircular

G-10 shims tapped in place on each side. It would be preferable to have the containment

machined from a single piece of G-10; however, a flange system is necessary for

expansion to a 6 meter long system.

5.3.2 Energy Modules

Six distributed energy modules are used to supply current to the rails and drive the

armature. With exception of the first stage, all of the distributed energy modules are

identical. This section will describe their design and components in detail.

A single distributed energy module of the prototype system is shown in Fig. 5.9.

The capacitors have a voltage rating of 1000 VDC and are manufactured by Electronic

Concepts (PN# UL30BL0150). Five of these 150 F film dielectric capacitors are wired

in parallel to comprise a 750 F capacitor bank. The diode and thyristor selected are both

solid state devices manufactured by ABB Semiconductors. The diode (PN#


63

5SDD11D2800) has a blocking voltage of 3000 V and a non-repetitive peak surge current

of 15 kA. This diode is placed in anti-parallel with the thyristor switch to act like a triac

switch and allow both positive and negative current flow.

Fig. 5.9. CAD Drawing of the Distributed Energy Module.

The resistor is a high power carbon disk and is connected in series with the diode

to attenuate the negative current amplitude as full reversal is undesirable. A computer

simulation of the system was used to determine an optimum value of 100 m should be

used; however, 0.5 resistors were used for the prototype due to availability. The

thyristor selected is manufactured by ABB Semiconductor (PN# 5STP10D1601) and has

a blocking voltage of 1600 V, a continuous 1 Hz dI/dt rating of 1000 A/ s, and a peak

non-repetitive surge current of 16 kA at 125 degrees Celsius with a 8.3 ms pulse. To

close the switch a 10 s, 15 volt pulse is applied across the gate and cathode. This gate

signal is generated using a custom pulser board designed and built at Texas Tech

University. The aluminum bus bars direct the released stored energy to the railgun rails


64

and are designed to provide low resistance and high power dissipation. To achieve the

desired discharge waveform, power conditioning is performed by 1.5 H of self-

inductance. A variable self-inductance scheme, Fig. 5.10, was developed to manipulate

stage inductance during the preliminary testing phase. The loop area can be

independently altered for each stage or be dependently altered over the entire system.

Attention must also be paid to mutual inductance between stages. A calculated value on

the order of tens of nano-Henries will not profoundly affect adjacent stages.

Fig. 5.10. Variable Self-Inductance Scheme.

Since multiple distributed energy stages are active during operation, the first stage of

the railgun requires a larger current magnitude to equal their current summation. Hence,

the first stage contains a high voltage 830 F oil filled capacitor rated to 12 kV. The

switch selected is an ABB Semiconductor (PN# 5STP34N5200) thyristor. This switch is

capable of a non-repetitive peak surge current of 60 kA for 8.3 ms and a blocking voltage

of 5.7 kV. A diode (PN# SDD303KT) is placed in anti-parallel for the same purpose

discussed for the distributed energy modules. The diode has a 6 kV blocking voltage and


65

is capable of conducting a non-repetitive peak surge current of 60 kA for 8.3 ms. A 0.5

carbon resistor in series with this diode limits the negative current magnitude.

5.3.3 Diagnostics

The prototype contains seven, rail B-dot probes mounted on the containment

exterior. These probes measure the local rail current at their respective location for

current diversion analysis and velocity measurements. Six of these probes are located

between stages and an additional probe is positioned at the muzzle. The seven rail B-dot

probes were located 11.4, 29.2, 42.5, 55.2, 69.2, 87.6, and 105.4 cm, respectively, from

the location of the first stage’s feed location. Each probe contains 20 turns of 18-gauge

magnet wire. They are positioned at a 45 degree angle from the rails, Fig. 5.11, with the

loop area perpendicular to the rail orientation to maximize coupling of the magnetic flux.

Shielded air-core Rogowski coils are used to measure the output current waveforms

produced by all of the energy modules. Both types of sensors are built in-house and are

all appropriately calibrated.


66

Fig. 5.11. Rail B-dot Probe Orientation.

5.3.4 Plasma Injector

A plasma injector at the breech reliably supplies plasma for each experimental

test. Plasma injection occurs in the breech region, 5 cm in front of the breech current

feed. This creates a small volume of magnetic pressure behind the plasma, encouraging

muzzle oriented propagation. The plasma injector is powered by a 5-stage solid-state

Marx generator that is charged using an external 200 VDC power supply. The Marx is

triggered by a TTL trigger pulse and provides an output pulse of 1 kV with a 10 s pulse

width. This signal is input into a 1:40 ratio pulse transformer to supply a pulse with a 40

kV magnitude to the electrodes. The injector is mounted into the G-10 containment

structure and has a coaxial electrode configuration. The plasma is generated by an

electrical breakdown across a tungsten rod cathode and stainless steel tube anode. A


67

hollow ceramic tube provides insulation between the anode and cathode. The plasma

generation system is displayed in Fig. 5.12.

Fig. 5.12. Plasma Generation System.

5.3.5 Control System

The control system implemented on the prototype is a hard-coded digital pulse

timing sequence determined by experimental trial and error. The trigger timing found for

each stage is 1, 45, 65, 85, 105, 135, 165 s, respectively. A feedback control system

utilizing sensors along the railgun will simplify this process and is implemented on more

complex systems discussed later.

A representation of the control system hardware is shown in Fig. 5.13. The brain

of the system consists is a National Instruments CompactRIO programmable automation

controller (PAC) that utilizes Field Programmable Gate Array (FPGA) technology to

provide real-time processing. The LabVIEW 2009 software package is used to develop


68

control code which is compiled into a bit-file and downloaded into the CompactRIOs’

512 MB flash memory where it is stored and is activated after the boot cycle.

Fig. 5.13. Control System Hardware.

To initiate the release of current from an energy module, an 8-channel NI 9401 TTL

digital output module provides a 10 s, 5 V pulse to a fiber optic board on the respected

stage channel. Gate driver boards receive the light signals and convert them to 10 s, 15

V analog pulses to trigger the stage’s corresponding SCR gate and release the stored

energy in the capacitor banks.

5.3.6 Support Structure and Built System

A support structure is necessary in order to mount the railgun and provide a platform

for the energy modules to rest on. Commercially available steel tripods have been

selected that provide a stable foundation and variable height adjustment. Besides

supporting the railgun weight, the support structure must also absorb recoil forces on the

railgun. The recoil force of a railgun is equal to the Lorentz force and acts on the current

feeds. In comparison to Mega-Ampere laboratory launchers that accelerate payloads,

only tens of kilo-Amperes are required to accelerate our plasma arc to hypervelocities.


69

This reduced current requirement drastically decreases the Lorentz force, so hard

mounting a support structure to the floor is unnecessary.

The built 7-stage DES railgun prototype is shown below in Fig. 5.14. The photograph,

Fig. 5.14(a), shows an side view of the system where the switches, diodes, and rail B-dot

probes are located. In Fig. 5.14(b), an isometric view displays the capacitors, Rogowski

coils, and vacuum pump connection. Two tripods support the railgun and switches while

a table is used to support the capacitors.

(a)


70

(b)

Fig. 5.14. Photographs of the 7-Stage Prototype System. (a) View of Switch and Diode

side. (b) View of Capacitor Bank Side.


The experimental results obtained from a 7-stage DES railgun prototype are

presented. The current waveforms for all seven stages, along with a summed armature

current waveform, are displayed in Fig. 5.15. During the shot, the containment structure

was evacuated to roughly 10 Torr. The first stage was charged to 1800 volts and sourced

approximately 30 kA for 120 s. The last six stages were charged to 500 volts and each

output approximately 10 kA with a 100 s pulse width. The trigger timing for each stage

was hard-coded into a digital pulse generator at 1, 45, 65, 85, 105, 135, 165 s

respectively.


71

Fig. 5.15. Current Waveforms for the Prototype System.

