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FIR Center Report

FIR FU-102 February 2010

Design of a Compact Sub-Terahertz Gyrotron

for Spectroscopic Applications

S. Sabchevski and T. Idehara

Research Center for Development of

Far-Infrared RegionUniversity of Fukui

Bunkyo 3-9-1, Fukui 910-8507, Japan

Tel 81 776 27 8657

Fax 81 776 27 8770

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Design of a Compact Sub-Terahertz Gyrotron for Spectroscopic

Applications

S. Sabchevski1, 2

and T. Idehara1

1Research Center for Development of Far-Infrared Region, University of Fukui,

Fukui 910-8507, Japan2Institute of Electronics of the Bulgarian Academy of Sciences, Sofia 1784, Bulgaria

Abstract

In this paper we present the initial design of a novel and versatile high frequency gyrotron with

parameters suitable for application to various spectroscopic studies that require coherent

radiation in the subterahertz frequency range (such as NMR/DNP spectroscopy, ESRspectroscopy, spectrometer based on the X-ray detected magnetic resonance etc.). The most

characteristic feature of the design is that it utilises a compact, cryogen-free 8 T superconducting

magnet. As a result, the overall dimensions of the entire device are considerably reduced in

comparison with the previously developed tubes belonging to the Gyrotron FU and Gyrotron FU

CW series. This makes the novel gyrotron highly portable to diverse laboratory environments and

easily embeddable to different measuring systems. The electron-optical system (EOS) of the tube

is based on a compact low-voltage magnetron injection gun (MIG), which has been specially

designed and optimized together with the resonant cavity using our problem-oriented software

package GYRSIM for CAD of gyrotrons. The tube operates at the second harmonic of thecyclotron frequency and generates a radiation with an output power of about 100 W and a

frequency tunable up to around 424 GHz, respectively.

Key words: compact gyrotron, cryogen-free superconducting magnet, sub-terahertz

spectroscopy

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1. Introduction

As the most powerful sources of coherent radiation in the sub-terahertz and the terahertz

frequency range, the gyrotrons are being widely used in many fields of the fundamental physical

research and in the technologies [1,2]. Their notable applications include, but are not limited to:electron cyclotron resonant heating (ECRH) and electron cyclotron current drive (ECCD) of

magnetically confined plasma in the reactors for controlled thermonuclear fusion; processing of

advanced materials (ceramic sintering, welding, annealing, thermal treatment of semiconductors,

glasses and plastics, polymer coating and curring of adhesives and so on); communication and

radar systems. Among the recently emerged applications are also various types of high frequency

spectroscopy like electron spin resonance (ESR) or electron paramagnetic resonance (EPR)

spectroscopy and nuclear magnetic resonance (NMR) spectroscopy with enhancement of the

signal by a dynamic nuclear polarization (DNP/NMR) at high magnetic fields [3]. For the latter

applications a number of gyrotrons have been developed or are under development now in US[4-7], Russia [8-9], Switzerland [10,11], Germany, India [12] as well as at the FIR FU Research

Center in Japan [13-18].

Since the gyrotron used as a radiation source is only a part of the whole spectroscopic system

to which it must be integrated, its dimensions are a critical issue and influence the overall

arrangement and functionality of the equipment. It should be noted also, that besides being bulky

the gyrotrons that use conventional superconducting magnets are difficult to maintain and operate

due to the considerable time for preparation of the cryogenic system (filling with liquid helium

which is both expensive and difficult to handle). An appealing alternative, which can solve these

problems, is offered by the availability of compact cryogen-free (aka liquid helium-free) andcompact superconducting magnets based on the Gifford-McMahon (GM) closed cycle

refregerators. The use of such magnets simplyfies the operation of the radiation source

significantly and makes it attractive to wider comunity of researchers.

In this paper we present the initial design of a novel compact high frequency gyrotron

operating at the second harmonic of the cyclotron frequency and delivering a continuous wave of

a frequency around 424 GHz and output power about 100 W. The article is organised as follows.

First we formulate the targeted design goals and outline the main features of the conceptual

design. Then we depict the main components, namely the magnetic system, the electron-optical

system (EOS) and the resonant cavity and discuss the design choices (type and configuration ofthe magnetron injection gun, shape and dimension of the resonant cavity, selection of the

operating mode etc.). Finally we make some conclusions, evaluating the current design and

formulating some further tasks directed forwards the optimization of the device.

