Campaign for Levitation in LDX

D.T. Garnier, M.E. Mauel, A.K. Hansen, E.E. Ortiz

Columbia University

A. Boxer, J. Ellsworth, I. Karim, J. Kesner, P. Michael, A. Radovinsky, A. Zhukovsky,

R. Bergmann - MIT PSFC

Columbia University

Synopsis

Levitation will greatly change plasma behavior in LDX

Dominant loss channel removed -> better confinement

Higher background density with high beta -> more stable to HEI

Radial transport dominated (broader) profile -> more stable

Levitation system nearly complete

Coil and control systems installation complete

Calibration and control algorithm development underway

Laser detection system nearly complete and undergoing refinement

Catcher system built and tested

Levitation system testing in progress

3 major tests completed give confidence in successful levitation

Integration of L-coil systems

Development of Realtime control system

Test of L-coil electrical and thermal performance

Development of Laser Detection System

Plasma "Noise" test

Launcher Catcher Upgrade

Catcher Test Campaign

Feedback Control Algorithm

Flight Tests

Levitation Campaign Milestones

Bulk plasma must satisfy MHD adiabaticity condition

Fast electron stability enhanced due to coupling of fast electrons to background ions

Hot Electron Interchange Stability

Krall (1966), Berk (1976)...

Rosenbluth and Longmire, (1957)

δ�

pb V γ�= 0

−

d ln pb

d ln V<γ−1

V =∮

d �B

whereor

−

d ln n̄ h

d ln V< 1+

m 2⊥

24

ωd h

ωc i

n̄ i

n̄ h

Increased Neutral Fueling Stabilizes HEI

Stabilizes small HEI

More background density

Smaller hot electron fraction

But loss of confinement

Pitch angle scattering to supports.

Levitation changes

Pitch angle scattering gives more isotropic distribution

Collisions lead to broader radial profile

Higher overall confinement

Low frequency modes reduced?

-10123456

kW

Heating Power (total)6.4 GHz 2.45 GHz

-1012345

kAm

ps

Plasma Current

0.6

0.8

1.0

1.2

m

Current Centroid

-202468

a.u.

Visible Intensity

-202468

10

a.u.

X-Ray Intensity

01234

1010

cm

-3 Edge Density

0 2 4 6 8Time(sec)

0102030405060

10-7 T

orr Neutral Pressure

LDX Levitation Basics

2 m

Levitation by upper lift magnet

Unstable only to vertical motion

Mostly undamped stable secondary modes

HTS lift magnet

First in US Fusion program

Much reduced power and cooling requirements

AC heating introduces unique requirements for control system

Large 5 m diameter vacuum vessel

Eddy current times << levitation times

Laser position detection

Many secondary diagnostics

Digital feedback system

L-coil

F-coil

L-Coil Design

High Temperature Superconductor.

Negligibly power consumption compared to resistive equivalent.

Nominal 105 A current, with ± 1 A, 1 Hz position control ripple.

Easier to manage position control ac loss than for LTS.

Funded by SBIR, first HTS coil in US fusion energy program.

Optimized, disk-shape geometry for F-coil levitation.

Double pancake winding.

Center support and cooling plate.

Conduction cooled coil.

Low maintenance, moderate cost,

high conductor performance.

Estimated 12 W hysteresis loss.

One-stage cryocooler for coil.

20W @ 20K

Liquid nitrogen reservoir

for radiation shield.

L-coil Heating Stress Test

Steady State Test

90-min, 1Hz, ±1-A ripple with 105-Adc bias test performed on Apr. 5, 2006

Demonstrates the thermal stability of HTS coil in expected levitation operation

Well below theoretical quench point

at ~40 K

Sub-cooling demonstrated

Evacuation of LN2 reservoir to 500 Torr.

Gives greater operational margin at warm end of HTS leads

L-coil Heating Model

Semi-empirical model estimates the steady-state temperature rise at the L-coil during electrical excitation

over the range from 0-A dc to 105-A dc bias current

ac excitation at frequency from -Hz to 2-Hz

AC ripple 0-Vac and 20-Vac.

accurate to within approximately 0.2-K over the entire fitting range.

17.0

17.5

18.0

18.5

19.0

19.5

20.0

20.5

0 0.5 1 1.5 2 2.5

Frequency [Hz]

Te

mp

era

ture

[K

]