The maximum armature current is close to 38 kA which accelerated the plasma to an

average velocity of ~ 6.7 km/s. This velocity is reached within 10’s of s of arc

formation and was calculated using the rail B-dot data shown in Fig. 5.16. The seven rail

B-dot probes were located 11.4, 29.2, 42.5, 55.2, 69.2, 87.6, and 105.4 cm respectively,

from the location of the first stage’s feed location. Analysis of the B-dot traces in Fig.

5.16 reveals no indication that plasma arc splitting has occurred at any of the feed


72

Fig. 5.16. B-dot Measurements from the Prototype System.

locations. In addition, these data show no presence of restrike arcs within the railgun

bore. Further analysis of the sensor outputs from the first three stages is presented in Fig.

5.17. The probe signals are integrated and multiplied by a calibration constant to produce

local rail current waveforms. The current contribution from the first three stages is

shown alongside three rail B-dot probe signals. Current diversion to secondary arcs is

not present as long as the sourced rail current waveform matches the local rail current

waveform. The probes signals show the rail current rise up to the full sourced current

magnitude and then match the sourced current waveforms shapes over the remaining

duration. This indicated an absence of current diversion.


73

Fig. 5.17. Current Distribution Analysis Data.

5.5 Conclusion

This chapter discussed the development of a prototype system to test all of the

components designed for a 40-stage DES plasma arc railgun. The prototype resembles

the first 7 stages of the overall design and proves to be feasible and functioning correctly.

A computer simulation was programmed to characterize component values and ultimately

determine economic feasibility. Values obtained from the simulation allowed for the


74

selection of realizable system components such as: capacitors, switches, and power

conditioning devices.

The objectives of the prototype were to design, built, and test:

a) A 7-stage DES railgun with successful arc propagation towards the

muzzle.

b) A containment structure capable of maintaining low pressures (mTorr range).

c) A bore compression technique to suppress plasma leakage.

d) A flange to couple multiple containment structures together while maintaining

vacuum and bore compression.

e) Compact distributed energy modules capable of sourcing the necessary energy.

f) Precision diagnostics including B-dot probes and Rogowski coils.

The B-dot probes waveforms, Fig. 5.16, confirm that the arc is accelerating towards the

railgun muzzle as all 7 stages discharge. A containment structure was designed and built

using G-10 with numerous o-ring seals to achieve mTorr pressures with air as the fill gas.

Plasma leakage was reduced by applying a mechanical horizontal and vertical

compression to the railgun core. The flange design proved to maintain vacuum and bore

compression. Energy modules were designed utilizing compact film dielectric capacitors

and a variable self-inductance scheme. When charged to 500 volts, the modules output

approximately 10 kA with a 100 s pulse width. These values agreed with the simulation

results. Finally, B-dot probes containing 20 turns and shielded air-core Rogowski coils

were built in-house and calibrated for current and velocity measurements. All of the

objectives were successfully completed for the prototype system.


75

The experimental results presented, show an armature current close to 38 kA. This

current magnitude accelerated the plasma to an average velocity of ~ 6.7 km/s. Analysis

of the B-dot traces revealed no indication that plasma arc splitting has occurred at any of

the feed locations. In addition, these data show no presence of restrike arcs within the

railgun bore. In conclusion, the design and experimental data fulfilled all of the

prototype system goals and hence allowed for transition to the full 40-stage DES railgun.


76

CHAPTER VI

A 40-STAGE DES PLASMA ARC RAILGUN

6.1 Introduction

The designed system components for the 40-stage DES plasma arc railgun were

demonstrated successfully on the 7-stage prototype. This allows for confident expansion

to the 40-stage system. A CAD drawing of the proposed 40-stage system is displayed in

Fig. 6.1. The assembled railgun is 7.4 meters in length. Although the large stage number

adds complexity, it will demonstrate the full potential of a DES railgun to confine the

electric flux in effort to examine theoretical restrike suppression. This chapter will

discuss the system construction and experimental results of two tested energy schemes to

examine restrike suppression on a multi-stage DES railgun.

Fig. 6.1. CAD Drawing of a 40-Stage DES Railgun.


77


6.2.1 Containment Structure and Rails

The containment structures resemble the design used for the prototype with an

increased length by 53.3 cm. The G-10 containment structures measure 10.16 cm x 10.16

cm x 114.3 cm. A photograph of the machined containments and additional components

(nylon tube fittings, o-rings, hardware) is shown in Fig. 6.2.

Fig. 6.2. Photograph of the Containment Structures.

The rails, Fig. 6.3, are machined from UNS C11000 ETP copper with a shoulder

machined at both ends to seat the bore insulators and set the rail-to-rail spacing. On the

back sides of the rails, 1/4’’-28 holes provide an electrical connection for the brass all-

thread distributed current feeds. The current feed spacing, or stage length, is 15.24 cm.

The rail design is similar to those used in the prototype; however, a lap joint is


78

incorporated on each end to build a six meter rail length. A bolt pattern on each end

fastens six 122 cm long rails together.

Fig. 6.3. Photograph of the Lap Joint Rail (Top-Back View, Bottom-Front View).

6.2.2 Energy Module Modification

A single distributed energy module of the prototype system is shown in Fig. 6.4.

Modifications to the switch were necessary due to repeated failure for experiments

exceeding 20 distributed stages. These switches were selected based on results obtained

from a circuit simulation and financial constraints. The simulation determined the

following switch requirements: blocking voltage of 800 V, dI/dt rating of 333 A/ s, 10 –

15 kA with a 100 s pulse width. The thyristor selected is manufactured by ABB

Semiconductor (PN# 5STP10D1601) and has a blocking voltage of 1600 V, a continuous

1 Hz dI/dt rating of 1000 A/ s, and a peak non-repetitive surge current of 16 kA at 125

degrees Celsius with a 8.3 ms pulse.


79

Fig. 6.4. CAD Drawing of the Distributed Energy Module.

Experimental testing verified that the switches could handle a maximum current of 15

kA for the 100 s pulse width; however, the relationship between the arc velocity and

module output current was overlooked. The velocity of the arc determines the distance it

will travel down the rail length. This distance corresponds to a variable resistive load on

the energy module. At high velocities, the arc travels further which results in a “high”

rail resistance and hence a “low” output current. As the velocity is reduced, the rail

resistance seen by the energy module also decreases and the output current is increased.

During preliminary testing (20<stage number<40), the arc did not always trigger a stage

upon its arrival. The cause for this has been corrected and is explained in the next

section. This trigger failure led to a reduction of armature current and consequently, arc

velocity. Stage currents up to 25 kA were measured, exceeding the peak current carrying

ability of the switch which led to thermal failure. Part of this problem was resolved by

placing an additional switch in parallel to share the output current through two switches.


80

Assuming equal current sharing, the modified energy modules would be able to withstand

magnitudes up to 30 kA for pulsed conditions.

6.2.3 Printed Circuit Board Diagnostics

The operation of the 40-stage DES railgun demands an extensive diagnostic

count. The firing sequence is controlled by a real-time feedback control system which

utilizes armature B-dot probes to detect arc arrival into a given stage. As a result, 39 of

these probes are required with one probe at each distributed current feed location. An

additional 20 rail B-dot probes, one between every other stage, monitor localized rail

current as a means of restrike detection. The requirement to monitor all of the energy

module current waveforms heightens the diagnostic count by 40. A decision was made to

manufacture all of the diagnostics (rail B-dot probes, armature B-dot probes, and

Rogowski coils) implemented on this 40-stage system on printed circuit boards (PCB) to

maintain sensor-to-sensor consistency, provide a compact package, and reduce labor

hours. Both PCB B-dot probes and PCB Rogowski coils described are designed and

manufactured in collaboration with Dr. Wetz at the IAT.