2. Goals and basic features of the design

The primary aim of this project is to develop a compact, sub-terahertz high performance gyrotron

which takes advantage of the beneficial properties of a 8 T liquid cryogen-free superconducting

magnet and is suitable for embedding as a powerful radiation source in various high frequencyspectroscopic systems. The main requirements regarding such sources are: (i) high stability of

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both the output power (at levels of several tens of Watt) and the frequency (typically of the order

of 10 ppm) in a CW mode of operation during long periods of time; (ii) frequency tunability in a

wide range (preferably of the order of 0.5 GHz); (iii) convenient output and transmission

system which delivers the radiation to the spectrometer in the form of a well collimated Gaussian

beam; (iv) ease of maintenance and operation.Bellow we present the results of an iterative process of a computer aided design (CAD)

performed using the problem oriented software package GYRSIM [20], developed at FIR FU and

used for study and optimization of the gyrotrons belonging to two series of devices, namely

Gyrotron FU and Gyrotron FU CW [2].

3. Magnetic system of the gyrotron

The main component of the magnetic system is a compact 8 T liquid cryogen-free (also called

cryo-cooled) superconducting magnet. Its basic dimensions are shown in Fig. 1 and itsspecification is given in the Table 1. It can be seen that it is indeed a table-top unit and has a

configuration which enables both simple installation and operation. Additionally the power

supply and the control system are characterized by small weight and dimensions too. Since there

is no liquid cooler around the coils the magnet can be installed not only vertically but in different

positions too. Other benefits of such magnet are low operating cost (no expenses for storage and

transport of liquid helium and nitrogen) and ease of use (no need for special safety measures and

training of the personal).

The main constraint imposed by the construction of the magnet which influences the overall

design of the tube is the inner bore diameter of 52 mm and length of 338 mm. It makes itnecessary to develop a very slim EOS which can be inserted inside the magnet.

Table 1. Specification of the superconducting magnet

Type 8T52, Liquid He-free conduction cooled (or,

cryo-cooled superconducting magnet

according to the recommendation of the

Cryogenic Association of Japan)

Wire material of the superconducting coils NbTi

Maximum central magnetic field 8 TOperating current of the magnet 72.2 A

Room temperature bore size 52 mm

Room temperature length of the bore 338 mm

The measured distribution of the magnetic field on the axis of the magnet at the nominal

excitation current (72.2 A) as well as the field profiles calculated by the COILS code (from

GIRSYM package) and POISSON/SUPERFISH code are shown in Fig.2. These data are used in

the numerical experiments for simulation of the EOS and the resonant cavity. For a fine tuning of

the magnetic field intensity in the region of the magnetron injection gun (MIG) a set of twoadditional coils is used together with the superconducting magnet.

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Fig. 1 Basic dimensions of the 8 T liquid helium-free superconducting magnet

Fig. 2 Magnetic field produced by the superconducting magnet

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4. Selection of the operating mode and design of the resonant cavity

Since the cyclotron frequencyc , that corresponds to the maximum field intensity 0B in the

cavity ( ][28][0TBGHzc ) produced by the magnet that has been described in the previous

section is about 224 GHz, it is clear that the maximum possible operating frequency f of the

gyrotron could be of the order of 224 sf GHz, where s is the harmonic number. Generally

speaking, for a high harmonic operation the concept of a large orbit gyrotron (LOG) [22,23],

which utilizes an axis encircling electron beam is much more advantageous than the conventional

gyrotron with a helical electron beam because it offers better mode selectivity and higher

harmonic numbers. The LOG however requires more sophisticated electron gun having a

non-adiabatic magnetic system with a reversal of the magnetic field (e.g. magnetic cusp) or

kicker. Seeking a simple and a compact design as well as taking into account the constrains

imposed by the magnet, in this project we selected a conventional type second harmonic ( 2s )

gyrotron.

The development of a gyrotron is usually an iterative process in which a compromise (i.e.

trade-off) between many contradicting requirements, design goals and constrains is sought out.

As a rule, it starts with a simple design rules based on the well known analytical and empirical

relations and is followed by a more detailed considerations based on the numerical experiments

carried out using the available simulation and CAD tools. Since such design considerations are

well known and described at length in the literature (see for example the most informative recent

monographs [24-26] and the references therein) here we will not discuss the design process and

intermediate iterations of the design loop, but rather will present the final results at which we

have arrived.

The mode that was selected as operating one, after a careful examination of the possible

candidates for the above mentioned frequency range is2TE82 (having an eigenvalue

11552.142,8 ) at second harmonic of the cyclotron frequency. The neighboring modes and

potential competitors are shown in Fig. 3. Here the values on the abscissa correspond to snm /, ,

where nm, is the eigenvalue of the mode TE with indices nm, or, in other words, the n -th zero

of the first derivative of the Bessel function )(xJm of orderm , and s is the harmonic number.