CR, meas. 50Adc bias

UP, meas, 50Adc bias

LP, meas. 50Adc bias

CR, fit 50Adc bias

UP, fit 50Adc bias

LP, fit 50Adc bias

CR, meas. 95Adc bias

UP, meas. 95Adc bias

LP, meas. 95Adc bias

CR, fit 95Adc bias

UP, fit 95Adc bias

LP, fit 95Adc bias

17.0

17.5

18.0

18.5

19.0

19.5

20.0

20.5

0 5 10 15 20 25

1 Hz, AC voltage [V]

Tem

pera

ture

[K

]CR, meas. 50Adc bias

UP, meas. 50Adc bias

LP, meas. 50Adc bias

CR, fit 50Adc bias

UP, fit 50Adc bias

LP, fit 50Adc bias

CR, meas. 105Adc bias

UP, meas. 105Adc bias

LP, meas. 105Adc bias

CR, fit 105Adc bias

UP, fit 105Adc bias

LP, fit 105Adc bias

L-coil Electrical Model

Semi-empirical fitted model

Takes into account known short and eddy currents in L-coil

Also models vacuum vessel eddy currents

Parameters matched to electrical open loop gain tests

(0.000989(s + 0.339)(s + 25.2)

(s + 0.008)(s + 0.4)(s + 0.654)(s + 22.4)

)Transfer function

L-coil System Model Comparison to Data

10 20 30 40 50t

2

4

6

8

10

v PS Voltage

10 20 30 40 50t

-8

-6

-4

-2

2

A Currents: �Il � I0� & Ip�100

10 20 30 40 50t

0.92

0.94

0.96

0.98

Actual & Vac Fields

10 20 30 40 50t

-0.0075

-0.005

-0.0025

0.0025

0.005

0.0075

Loop Flux

0

2

4

6

8

10

12 PS Voltage S5741

94

96

98

100

102

104

106 PS Current

-10

-8

-6

-4

-2

0

2 Flux (mV s)

-0.02

0.00

0.02

0.04

0.06 Mag5p (G)

0 10 20 30 40time (s)

-1.5-1.0-0.50.00.51.01.5 Loop LFlux (V)

LDX Control System Description

150A, +/- 100V Power Supply

Integrated dump resistor for rapid discharge

Realtime digital control computer

Matlab/Simulink Opal-RT development environment

4 kHz feedback loop

Failsafe backup for upper fault

Programmable Logic Controller

Slow fault conditions

Vacuum & Cryogenic monitoring

PS user interface

Optical link to control room

User interface

LDX data system

Levitation Control System

Levitation Control System Schematic

Laser Alignment Ring

Ring placed on floating coil to occult laser beams

Horizontal lasers pass through small ports (4 of 8 shown here)

Alternating bands of specular reflective silver and rough stainless steel to allow rotation monitoring

Optical Position Detection System

Position/Attitude Sensing

Occulting system of 8 beams

Provides measurement of 5 degrees of freedom

of coil with redundancy in each measurement

Specification

± 1 cm detection range

5 m resolution

5 kHz frequency response

Keyence LH-300 COTS units

Exceed all specifications

Procured with 2 channels installed on prototype

mounting hardware

• Require plasma test for final mount production OK

Rotation Sensing

Reflecting system to sense final degree of freedom

Remove Nonaxisymmetry systematic noise correction

Laser Position Detector Testing

Prototype mounting and amplifiers in place for July 2006 plasma run

RF electrical pickup noise measured

Plasma light not important

Vibration somewhat important

Measured motion of F-coil on stiff spring of fixed launcher

Further development since

Better vibration immunity (higher frequency)

Reduced electrical noise

Supported F-coil Motion

Observed motion of F-coil due to L-coil interaction

F-coil supported (with stiff spring)

motion smaller than nominal resolution of detectors

0

2

4

6

8

10

mic

rons

L-coil DC

0

2

4

6

8

10

mic

rons

L-coil DC + 1 AAC at 0.3 Hz

0

2

4

6

8

10

mic

rons

L-coil DC + 1 AAC at 0.5 Hz

0.1 1.0 10.0 100.0 1000.0Freq (Hz)

0

2

4

6

8

10m

icro

ns

L-coil DC + 1 AAC at 1.0 Hz

7778

79

80

8182

Am

ps

L-coil Current

8.988.99

9.00

9.01

9.029.03

mm

Vertical Position

2 4 6 8 10 12Time (sec)

3.9153.920

3.925

3.930

3.9353.940

kN

Upper Launcher Cable Stress

Improved noise isolation

Steady development of mount hardware has reduced noise in system.

Reduced electrical noise at 200 Hz with better cabling

Removing rubber mounts increased vibrational mode frequencies

0

2

4

6

8

10

mic

rons

Vertical Laser

0.1 1.0 10.0 100.0 1000.0Freq (Hz)

0

2

4

6

8

10

mic

rons

Horizontal Laser

0

2

4

6

8

10

mic

rons

Vertical Laser

0.1 1.0 10.0 100.0 1000.0Freq (Hz)

0

2

4

6

8

10

mic

rons

Horizontal Laser

July October

Upper Catcher / Space frame

Upper catcher

Limit upward motion

Align radial motion for fall to catcher

Space frame structure

Allows installation of new internal magnetic flux loops near plasma

Generation II Catcher

New catcher constructed and tested

Lightweight cone to minimize impulse on F-coil contact

Partial F-coil deceleration while launcher mass accelerates

Limit all accelerations to less than 5 g

Catcher Drop Test

Accurately test catcher outside of vacuum vessel

Uses “practice” f-coil made from lead bricks

Results

Works as expected with no deformation of f-coil ring

Dodge Ram Springs

Lead bricks in test shell

Spinniker sheet quick release

Low stretch Spectra line

Free flight

Catcher Worst Case ~ 5g

-10

-505

10

(g)