A preliminary test of both sensors was conducted and compared to previously

used diagnostics. The PCB B-dot, Fig. 6.5, is a two-turn design with a 2.54 cm loop

diameter. Observed in the raw data (not shown), one volt was induced for a ~10 kA rail

current. The probe is designed to output a low voltage in accordance with the maximum

input voltage ratings of the control system and data acquisition system. A comparison is

made between the output waveforms produced by a previously used rail B-dot (discussed

in Chapter VI) and a PCB rail B-dot, shown in Fig. 6.5. These raw data are integrated


81

and calibrated to compare waveform shapes of the local rail current at one location. A

discrepancy between the two diagnostics is visible after 150 s. Since the two probes

were not located in exactly the same location (one +45 degrees from the positive rail and

the other -45 degrees), the d /dt is slightly different.

Fig. 6.5. Photograph of the PCB B-dot Probe and Plot of the Integrated and Calibrated

Data.

The PCB Rogowski coil, Figure 6.6, contains 15 turns and is printed on a 2-layer

board to include the inner coil conductor. These raw data are integrated and calibrated to

compare waveform shapes of the source current. The Rogowski coil used in past

experiments (discussed in Chapter VI) output 50 volts while just half a volt was induced

on the PCB Rogowski coil. A high correlation exists between the two waveform shapes

over the pulse width. Results can be improved by adding shielding to the PCB probe.


82

Fig. 6.6. Photograph of the PCB Rogowski Coil and Plot of the Integrated and Calibrated

Data.

The PCB B-dot, shown again in Fig. 6.7(a), has two turns and is designed to

output 5 volts for a d /dt produced by an 8 km/s arc velocity. A low output voltage is

desired to comply with the maximum input voltage ratings of the control system and data

acquisition system. This probe’s induced output voltage proved sufficient to trigger the

first 20 stages of the DES railgun but fell short thereafter. Beyond the 20th

stage, the flux

coupling reduced and the induced voltage magnitude fell short of the 2.3 volts required

for triggering the TTL digital input modules within the active control system. This flux

reduction is believed to be a product of the growing arc length that smears out the current

density flowing through the arc body. This trend increases until the arc’s magnetic flux

fails to couple into the B-dot loop. To resolve this issue and induce more voltage, two

approaches were examined.


83

(a) (b) (c)

Fig. 6.7. PCB Armature B-dot Probes. (a) 2-Turn Design. (b) 14-Turn Design. (c) 28-

Turn Design.

The first approach would be to move the probe closer to the plasma arc and the

second approach would be to increase the number of turns on the probe. The latter was

selected because the containment design would not allow the probes to be moved closer

to the railgun bore. A new probe design, Fig. 6.7(b), was implemented that consisted of

14 turns. These new probes provided enough signal amplification to trigger 10 additional

stages but lacked signal strength to trigger the last ten. To induce enough voltage to

trigger stages 31-40, two of the 14-turn PCB probes were electrically connected in series,

Fig. 6.7(c), doubling the turn ratio to twenty eight. This magnetic flux reduction problem

would not be encountered with a solid armature embodying a fixed length.

6.2.4 Data Acquisition System

Progression to the 40-stage system requires 79 signals to be recorded for each

experimental test. A large scale data acquisition (DAQ) system is therefore required.

The hardware, Fig. 6.8, and software selected for the task are designed and manufactured

by National Instruments.


84

The selected DAQ system is a stand-alone device equipped with a controller (PN#

PXI-8106) that contains:

2.16 Intel GHz Core 2 Duo T7400 dual-core processor

250 GB SATA hard drive

1 GB DDR2 RAM

Windows XP

Only analog input modules are required since both the B-dots and the Rogowski

coils output analog signal waveforms. The purchased DAQ system contains 10, 8-

channel analog input modules (PN# PXI-6133) capable of simultaneous sampling at a

maximum 2.5 MS/s using an onboard sample clock. The appropriate sampling rate was

determined from past B-dot and Rogowski coil experimental data. Four input voltage

ranges can be set from ±1.25 to ±10 V (±10 V was set for our system). The analog input

modules have a 14 bit resolution which allows them to detect voltage differences of 0.5

mV. Provided with 16 MS of onboard memory, the device can collect 0.8 seconds of

data while sampling all eight channels at 2.5 MS/s. This fell well within our data

collection time interval because the 40-stage railgun current pulse width is expected to be

approximately 1 ms. In addition, the modules contain two 24 bit counter/timers and eight

hardware-timed digital I/O lines. Additional over voltage/current protection was added to

protect the sensitive inputs. External circuitry consisting of fast-acting fuses and

transient voltage suppressors (TVS) clamped the input voltage to ±10 V and limited the

current to 62 mA.


85

Fig. 6.8. National Instruments DAQ System.

6.2.5 Built System

A photograph of the assembled 7.4 meter long 40-stage DES railgun system is

shown below in Fig. 6.9. The top/side view shows the railgun, distributed energy

modules, support structure, diagnostics, gate driver board boxes, fiber optic and electric

cabling, and the vacuum connection and dry scroll pump. The capacitor banks, PCB

Rogowski coils, and rail B-dot probes can be viewed in Fig. 6.10. Steel tripods have

proven to be an adequate support platform for the gun to rest on. The overall design and

construction mimics the 7-stage prototype, but has been expanded to a length of 7.4

meters to allow for the connection of the additional distributed stages.


86

Fig. 6.9. Photograph of the 40-Stage DES Railgun (Top/Side View).

Fig. 6.10. Photograph of the 40-stage DES Railgun (Isometric View).


87

6.3 Control System

6.3.1 Introduction

The six distributed stages on the 7-stage prototype were triggered using a hardcoded

timing sequence determined by experimental trial and error. This proved to be an

adequate technique for a system with a low stage number but became tedious when the

complexity heightened as the number of stages grew. To overcome this problem, a real-

time feedback control system was integrated into the system for a precise release of

energy upon the armature’s arrival to a distributed stage. A control system is not

essential for the operation of a DES railgun; however, it simplifies the timing control of

latter stages without the need for a complicated simulation to predict switch timing. This

became especially evident when dynamic variables such as bore pressure, ablation, and

current magnitude affected the arc velocity from shot to shot. The probability of firing a

stage prematurely is heightened without the implementation of a control system, which

can result in velocity reduction. Additional flexibility of the trigger timing is

accomplished by a user defined time delay after the armature arrival.

6.3.2 Hardware

The control system functions to determine the armature real-time position and make

decisions accordingly. A partial representation of the real-time feedback control system

hardware is shown in Fig. 6.11. The brain of the system consists of two (only one

shown) National Instruments CompactRIO PACs that utilize FPGA technology to

provide real-time processing. The LabVIEW 2009 software package is used to develop


88

control code which is compiled into a bit-file and downloaded into the CompactRIOs’

512 MB flash memory where it is stored and is activated after the boot cycle.

Fig. 6.11. Control System Hardware.

Thirty nine armature B-dot probes measure armature position and supply the real-time

feedback signals. These probes are incrementally located at each distributed current feed.

The induced armature B-dot voltage signals resemble a single cycle of a sine wave. A

positive voltage is induced as the armature approaches the probe and the polarity flips as

the armature moves away from the probe. The armature detection occurs on the rising

edge of the feedback signal which indicates its arrival to the probe location. The B-dot

voltage signals are sent to the CompactRIOs where five, 8-channel NI 9401 TTL digital

input modules measure the induced voltages. The AND gates within the digital input

module provide a faster detection method vs. measurement using analog input modules.

This device functions as a switch because of its digital nature, which can interpret the

signals in two ways. When the signal amplitudes are below 2.3 V, the TTL device


89

remains in a “low” state or open by representation of a switch. Signal amplitude above

2.3 V corresponds to a “high” state or closed by representation of a switch. The induced

voltage within the B-dot probes typically exceeds 5 volts due to the d /dt and probe

design. Input signals in excess of 5 volts can damage the module’s channels; therefore,

external ±10 V transient voltage suppressors were integrated to clamp the circuit voltage

and are used for protection.