Therefore, snm /, can be referred to as a dimensionless magnetic field at the resonance. The

values on the ordinate are1,sm and correspond to the first maximum of the coupling

factor )]()/[()/( 222,2

mnmmncavbnmsmmn JmRRJC , where bR and cavR are the radius of the

beam and the cavity, respectively. The minus sign in the expression sm corresponds to a

coupling of the beam to a co-rotating mode while the plus sign corresponds to a counter-rotating

mode. Thus, the height of the bars that represent the spectral lines in Fig.3 can be considered as

the normalized (dimensionless) radius of the first maximum, which is given by the relation

cav

sm

smRR

,

1,1

max

, where cavR is the radius of the regular (central) part of the resonator. It is

customary to select an injection radius of the beam coinciding with the first maximum, i.e

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1

maxRRb . From Fig. 3 it follows that the closest potential competitor to the operating mode,

namely1TE02 at the fundamental of the cyclotron frequency is separated by less than 1 % with

respect to the magnetic field but about 30 % in respect with the optimal injection radius. This

observation suggests that the mode selectivity should relay on an accurate and precise control of

the position of the Larmor orbits of the electrons in the cavity. Below we will show that moreadequate considerations based on numerical simulations corroborate this possibility. It should be

noted however that such observation apply also to the other two satellite modes that could be

considered as potential competitors, notably2TE5,3 and

2TE12,1.

Fig. 3 Spectrum of the considered modes and position of the maximum of the coupling factor

The configuration and the dimensions of the resonant cavity, which has been optimized for asingle mode operation on

2TE8,2 at second harmonic is shown in Fig. 4. It consists of a regular

central section of length 20 mm and radius 1.588 mm and three tapered sections (one at the cavity

entrance and two down tapers after the interaction area of the resonator. The dispersion relation

for such cavity gives a cut-off frequency of 424.19 GHz. Also shown in Fig.4 is the longitudinal

profile of the amplitude of the electric field along the axis of the cavity, calculated by a

self-consistent single mode code. This field profile corresponds to a mode2TE82q with effective

axial index [14] 486.1q and operating frequency of 424.256 GHz at a magnetic field in the

resonator 0

B 7.76 T. Tracing an ensemble of particles in the self-consistent electromagnetic

field allows estimating the efficiency of the operation at different parameters. The highest

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efficiency of 19 % has been obtained in a numerical experiment with accelerating voltage

aU 15 kV, beam current bI 0.36 A, magnetic field 0B 7.76 T and output power of 100 W.

Fig. 4 Configuration of the resonant cavity a), and amplitude and phase of the field, b)

Another estimate of the conditions for excitation of the operating mode as well as of the

possible competing modes is given by the calculation of the starting currents, presented in Fig. 5.

They however are made for a shorter cavity with a length of the regular section cavL 12 mm.

The selection of the cavity length is a good example for a tradeoff between different

requirements. From the point of view of the starting current it is desirable to have a longer cavity.From another point of view however, the efficiency is expressed as DQQQ / , where

Q and DQ are the ohmic and the diffractive quality factor of the cavity respectively. From this

relation it is clear that in order to obtain high total efficiency we need

QQD . In a case of a

short-wavelength gyrotron it is more difficult to satisfy this requirement

because 222 / fLQ cavD , while fRQ cav / , where is the skin depth for a given

conducting material of the cavity wall at frequency f . In our design study the ohmic quality

factors, obtained for the conductivity of ideal copper 5.8x107

S/m and for the radius of the cavity

given above are estimated to be )( 2,8TEQ 10620 and )( 2,0TEQ 11050, respectively.

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Therefore, taking into account that 2)/( cavD LQ , the length of the cavity was reduced further

in order to satisfy the minimalistic design rule

QQD 2/1 . The other possibility for decreasing

the ohmic loses, namely increasing the radius of the resonant cavity is excluded from

consideration here as it makes the problem of mode competition more severe.

Fig. 5 Starting currents of the considered modes

It is well known that in the resonant cavities of the gyrotrons a variety of mode interactions can

take place, e.g. mode competition, mode cooperation, mode switching, multimode oscillation etc.

The literature on this topic is vast; see for example [27-31] and, especially the review paper [29]as well as the references therein. A single mode operation however is possible provided an

appropriate operating mode is chosen and, additionally, if both the beam and the cavity

parameters are tuned accordingly in order to insure excitation selectively only of this mode.