F-coil Acceleration

-10

-505

10

(g)

Catcher Acceleration

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2Time (sec)

-10-505

10

(g)

Post Acceleration

Free flight after bounce

Drop Test Results

F-coil acceleration in acceptable range

~ 5g

Small (and expected) plastic deformation of lightweight cone

~ 3 mm

future drops will be elastic

Installation imminent

Levitation Physics

x

y

z

L-coil

F-coil

Fgrav

Fmag

We can choose a Lagrangian formulation of the equation of motion so the constraints above can be easily incorporated:

L = 12 mi

˙ x i2

i=1

6

MLFIFIL12 LFIF

2 12 LLIL

2mgz

F-coil is a superconducting loop, so its flux is conserved, whereas we can vary the flux in the L-coil by applying our control voltage:

F = MLFIFIL + LFIF = constant

L = MLFIFIL + LLIL = VL( t)dt

MLF = MLF (r x 1 5)Where:

And:

Feedback stabilization

IL (t )= I0 a0 (t)dt a1 (t) a2 ' (t)

Automatic correction to I0 Damping term, acts like friction

The upward force on the F-coil is proportional to the radial magnetic field at

its position, generated by the L-coil.

Hence, it is proportional to the current in the L-coil.

Without feedback, the vertical position is unstable because dBR/dz>0, so if

the F-coil moves up, the upward electromagnetic force will increase, and the

coil will move even further up.

If we detect a small increase in vertical position, and decrease the L-coil

current appropriately, we can bring the coil back to its original position.

Simple Approach: Use proportional-integral-derivative (PID) feedback:

Control System Development

Integrated test results

System identification to ensure observed behavior

matches system model

Identification of model parameters

Formal check of observability and controllability

Optimal Control Theory

Optimal control with balance of minimization of

noise and L-coil heating explicitly

Ensure control system won’t add noise to stable

modes

Further state machine testing

Output PointInput Point

In1 Out1

Floating Coil Dynamics

F-coil state measurementcoil voltage output

Feedback System

LCX II: Digitally Controlled Levitation

Levitated Cheerio Experiment II

Uses LDX digital control systemLCX I was analog demonstration

Modified PID feedback systemLow pass filter added for high frequency roll-off of derivative gain

Integral reset feature for launch transition

Dynamic model block replaced by I/O and estimators

Real-time graph shows position and control voltage

Wiggles indicate non-linearly stable rolling mode…

Noise reduction necessary

Noise reduction necessary for derivative gains

Multipole filter noise reduction limited due to added phase delay

2 4 6 8 10

-0.04

-0.02

0.02

0.04z�t� with Single�Pole Filters

2 4 6 8 10

103

104

105

I�t�

Kalman Filter Simulation

Kalman filter can be used to reduce noise with minimal latency

Uses a physics based predictor that tracks the real motion and is updated with every time step

2 4 6 8 10

-0.1

0.1

0.2

0.3

0.4

Actual F�Coil z�t�

2 4 6 8 10

-0.1

0.1

0.2

0.3

0.4

Meas & State F�Coil z

2 4 6 8 10

-15

-10

-5

Volt�t�

2 4 6 8 10

103.2

103.4

103.6

103.8

L�Coil Current

Kalman Filter Reduces L-coil AC Losses

Kalman filter results

Improved filter greatly reduces noise in system

Reduced noise leads to reduced AC heating of L-coil

Kalman filter with simple feedback sufficient

Simulations show this method should meet our requirements for stable levitation

2 4 6 8 10Hz

0.01

0.02

0.03

0.04

0.05�I�2L�Coil Current Power Spectrum

2 4 6 8 10Hz

0.25

0.5

0.75

1

1.25

1.5

1.75

2�I�2L�Coil Current Power Spectrum

Single Pole Filter

Kalman Filter

2006 Levitation Test Program

System integration test

Test inter-operation of cryogenic and two control systems

L-coil Integrated Performance Test

Test L-coil cryogenic performance under worst-case operation point

Also gather data to determine HTS coil quench detection algorithm

Calibrate “transfer function” of L-coil System

Integrated System Plasma Test

Characterize noise on levitation diagnostics in plasma environment

Operate L-coil systems at 1/2 current with plasma present

Calibrate system using measured lift forces

Catcher Drop Test

Operated successfully from worst-case scenario

Measured acceleration in acceptable range

Levitation Test Next

Alternative Levitation System

Greatly simplified

Reduced cost

Easily manufactured

numerous local vendors: Starbucks, Dunkin’ Donuts, etc.

Implementation likely to be “challenging”