A LabVIEW 2009 program determines the appropriate switch timing for each energy

module. To initiate the release of current from an energy module, five, 8-channel NI

9401 TTL digital output modules provide a 10 s, 5 V pulse to a fiber optic board on the

respected stage channel. Gate driver boards receive the light signals and convert them to

10 s, 15 V analog pulses to trigger the stage’s corresponding SCR gate and release the

stored energy in the capacitor banks.

6.3.3 Software

The control code discussed in this section is developed using the LabVIEW 2009

software package and then compiled into a bit-file and finally downloaded into the

CompactRIOs’ 512 MB flash memory where it is stored and is activated after the boot

cycle. A flow chart of the control program is displayed in Fig. 6.12 below. The program

begins with an event sequence (not shown) that starts by waiting 1 second to allow time

for the CompactRIO to complete its boot configurations. The next event sets line

directions and checks the status of the digital input/output modules. After these tasks are

completed a Boolean TRUE is assigned to two local variables that control triggering of

the DAQ system and plasma gun. These local variables are read by a pulse generating


90

program to output two 10 s, 5 V digital pulses required to initiate the DAQ and fire the

plasma source. The following event waits 1 s to allow time for the plasma to disperse in

the breech region. As the plasma expands, a Boolean TRUE is assigned to a local

variable that controls the first stage firing. Once again this local variable is read by a

pulse generating program which outputs a signal to fire the first energy module, causing a

high voltage breakdown across the rail gap and initiating the Lorentz driving force to

accelerate the arc.

Fig. 6.12. Flow Chart of the Control Program.

As the plasma travels through the bore, the distributed stage firing sequence

begins with an event to read the armature B-dot sensor located at the second stage current

feed. This event continues to loop until a 2.3 V threshold voltage is obtained or

exceeded. A user defined time delay is then executed to control the fire timing of the

second stage. This distributed stage firing sequence procedure is continued to detect the

armature position and trigger the remaining stages.


91


Two different energy schemes were experimentally tested and the results are

discussed in this section. The first energy scheme is referred to as “asynchronous” and

allows only positive current to be discharged by the capacitor banks. This is

accomplished by opening the current loop containing an anti-parallel diode which is

electrical connected in parallel with the thyristor. The second energy scheme is referred

to as “synchronous” and allows negative current to flow through the system. An anti-

parallel diode connected in parallel with the thyristor allows the capacitor bank to ring

and produces under-damped waveforms. This energy scheme provides negative current

to cancel out residual positive current that is trailing behind the armature. The result is an

enhanced isolation of the electric flux in the bore behind the armature.

6.4.1 Asynchronous Energy Scheme

The current waveforms for a 40-stage asynchronous DES plasma arc railgun shot, along

with a summed armature current waveform, are displayed in Fig. 6.13. During the shot,

the containment structure was evacuated to roughly 14 mTorr. The first stage was

charged to 1000 volts and sourced a maximum 31 kA for a pulse width of 150 µs. Stages

2 through 40 were charged to 650 volts and each output 10-15 kA with a 100 µs pulse

width. The triggering of stages 2 through 40 were controlled by the active feedback

control system.


92

Fig. 6.13. Current Waveforms from a 40-Stage asynchronous DES Railgun.

An attempt was made to produce a square pulse armature current waveform. The

waveform produced loosely resembles a square wave with a pulse width of 550 s. The

maximum armature current is ~ 83 kA seen at 500 µs. The plasma accelerated to a

maximum velocity of ~ 19.1 km/s from 400 µs to 416 µs. The average measured velocity

was ~13.8 km/s calculated using the armature B-dot data shown in Fig. 6.14. Analysis of

these B-dot traces reveals no indication that arc splitting has occurred at any of the feed

locations or that a restrike arc was formed.


93

Fig. 6.14. Armature B-dot Waveforms from a 40-Stage asynchronous DES Railgun.

6.4.2 Synchronous Energy Scheme

The current waveforms for a 40-stage synchronous DES plasma arc railgun shot, along

with a summed armature current waveform, are displayed in Fig. 6.15. During the shot,

the containment structure was evacuated to roughly 12 mTorr. The first stage was

charged to 1000 volts and sourced a maximum 31 kA for a pulse width of 150 µs. Stages

2 through 40 were charged to 825 volts and each output 12-21 kA with a 100 µs pulse

width. As in the asynchronous test, triggering was done with the active feedback control

system.


94

Fig. 6.15. Current Waveforms from a 40-Stage Synchronous DES Railgun.

The maximum armature current, shown in Fig. 6.15, is close to 85 kA which accelerated

the plasma to a peak velocity of ~19.3 km/s. The average measured velocity was ~12.6

km/s calculated using the armature B-dot data shown in Fig. 6.16. Analysis of the B-dot

traces reveals no indication that arc splitting has occurred at any of the feed locations or

that a restrike arc was formed.


95

Fig. 6.16. Armature B-dot Waveforms from a 40-Stage Synchronous DES Railgun.

6.5 Conclusion

The development process pertaining to the design, fabrication, and testing of a 40-stage

DES plasma arc railgun was discussed. Investigation of this type of system will

determine the effectiveness of a distributed energy scheme to suppress the plasma restrike

phenomenon.

Experimentation with the 40-stage system discovered a loss of probe signal as the arc

traveled down the bore. This flux reduction is believed to be a product of the growing arc

length that smears out the current density flowing through the arc body. To resolve this

issue and induce more voltage, additional turns were added to the B-dot sensor. Before


96

this new sensor was implemented, the loss of the probes’ signals caused the arc velocity

to dramatically decrease and led to thermal damage to the thyristor switches. This was

caused by exceeding the peak current carrying ability of the switch. As a result of these

switches failures, a relationship between the arc velocity and module output current was

identified. The problem was resolved by placing an additional switch in parallel to share

the output current through two switches.

A real-time feedback control system was integrated into the system for a precise release

of energy upon the armature’s arrival to a distributed stage. The control system functions

to determine the armature real-time position and make decisions accordingly. A control

system is not essential for the operation of a DES railgun; however, it simplified the

timing control of latter stages without the need for a complicated simulation to predict

switch timing.

Initial testing of a 40-stage system has been completed. Two energy schemes were

examined. Both accelerated the arc down the full rail length and achieved

hypervelocities. Analysis of the B-dot traces reveals no indication that arc splitting has

occurred at any of the feed locations or that a restrike arc was formed. Continued

analysis of these data is necessary before any conclusions can be made about the

effectiveness of a distributed energy scheme to suppress the plasma restrike phenomenon.

In the future, researchers at TTU plan to use this railgun to test a breech-fed configuration

with equivalent energy in attempt to create restrike arcs. This breech-fed experiment is

essential to determine the restrike prevention theory of DES railguns.


97

CHAPTER VII

SUMMARY AND CONCLUSION

After proving the DES principle with solid armatures9, the design of a plasma source

commenced to transition toward plasma arc experiments. This technique allowed for

more realistic armature velocities (>6 km/s) without the requirement for a large stored

energy facility. The higher velocity is owing to the fact that instead of pushing a “heavy”

solid armature we will be pushing a “light” plasma arc.

Movement to a DES plasma arc launcher called for the design and construction of a

completely new system. In order to operate in a hypervelocity regime, system

modifications included:

a) A vacuum chamber containment structure ( 1 to 10 Torr)

b) A plasma source to create/form the armature

c) Increased rail and stage lengths

d) Energy sources that produce a larger current magnitude with a shortened pulse

width

e) A real-time feedback control system

As a result, a 15 kJ, 4-stage DES plasma arc railgun was developed. A 4-stage

system allowed three different switching or energy schemes to be examined: breech-fed,

pseudo-asynchronous, and pseudo-synchronous. To intentionally create restrike arcs for

analysis, highly ablating G-10 bore insulators were utilized. Although classical restrike

was observed for the breech-fed configuration, both asynchronous and pseudo-


98

synchronous schemes suppressed the phenomenon. However, analysis of these data

collected from the latter energy schemes revealed an unusual current diversion away from

the primary arc with dissimilar characteristics observed from restrike.