In this conceptual design study an analysis of the interaction between the selected operating

mode2TE8,2 and the neighboring modes possible competitors has been carried out using the

multimode time dependent code CS-MMTD from the GYRSIM software package [20]. The

results of the numerical experiments show that a stable single mode operation at2TE8,2 is feasible

for a range of appropriate electron beam parameters and values of the magnetic field. This is

illustrated in Fig. 6, where the time evolution of the modes is presented. Also shown in this figureis the bunching of the electrons. These illustrative results have been obtained at the following

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parameters: cavity radius cavR 1.5877 mm, cavity length cavL 10 mm, accelerating beam

voltage aU 15 kV, and detuning parameter 0.1, which corresponds to magnetic field

intensity in the cavity of 0

B 7.78 T. The efficiency of the operation and the levels of the output

power depend strongly on the velocity ratio (pitch factor) and the beam current. The results

presented in Fig. 6a) are for beam current of 0.15 A and velocity ratios ranging from 1.7 to

1.9, while these on Fig.6b) are obtained for beam current 0.2 A and between 1.5 and 1.7.

As a whole, the results of the multimode simulations suggest the feasibility of gyrotron operation

at output power levels around 100 W and electron efficiency around 10 % using a low voltage

and low current electron beam with an appropriate velocity ratio. In the next Section we consider

the design of the EOS which forms a helical electron beam with the desired parameters.

5. Design of the electron-optical system of the gyrotron

Since our pivotal design goal is the realization of a compact sub-terahertz gyrotron, not only the

dimensions of the tube had to be minimized but also the whole system, which includes the power

supply of the electron gun as well. This requirement, together with the considerations related to

the safety issues dictates a selection of low voltage and low current electron gun. As already

demonstrated, discussing the design of the resonant cavity, for excitation of the design mode by

an electron beam with energy of 15 keV, currents of the order of 200 mA are necessary, provided

the velocity ratio is in the range 1.5 to 1.7 and the radius of the beam is at the first maximum

of the electric field (which for the above discussed cavity is bR =0.84 mm). In principle it is

possible to use a simple diode type magnetron injection electron gun (MIG) for generation ofsuch beams. In a diode gun however one can control to some extent only the beam current and

the accelerating voltage. The triode MIG offers additional option to finely tune the beam

controlling the potential of the intermediate anode. For the gyrotron under consideration we have

developed a triode MIG in order to retain the possibility for flexible control of the electron beam

parameters but it is optimized in such a way as to provide the nominal (required) beam

parameters in a diode regime.

The CAD of the EOS has been carried out using the GUN-MIG/CUSP code of the GYRSIM

package [20]. It is based on a self-consistent fully relativistic physical model which takes into

account the space charge and initial velocities effects. As a starting point an existing MIGdeveloped previously for some other tubes of the Gyrotron FU series has been selected as a

prototype and scaled down (using the well known analytical relations [26,32-34]) in order to

produce the initial variant of the design. Then as a result of an a iterative design loop, performing

trajectory analysis (ray tracing) after each change of the configuration, positions and dimensions

of the electrodes (including the emitting ring) a system which produces an electron beam with

appropriate parameters has been selected. It is shown in Fig. 8 together with the electron

trajectories and the intensity of the magnetic field along the axis. Fig. 9 shows the projection of

the central particle orbit of the helical electron beam on the transverse X-Y plane. The inclination

of the emitter on the cathode cone is 17.22o

, which (for the selected configuration) produces alaminar electron beam as shown in Fig.8.

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Fig 7 a) Time evolution of the output power and the efficiency of the traced modes: beam currentof 0.15 A and velocity ratios ranging from 1.7 to 1.9

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Fig 7 b) Time evolution of the output power and the efficiency of the traced modes: beam currentof 0.20 A and velocity ratios ranging from 1.5 to 1.7

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Fig. 8 Configuration of the magnetron injection gun, magnetic field profile and trajectories of the

electron beam

Fig.9 Projection of the central orbit of the beam on the transverse XY plane

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This illustrative example has been obtained for beam current of 0.200 mA, and potentials of the

first and the second anode equal to 14 and 15 kV, respectively. In this case the magnetic field in

the center of the emitting strip has been set to 0.378 T, and was produced by the main solenoid

only, i.e. with the current of the additional coils switched off. In a real operation however it is

possible to finely adjust the magnetic field on the cathode controlling the current of the twoadditional coils envisaged by our design. In particular, one can tune the field of the additional

coils in order to keep constant the pitch factor during the changes of the anode potential.