Upon further examination, alternative diagnostics provided supporting evidence that

the restrike phenomenon was not responsible for this current diversion. Instead of

restrike, the current diversion was attributed to a secondary arc formation by plasma arc

splitting at the distributed current injection locations. This problem was resolved by

waiting until the full length of the armature was ahead of the distributed feed location

before the release of energy, maintaining magnetic pressure behind the plasma body.

Knowledge of the plasma armature length was determined to be an important parameter

to correctly time the triggering of distributed stages. An objective to accurately calculate

the length was hence put forth. Optical diagnostics were integrated into a 2-stage DES

system at five different locations along the railgun bore for the analysis. These data

revealed a luminosity gradient along the length of the plasma armature body, suggesting a

hot, dense, compact head followed by a cooler, less dense body/tail region. As

expected, the armature length grew when the background pressure was increased. When

conditions for arc splitting were applied, the length was found to fluctuate near the

distributed current feed location. This fluctuation is theorized to be a perturbation of the

plasma by gradient magnetic pressures located near the distributed feeds.

The final objective was to design a 40-stage synchronous DES plasma arc

railgun. A computer simulation was developed to determine the necessary component

values for each stage. The code neglects complex plasma physics and was developed in

accordance to derived circuit equations2 for a distributed energy model. Values obtained


99

from the simulation allowed for the selection of realizable system components such as:

capacitors, switches, and power conditioning devices. This led to the development of a

prototype system to test all of the components designed for the 40-stage system. The

prototype resembled the first 7 stages of the overall design. All of the objectives were

successfully completed for the prototype system. The B-dot probes waveforms, Fig.

5.16, confirmed that the arc is accelerating towards the railgun muzzle as all 7 stages

discharge. A containment structure was designed and built using G-10 with numerous o-

ring seals to achieve mTorr pressures with air as the fill gas. Plasma leakage was reduced

by applying a mechanical horizontal and vertical compression to the railgun core. The

flange design proved to maintain vacuum and bore compression. Energy modules were

designed utilizing compact film dielectric capacitors and a variable self-inductance

scheme. When charged to 500 volts, the modules output approximately 10 kA with a 100

s pulse width. These values agreed with the simulation results. Finally, B-dot probes

containing 20 turns and shielded air-core Rogowski coils were built in-house and

calibrated for use as current and velocity measurements. The experimental results

showed an armature current close to 38 kA and an average arc velocity of ~ 6.7 km/s.

Analysis of the B-dot traces revealed no indication that plasma arc splitting has occurred

at any of the feed locations. In addition, these data show no presence of restrike arcs

within the railgun bore. In conclusion, the design and experimental data fulfilled all of

the prototype system goals and hence allowed for transition to the full 40-stage DES

railgun.

The development process pertaining to the design, fabrication, and testing of a 40-stage

DES plasma arc railgun was discussed. Investigation of this type of system will


100

determine the effectiveness of a distributed energy scheme to suppress the plasma restrike

phenomenon.

Experimentation with the 40-stage system discovered a loss of probe signal as the arc

traveled down the bore. This flux reduction is believed to be a product of the growing arc

length that smears out the current density flowing through the arc body. To resolve this

issue and induce more voltage, additional turns were added to the B-dot sensor. Before

this new sensor was implemented, the loss of the probes’ signals caused the arc velocity

to dramatically decrease and led to thermal damage to the thyristor switches. This was

caused by exceeding the peak current carrying ability of the switch. As a result of these

switches failures, a relationship between the arc velocity and module output current was

identified. The problem was resolved by placing an additional switch in parallel to share

the output current through two switches.

A real-time feedback control system was integrated into the system for a precise release

of energy upon the armature’s arrival to a distributed stage. The control system functions

to determine the armature real-time position and make decisions accordingly. A control

system is not essential for the operation of a DES railgun; however, it simplified the

timing control of latter stages without the need for a complicated simulation to predict

switch timing.

Initial testing of a 40-stage system was completed. Two energy schemes were

examined. Both accelerated the arc down the full rail length and achieved

hypervelocities. Analysis of the B-dot traces reveals no indication that arc splitting has

occurred at any of the feed locations or that a restrike arc was formed. Continued

analysis of these data is necessary before any conclusions can be made about the


101

effectiveness of a distributed energy scheme to suppress the plasma restrike phenomenon.

In the future, researchers at TTU plan to use this railgun to test a breech-fed configuration

with equivalent energy in attempt to create restrike arcs. This breech-fed experiment is

essential to determine the restrike prevention theory of DES railguns.

The future of the plasma railgun relies on the distributed energy scheme to reduce

the trailing E-field, suppress secondary arc formation, and allow the powerful Lorentz

magnetic force to demonstrate its full potential. This would open the door to a variety of

exciting applications such as cheap space access, particle accelerators for further

characterization of quarks and other sub-atomic particles, the possibility of developing

new elements, advancing the physics of fusion, and extremely powerful weapons.


102

REFERENCES

[1]: J. V. Parker, “Why Plasma Armature Railguns Don’t Work (And What Can Be Done

About It),” IEEE Transactions on Magnetics, vol. 25, pp. 418 – 424, January 1989.

[2]: J. V. Parker, “Electromagnetic Projectile Acceleration Utilizing Distributed Energy

Sources,” Journal of Applied Physics, vol. 53, pp. 6710 – 6723, October 1982.

[3]: R. A. Marshall and W. F. Weldon, “Analysis of Performance of Railgun Accelerators

Powered by Distributed Energy Stores,” 14th

Pulse Power Modulator Symposium,

Orlando, Florida, June 3-5, 1980.

[4]: U. S. Inan and A. S. Inan, Electromagnetic Waves, New Jersey: Prentice Hall, 2000,

p. 417.

[5]: S. C. Rashleigh, R. A. Marshall, “Electromagnetic Acceleration of Macroparticles to

High Velocity,” Journal of Applied Physics, vol. 49, p. 2540, 1978.

[6]: J.V. Parker, W. Condit, and Y. Thio, “Investigation of Plasma Armature Dynamics,”

AFATL report, Part 2, pp.6, December 1990.

[7]: C. H. Haight and M. M. Tower, “Distributed Energy Store (DES) Railgun

Development,” Proc. of 3rd

EML Symposium, pp. 81-84, Austin, Texas, April 1986.

[8]: J. P. Barber and A. Challita, “Monthly Progress Letter,” IAP Research, Inc., Dayton,

Ohio, LTVAD P.O. P-350272, April 1984.

[9]: R. Karhi, “Instrumentation and Control of Electromagnetic Launchers,” Master’s

Thesis, Texas Tech University, Lubbock, Texas, 2007.

[10]: R. Karhi, J. Mankowski, J. Dickens, M. Kristiansen, and D. Wetz, “Secondary Arc

Formation within a Distributed Energy Railgun,” IEEE Transactions on Plasma Science,

vol. 36, Issue 5, pp. 2738-2746, October 2008.

[11]: Hamamatsu Photonics, “Photodiode Technical Information,” Technical notes.

[12]: MATLAB® Help file.

[13]: J. F. Kerrisk, “Current Distribution and Inductance Calculations for Railgun

Conductors,” LA-9092-MS, November 1981.


103

APPENDIX A

MULTI-STAGE DES FREE-ARC SIMULATION

function DES_FreeArc

% Multi-stage DES free-arc simulation.

% John Mankowski and Ryan Karhi, 4/12/10

clear all; close all;

% Initial conditions and first stage parameters -----------------------

points = 1000; % set number of point per iteration

Nstages = 40; % number of stages.

L = zeros(Nstages,1); % pad L column vector with zeros. Q0 = zeros(Nstages,1); % pad Q0 column vector with zeros. C = zeros(Nstages,1); % pad C column vector with zeros. R = zeros(Nstages,1); % pad R column vector with zeros. C(1) = .00083; % capacitor value in stage one [F]. R(1) = .001; % resistor value in stage one [ohm]. Q0(1) = 2.5; % initial charge on capacitor in % stage one [C]. L(1) = 2.5*10^-6; % inductor value in stage one [H]. Lrail = 0.451*10^-6; % inductance gradient of the railgun [H/m]. press = 5; % pressure in the bore [torr]. rho_0 = 1.204; % density of air at atmosphere [kg/m^3]. rho = rho_0*(press/760); % density of air in the bore [kg/m^3]. h = 0.01; % rail separation [m]. gamma_star = 1.2; % specific heat ratio [unitless]. Cf = 0.0049; % drag coefficient [unitless]. x_const = 6.096; % Shock front distance [m]. S = 0.1524; % distance between stages [m]. tfinal = .001; % estimated final time [s].

x_s = (gamma_star+(1/4))*(h/Cf); % scale length related to viscous % forces.

tt = zeros(points*Nstages,1); % pad tt column vector with zeros. position = zeros(points*Nstages,1);% pad position column vector with % zeros. ir = zeros(points*Nstages,Nstages);% pad rail current matrix with % zeros.

tstart = 0; % initialize start time.

y0 = [Q0(1); 0; 0]; % load vector of initial conditions for


104

% y,where y=[q;q';x] % =[charge;current;position].

% ---------------------------------------------------------------------

% Latter stage parameters ---------------------------------------------

Rrail = 0.0001; % rail resistance per meter [ohm/m].

for a = 2:Nstages;

L(a) = 1.5*10^-6; % inductunce value in latter stages [H]. Q0(a) = .525; % capacitance value of latter stages [C]. C(a) = .00075; % initial charge on latter stages [F]. R(a) = 0.005; % resistance value in latter stages [Ohm].

end

% ---------------------------------------------------------------------

% Calculate I,dI/dt,velocity ------------------------------------------

for N = 1:Nstages-1;

tspan = linspace(tstart,tfinal,points); % creates linear space %of time.

options = odeset('Mass',@Lprime); % A built-in MATLAB % mass matrix % is used to calculate the % variable inductance. % produces: f(t,y)=LP*y'

[t y] = ode45(@f,tspan,y0,options); % solve the ODE with ode45. % f is the function. % tspan is the time span. % y0 is the initial % conditions.

% ---------------------------------------------------------------------


105

% Detects armature arrival to the next stage and sets the trigger % timing for each stage -----------------------------------------------

k = 0; % initialize variable.

for j = 1:points;

if y(j,2*N+1) <= S*N; % if arc position is <= next stage.

k = k+1; % number of data points behind % next stage.

end end

a = t(k); % time to trigger next stage.

% ---------------------------------------------------------------------

% Calculate derivatives for the new stage -----------------------------

tspan = linspace(tstart,a,points); % creates linear space % of time. % tstart is arrival % time to the previous % stage and a is the % arrival time to the % next stage.

options = odeset('Mass',@Lprime); % A built-in MATLAB % mass matrix % is used to calculate the % variable inductance. % produces: f(t,y)=LP*y'

[t y] = ode45(@f,tspan,y0,options); % solve the ODE with ode45. % f is the function. % tspan is the time span. % y0 is the % initial conditions.

% ---------------------------------------------------------------------


106

% Transfer stage data into one large array ----------------------------

for j = 1:points;

tt(points*(N-1)+j)=t(j); % load stage time % data into master % time vector. position(points*(N-1)+j)=y(j,2*N+1); % load stage position % data into master % position vector. for c = 1:N;

ir(points*(N-1)+j,c)=-y(j,2*c); % load stage current % data into master % current vector. end

end

% ---------------------------------------------------------------------

% Reset initial conditions for next stage -----------------------------

tstart = a; % tstart = next stage trigger time. y0 = zeros(2*N+3,1); % pad y0 column vector with zeros.

y0(2*N+3) = y(points,2*N+1);% load the last position data point as % the next stage's initial condition. y0(2*N+1) = Q0(N+1); % load the next stage's charge as an % initial condition.

for b = 1:2*N;

y0(b) = y(points,b); % set the last data point calculated % as the next stage's initial % conditions. end

% ---------------------------------------------------------------------

end

% ---------------------------------------------------------------------


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% Calculate I,dI/dt,velocity for last stage ---------------------------

N=Nstages; % equate N to the last stage #.

tspan = linspace(tstart,tfinal,points);% creates linear space of time. % tstart is arrival time to the % next to last stage.

options = odeset('Mass',@Lprime); % A built-in MATLAB mass matrix % is used to calculate the % variable inductance. % produces: f(t,y)=LP*y'

[t y] = ode45(@f,tspan,y0,options); % solve the ODE with ode45. % f is the function. % tspan is the time span. % y0 is the initial conditions.

% ---------------------------------------------------------------------

% Transfer stage data into one large array ----------------------------

for j = 1:points;

tt(points*(N-1)+j)=t(j); % load last stage time data % into master time vector. position(points*(N-1)+j)=y(j,2*N+1);% load last stage position data % into master position vector. for c = 1:N;

ir(points*(N-1)+j,c)=-y(j,2*c); % load last stage current data % into master current matrix. end

end

% ---------------------------------------------------------------------


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% Solve for velocity, acceleration, and armature current --------------

V = diff(position)./diff(tt); % calculate velocity. V(points*N) = V(points*N-1); % copy the second to last data % point and paste into the last % data point to match the % velocity vector length % to the time vector length.

accel = diff(V)./diff(tt); % calculate acceleration. accel(points*N) = accel(points*N-1); % copy the second to last data % point and paste into the last % data point to match the % acceleration vector length % to the time vector length.

armature_current = sum(ir,2); % adds up stage current to % calculate armature current. % 2 indicates a summation of % ir's rows.

% ---------------------------------------------------------------------

% Plot waveforms ------------------------------------------------------

figure(1); plot(tt*1000,accel); % plot acceleration waveform. title('Arc Acceleration'); xlabel('Time [msec]'); ylabel('Acceleration [m/sec/sec]');

figure(2); plot(tt*1000,position); % plot position vs. time. title('Arc Position'); xlabel('Time [msec]'); ylabel('Position [m]');

figure(3); plot(tt*1000,armature_current/1000); % plot armature current. title('Armature Current'); xlabel('Time [msec]'); ylabel('Projectile current [kA]');

figure(4); plot(tt*1000,V); % plot velocity waveform. title('Arc Velocity'); xlabel('Time [msec]'); ylabel('Velocity [m/sec]');

figure(5);

for z = 1:Nstages;

hold all; % changes trace color. plot(tt*1000, ir(:,z)/1000); % plot individual current


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% waveforms.

end

title('Current Waveforms'); xlabel('Time [msec]'); ylabel('Current [kA]'); axis([0 1 -20 80]);

hold off

% ---------------------------------------------------------------------

% Derivative function -------------------------------------------------

function dydt = f(t,y) % dy/dt = [qi'';V';x''] % = [dI/dt;dV/dt;acceleration]

dydt = zeros(2*N+1,1); % pad dy/dt column vector with zeros.