Similarly, at constant beam voltage one can tune precisely the velocity ratio by changing the

current of the additional solenoids simultaneously with the changes of the field of the main

magnet. Such relations, that characterize the electron-optical performance of the gun and suggest

an optimal set of operational parameters have been obtained in the conducted numerical

experiments, but will be presented elsewhere. It suffices to mention here only that in the

simulations, pitch factors as high as 2.0 have been obtained without reflection of the beam

electrons. Other important parameter which characterizes the quality of the beam is the transversevelocity spread, which in this simulation was found to be of the order of about 5.5 %. Although

the current design of the gun meets the target requirements it seems that there are some

possibilities for its improvement. We intend to introduce such optimization during the next step

of the development which will combine this initial conceptual design with the engineering and

technological design of the tube. For example, since using advanced emitting materials it is

possible to extract the necessary beam current even from a narrower emitting ring on the cathode

it is feasible to reduce further the spread of the velocities and the pitch factor. It should be

mentioned that as usual for the MIG, the cathode works in a temperature limited regime of the

emission, and thus it could be controlled changing the current of the heating filament. Otherimportant design goals are minimization of the influence of the magnetic field of the heather

(using a bifilar filament), ensuring a homogenous heating of the emitter and uniform emission

and last but not least minimization of the changes and misalignment of the electrodes due to

thermal expansion/contraction during the operation of the gyrotron. These tasks are also

envisaged for the next stage of the design process.

The main characteristics of the EOS are summarized in the Table 2.

6. Conclusions

In this paper we presented the design of a novel prospective member of the Gyrotron FU CW

Series. It is a compact sub-terahertz tube with a 8 T liquid helium-free superconducting magnet

and operates on the2TE8,2 mode at the second harmonic of the cyclotron frequency. The output

power is of the order of 80-100 W in a CW regime at frequency about 424 GHz. Its parameters

and functional characteristics (small weight and dimensions, portability) are suitable for various

existing and newly emerging high-frequency spectroscopic systems. It utilizes a new compact

and simple triode MIG developed and optimized specially for this gyrotron. The overall design

was carried out using our problem oriented software package for CAD and simulation of

gyrotrons GYRSIM.

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Table 2. Specification of the EOS design

Type Triode MIG

Max. accelerating voltage

Relativistic Lorentz factor

15 kV

1.0294Beam current 200-220 mA

Maximum beam power 3.3 kW

Cathode loading 1 A/cm2

Maximum electric field at the cathode 5 kV/mm

Angle of the emitter (cathode cone) 17.22o

Mean radius of the emitting ring 3.8 mm

Mean beam radius in the cavity 0.84 mm

Mean Larmor radius of electron orbits in the cavity 0.0452 mm

Magnetic field in the middle of the emitter 0.378 T

Magnetic compression ratio 20.7

Distance between the middle of the emitter and the magnets center 22 cm

Parameters of the water-cooled copper additional coils

Maximum excitation current

Inner and outer diameter and length

300 A

200, 326 and 54 mm

Velocity ratio (pitch factor) 2.0

Velocity spreadvv / 5.5 %

In the present design, the radiation is emitted axially from a waveguide terminated by a boron

nitride (BN) output window. For the spectroscopic applications however, a Gaussian beam is

needed. Therefore an internal mode converter is considered as the most appropriate solution.

Currently we are working on several modules for calculation of quasi-optical systems that are

intended to be included in the GYRSIM package. They will be used on the final stage of the

design for CAD of the elements (the launcher and the system of reflectors) of the mode converter

and the low-loss transmission line which delivers the radiation to the irradiated sample of the

spectrometer.

As already underlined, the frequency tunability is absolutely essential for the spectroscopic

applications. A comprehensive review of the methods for frequency control is given in [14]. One

of them is based on the excitation of high order axial modes ( )1q and continuous variation of

the axial index q of the operating mode TEm,n,q changing appropriately the parameters of the

electron beam and magnetic field in the cavity resonator. The current design envisages the same

approach. A detail analysis of the tunability of the gyrotron under development is in progress now

and its results will be reported elsewhere.

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Acknowledgements

This work has been carried out in the framework of the longstanding collaboration,

Memorandum of Understanding and Agreement for Scientific Exchange between the Institute

of Electronics of the Bulgarian Academy of Sciences (IE-BAS) and the Research Center for

Development of the Far-Infrared Region (FIR FU) at the University of Fukui and was supported

by a Special Fund for Education and Research from the Ministry of Education, Culture, Sports,

Science and Technology (MEXT) and Project Allocation Fund of the University of Fukui.

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