% Apply capacitor bank resistance -------------------------------------

for d = 1:N;

if -y(2*d) < 0 % Applies to stages 2-N

R(d) = .1; % Resistance for negative current

else

R(d) = .0001; % Resistance for positive current

end

end

% ---------------------------------------------------------------------

% Calculate derivatives ----------------------------------------------

isum = 0;

for i = 1:N;

isum = isum+y(2*i); % current summer routine dydt(2*i-1,1) = y(2*i); % store current values in % dy/dt to calculate dI/dt

dydt(2*N+1,1) = ((sqrt(Lrail/((gamma_star+1)*rho)))... *(abs(isum)/h)*(1/(sqrt(1+(x_const/x_s)))));


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% The equation above is Jerry Parker's velocity derivation for % a free-arc under ablation-free operation and assuming % dm_a/dt = 0. I replaced the variable, x, in the original % equation to a constant, x_const, for simplification.

if i < N

% The equation below is part of Jerry Parker's derivation of % the lumped element circuit equation for each stage which the % armature has passed entirely through. The terms containing % inductance(that are present in the origional equation) % have been removed here, but are added back in with % excecution of the function LP.

dydt(2*i,1) = -y(2*i-1)/C(i)-R(i)*y(2*i)-Rrail*S*isum... +y(2*i+1)/C(i+1)+R(i+1)*y(2*i+2);

else

dydt(2*N,1) = -y(2*N-1)/C(N)-R(N)*y(2*N)-Rrail*(y(2*N+1)... -(N-1)*S)*isum-Lrail*dydt(2*N+1,1)*isum;

% The equation above is part of Jerry Parker's derivation of % the lumped element circuit equation for the stage containing % the armature. The terms containing inductance(that are % present in the origional equation) have been removed here, % but are added back in with excecution of the function LP.

end

end

% ---------------------------------------------------------------------

end

% ---------------------------------------------------------------------

% Variable inductance function ----------------------------------------

function LP = Lprime(t,y)

LP = zeros(2*N+1,2*N+1); % pad LP matrix with zeros LP(2*N,2*N) = L(N)+Lrail*(y(2*N+1)-(N-1)*S);

% The above equation calculates the inductance gradient % for the stage containing the armature ( L'*(x^*)) and % adds the capacitor bank inductance L(N).

for i = 0:N;


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LP(2*i+1,2*i+1)=1;% set alternating terms in diaganol with ones

if i < N-1

LP(2*i+2,2*i+2) = L(i+1)+Lrail*S;

% The above equation adds up the capacitor bank % inductance (L(i+1)) and the rail inductance (L'*S) for % each stage behind the armature.

LP(2*i+2,2*i+4) = -L(i+2);

% The above equation adds the next stage's % capacitor bank inductance (L(i+2)).

for e = 1:N-1

LP(2*N,2*e) = Lrail*(y(2*N+1)-(N-1)*S);

% The above equation calculates the inductance % gradient for the stage containing % the armature. L'*(x^*)

end

end

if i < N-2

for l = 1:N-2

for m = 1:l

LP(2*l+2,2*m) = Lrail*S;

% The above equation calculates the rail % inductance of a single stage. L'*S

end

end

end

end

end

% ---------------------------------------------------------------------

end


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APPENDIX B

CONTROL SYSTEM CODE

B.1 Control Program for Stages 1-24

The LabVIEW program, Fig. B.1, is compiled into a bit-file and downloaded into

the CompactRIO’s 512 MB flash memory where it is stored and activated on each boot

cycle. The program begins by simultaneously running 26 sub-routines. This is

accomplished by the parallel processing capability of the FPGA. The first sub-routine

Fig. B.1. LabVIEW Control Program for Stages 1-24 with Red Zoom Box Labels.


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(containing Z1-Z6) initializes digital input/output modules, triggers devices (DAQ,

plasma generation, etc.), and waits to receive B-dot signals from the DES railgun. The

sequence of operations for each DES stage is identical; therefore, the program flow for a

single DES stage will be discussed in detail. The graphical user interface (GUI) is

difficult to read in Fig. B.1, so portions of the code are that are discussed are highlighted

and labeled using red boxes and red label text.

Upon entering the first sub-routine (containing Z1-Z6) a sequence of eight event

frames are initialized inside a while loop. This loop continues execution until stage 24 is

triggered. The first of the eight frames is a wait function which is configured for time

intervals in milliseconds, shown in Fig. B.2. The wait function is set to three seconds to

Fig. B.2. 3 Second Wait Function (Z1).

allow time for the CompactRIO to complete its own boot cycle and the boot cycle of an

additional CompactRIO that is a part of the full control system. The second frame sets

the line directions for the digital input/output modules, shown in Fig. B.3. The line

direction must be specified since the channels of the NI 9401 TTL digital modules can be

configured as inputs or outputs. The third frame checks the status of each digital module,

displayed in Fig. B.4, to ensure a “ready” state. Boolean case structures receive values

from the while loop iteration counter to limit this status check to execute on the first


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Fig. B.3. Set Line Direction for Digital Input/Output Modules (Z2).

Fig. B.4. Check Digital Input/Output Modules Status (Z3).


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iteration only. Frames 4-7 are shown in Fig. B.5. The fourth frame assigns Boolean

TRUE values to two local variables, Mod7/DO0 and Mod7/DO1. Mod7 refers to the

Fig. B.5. Trigger Sequence for DAQ, Plasma Generation, and Stage 1 (Z4).

seventh module connected to the CompactRIO chassis which is an 8-channel, 24V,

digital output module (NI 9474). These local variables are read by control variables

contained within a pulse generating sub-routine (Z8) to output a 10 s pulse, shown in

Fig. B.6. Channel 0 outputs a trigger signal to the DAQ system and Channel 1 outputs a

trigger signal to generate the plasma in the railgun bore. The pulse generating sub-

Fig. B.6. Pulse Generating Sub-Routine for Module7 with TRUE Input (Z8).


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routine contains two event frames inside of a while loop. In the first frame, control

variables write Boolean values to three digital channels (0-2) of module7. The local

variables, Mod7/DO0 and Mod7/DO1, in Z4 are linked to these controls which have

FALSE default Boolean values. In the given example, values of TRUE are written to

channels 0-1 while a FALSE is written to channel 2. Channels 0-1 are now in a digital

high state, where 24V is seen across their outputs. In the second frame, the control

variable values are placed into an array and compared using an OR gate. Continuing with

our example, a value of TRUE is output from the OR gate and sent to a Boolean case

structure. When a value of TRUE is input to this case structure, an event frame sequence

waits 10 s, writes a FALSE to all three digital channels, and resets the control variables

to a value of FALSE. These actions produce a 10 s trigger pulse. If a value of FALSE

is input to the case structure, no action is taken, Fig. B.7, and the while loop starts a new

Fig. B.7. Pulse Generating Sub-Routine for Module7 with FALSE Input (Z8).

iteration. Returning to Z4, the fifth frame contains a wait function with microsecond time

intervals. This frame waits 1 s to allow time for the plasma to diffuse inside of the


117

railgun bore. The sixth frame assigns a Boolean TRUE to a local variable named

MOD1/DIO0. This initializes the fire sequence to release the stored energy within the

first stage, create a current path through the plasma, and accelerate the arc. The local

variable MOD1/DIO0 is linked to a control variable within a different pulse generating

sub-routine (Z7), displayed in Fig. B.8. The figure shows two pulse generating sub-

routines for Module 1 (one for channel 0 and the other for channel 1). With exception of

the channel number, the two sub-routines have identical program flow and are both

shown to view two cases of a Boolean case structure. Modules 1-6 are 8-channel TTL

digital input/output modules (NI 9401). Modules 1, 3, 5 are configured as outputs that

provide trigger signals to fire the energy stores. While, Modules 2, 4, 6 are configured as

inputs that read voltage signals produced by B-dot probes to determine the appropriate

fire times of the energy stores. The pulse generating sub-routine (Z7) is embedded within

Fig. B.8. Pulse Generating Sub-Routine for Module1 (Z7).


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a while loop. The control variable Mod1/DIO0 writes Boolean values to channel 0 and a

Boolean case structure. In the given example, values of TRUE are written to channel 0

and the case structure. Channel 0 is now in a digital high state, where 5V is seen across

its output. When a value of TRUE is input to the case structure, an event frame sequence

waits 10 s, writes a FALSE to the digital channel, resets the control variable to a value

of FALSE, and stops the while loop execution. These actions produce a 10 s trigger

pulse. If a value of FALSE is input to the case structure, no action is taken and the while

loop starts a new iteration. We now return to the seventh frame within the first discussed

sub-routine (containing Z1-Z6) shown in Fig. B.5. This frame waits 20 s to prevent a

false trigger on one of the distributed energy stores. During this time interval, the plasma

arc formation and initial acceleration produce electromagnetic interference (EMI). This

EMI couples into B-dot probes of close proximity to the breech and can produce a false

trigger on one or multiple stages. The eighth and final frame contains plasma arc

detection routines for the first 23 distributed energy stores. This routine, displayed in

Fig. B.9, initializes a read function of individual B-dot probe voltages. The figure

shows conditions for different Boolean inputs to the case structures. In the first arc

detection routine, shown at the top of Fig. B.9, a while loop containing the detection

program is executed. The voltage signal produced by the 2nd

stage B-dot probe is read

and Boolean output values are sent to a Boolean case structure. When the input voltage

to the channel is below 2.3 V, a value of FALSE is input to the case structure and the

while loop begins a new iteration to continue reading the B-dot voltage signal. This

action begins a chain reaction, sending a Boolean FALSE to the case structure containing

the arc detection routine of the 3rd

stage, and the 4th

stage, and the 5th

stage, ect. The


119

program is coded in this fashion to read one B-dot probe signal at a time in order to

prevent the catastrophic event of all the stages firing at the same time. If the induced

voltage on the B-dot probe exceeds 2.3 V (indicating the arrival of the plasma arc), an

event frame sequence is initialized. The first frame of this sequence sends a Boolean

TRUE to the next arc detection routine to begin reading the 3rd

B-dot probe signal.

Following that frame, a user defined wait function is executed to delay the trigger signal

Fig. B.9. Plasma Arc Detection Routine (Z5).


120

and allow time for the full arc length to be ahead of the current feed location before it is

fired. In this example, a 10 s wait is programmed. The user defined wait can vary from

shot to shot and is determined by the initial conditions. The delay is a function of the arc

velocity and length which are established by the current magnitude through the arc and

background gas pressure. The third frame sends a Boolean TRUE to the local variable

Mod1/DIO1 to generate the trigger pulse required to fire the 2nd

stage. This pulse

generating sub-routine was discussed above and can be viewed in Fig. B.8. The fourth

frame halts the while loop to prevent multiple triggering of the stage’s switch. When the

arc arrives at stage 20, the plasma arc detection routine, shown in Fig. B.10, contains a

local variable to send a trigger signal to the second CompactRIO in the control system.

This action initiates the control program for stages 25-40 to begin reading the B-dot

probe voltage signal located at the 25th

stage. Initializing this read prior to the arc arrival

allows the program to read multiple data points before the arc is detected.

Fig. B.10. Trigger Signal for the Second cRIO (Z6).


121

B.2 Control Program for Stages 25-40

The LabVIEW program, Fig. B.11, controls the firing sequence for stages 25-40. Similar

to the control program for stages 1-24, it is stored into a second CompactRIO’s 512 MB

flash memory where it is activated on each boot cycle. The program flow and

architecture are analogous to the program described in Appendix B.1; therefore, only the

non-correlating portions of code will be highlighted and discussed.

Fig. B.11. LabVIEW Control Program for Stages 25-40 with Red Zoom Box Labels.


122

In the first frame of the first sub-routine (containing Z9-Z10), a one second wait

function, shown in Fig. B.12, is executed. This allows enough time for the CompactRIO

to complete its boot cycle. In contrast, the control program for stages 1-24 has a three

second delay. A shorter delay is implemented here to ensure the code controlling these

latter stages it ready before the firing sequence is started. The other difference between

Fig. B.12. 1 Second Wait Function (Z9).

the two control programs is found in the fourth frame of the first sub-routine, shown in

Fig. B.13. A while loop is configured to continuously read a digital input channel

(Mod5/DI0) until a Boolean value of TRUE is read. This value is obtained from

Mod7/DO2 discussed above and displayed in Fig. B.10. Once a value of TRUE is read,

the next frame of the sub-routine is executed and starts to read the B-dot probe signals.

Module 5 is a 32-channel, 24V, digital input module (NI 9425). Modules 1-4 are 8-

channel TTL digital input/output modules (NI 9401). Modules 1 and 3 are configured as

outputs that provide trigger signals to fire the energy stores. While, Modules 2 and 4 are

configured as inputs that read voltage signals produced by B-dot probes to determine the

appropriate fire times of the energy stores. All remaining sub-routines and pulse

generating function are programmed similar to the control program for stages 1-24.


123

Fig. B.13. Trigger Loop to Start Reading the B-dot Probes (Z10).


124

APPENDIX C

RAILGUN SYSTEM OPERATION MANUAL

1. Notify appropriate personnel about the experiment.

2. Wear safety goggle/glasses.

3. Turn on warning light.

4. Evacuate all unauthorized personnel from lab space.

5. Provide utility power to devices (120V 60Hz):

HV power supply (12 kV, 180mA)

DC power supplies (two Sorensen XHR 600-1.7 wired in series)

DC power supply (Sorensen XHR 300-3.5)

Ross HV relay switches ( used for electrical isolation and dump)

Dry scroll vacuum pump (Varian TriScroll 300 series)

Capacitive pressure sensors LED display (Terranova model 908A)

Two NI CompactRIOs (cRIO-9004)

Five fiber optic boards (designed and built in-house)

NI DAQ system (PXI-8106)

40 gate driver boards (designed and built in-house)

6. Open the isolation valve, close the release valve, and turn the vacuum pump on.

The pump remains running during experimentation. Set the desired pressure

using the bleed valve.

7. Open the resistive dump circuit switch.

8. Charge the Marx generator capacitors to 250V using the Sorensen XHR-300 DC

power supply.

9. Turn off the Sorensen XHR 300 DC power supply.

10. Charge the DES stages to the desired voltage using the two Sorensen XHR 600

DC power supplies wired in series.

11. Turn off the two Sorensen XHR 600 DC power supplies.

12. Charge stage-1 HV capacitor to the desired voltage using the HV power supply.

13. Turn off the HV power supply.

14. Open the Ross relay switch that isolates the HV power supply.

15. Check again to ensure all unauthorized personnel have exited the lab space.

16. Enter the screen room and close the door.

17. Run the DAQ system program that waits for a trigger signal.

18. Using a LOUD voice, yell “FIRING!!”

19. Turn on the NI CompactRIOs to initialize the control program stored in the Flash

memory which begins the firing sequence.

20. After the system fires, turn off the NI CompactRIOs.

21. Exit the screen room.

22. Close the resistive dump circuit switch.

23. Monitor the capacitor bank voltage gauges until zero volts are displayed.


125

24. Use a resistive “chicken stick” on all capacitors to ensure no remaining energy is

stored in the capacitor banks.

25. Turn off warning light.

26. Notify appropriate personnel the area is safe.

27. Enter screen room and save all collected data.

Fig. C.1. DES Railgun System Layout and Components.


126

PERMISSION TO COPY

In presenting this dissertation in partial fulfillment of the requirements for a

doctorate’s degree at Texas Tech University or Texas Tech University Health Sciences

Center, I agree that the Library and my major department shall make it freely available

for research purposes. Permission to copy this dissertation for scholarly purposes may be

granted by the Director of the Library or my major professor. It is understood that any

copying or publication of this dissertation for financial gain shall not be allowed without

my further written permission and that any user may be liable for copyright infringement.

Agree (Permission is granted.)

__________ Ryan W. Karhi___________ _____12/07/2010 ___

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