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Tunable coaxial gyrotronfor plasma heating anddiagnosticsO. DUMBRAJS & A. MOBIUSPublished online: 10 Nov 2010.

To cite this article: O. DUMBRAJS & A. MOBIUS (1998) Tunable coaxial gyrotronfor plasma heating and diagnostics, International Journal of Electronics, 84:4,411-419, DOI: 10.1080/002072198134751

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INT. J. ELECTRONICS, 1998, VOL. 84, NO. 4, 411± 419

Tunable coaxial gyrotron for plasma heating and diagnostics

O. DUMBRAJS² and A. MOÈ BIUS³

The possibility of tuning the frequency of a coaxial gyrotron by moving the innerconductor in the axial direction is investigated. A 1.5 MW coaxial gyrotron at140 GHz with the TE28,16 operating mode is considered as an example.

1. Introduction

Frequency tunable gyrotrons can be useful for both plasma heating and diag-nostics. The frequency tuning of a gyrotron can be accomplished in several ways. Ithas been shown theoretically (Dumbrajs and Nusinovich 1992) that the frequency ofa high-power gyrotron can be changed very fast (in microseconds) in steps of a fewgigahertz by changing the accelerating and modulation voltages. This requires a verysophisticated power supply. This method of frequency tuning has been demonstratedexperimentally (Idehara et al. 1994), albeit for a low-power gyrotron. Another wayof tuning the gyrotron frequency is to change the magnetic ® eld. In an experiment(Piosczyk et al. 1996) it was demonstrated that in this way it was possible to step-tune a high-power coaxial gyrotron between 116 and 164 GHz. Unfortunately, dueto the large inertia of the magnetic ® eld, this process may take several minutes. Muchfaster tuning should be possible in a smaller frequency range of a few gigahertz bykeeping the main magnetic ® eld constant and varying only the additional magnetic® eld produced by an extra small solenoid.

As long as the cavity geometry is not changed during operation the tuning ispossible only in discrete steps with the step size determined by the di� erence betweenthe eigenvalues of the modes. However, one can imagine applications for which afrequency continuum from a gyrotron would be bene® cial. For example, ® ne tuningwould be useful to follow drifts of the power deposition spot caused by smallchanges of the toroidal ® eld of the fusion device. Sometimes changes of the strongtoroidal magnetic ® eld in¯ uence the magnetic ® eld at the cavity of the gyrotron itself.In such a situation it would be useful to have the possibility of correcting thefrequency of the gyrotron in order to restore its high e� ciency. In the case ofexperiments on collective Thompson scattering the frequency of several gyrotronsshould match the frequency of the notch ® lter which suppresses the stray radiation.Fine tuning of the gyrotron frequencies may be useful also in this case.

So far there has been an approach of Brand (1985) to make a gyrotron continu-ously tunable by cutting the cavity into two half conical cylinders that can be movedin a transverse direction. Due to the break of azimuthal symmetry this leads toazimuthally standing modes. The gap leads to a leakage of radiation. These twodisadvantages limit the tube to low-power operation in the range below 1 kW.

0020± 7217/98 $12.00 Ñ 1998 Taylor & Francis Ltd.

Received 22 October 1996; accepted 16 June 1997.² Department of Technical Physics, Helsinki University of Technology, FIN-02150 Espoo,

Finland. E-mail: olgierd.dumbrajs@hut. ® .³ Innovative Microwave Technology GmbH, Luisenstrasse 23, D-76344 Eggenstein,

Germany. E-mail: arnold@itpgyrol.fzk.de.

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In this paper the idea of making a gyrotron continuously tunable by integratingan axially movable tapered inner conductor into a coaxial cavity is investigated. Anaxial displacement of the inner conductor leads to a continuous change of theeigenvalue of the mode. This idea was ® rst applied to an industrial gyrotron(Dumbrajs et al. 1995). In the present work we consider high-power gyrotrons.We limit our study to the cavity behaviour. The impact on the behaviour of micro-wave components following the cavity, such as the taper, the converter and thewindow has not been studied here. We also do not discuss technical realizations ofmoving the inner conductor.

Coaxial cavities are also used in mode excitation units (Alexandrov et al. 1995,Pereyaslavets et al. 1997). For these units the principle of moving the inner con-ductor to tune the frequency and to modify the quality factor can be applied.However, we will not elaborate this point in detail.

2. Theoretical background

While mode selection in gyrotrons by means of radial electron beam displace-ment and tuning of the external magnetic ® eld or the accelerating voltage is wellestablished, the in¯ uence of the inner conductor, with or without axial grooves, onmode selection has been discussed only in a relatively small number of papers. Anexcellent discussion can be found in the paper of Iatrou et al. (1996).

To establish a particular volume mode, the inner conductor is chosen such that itonly weakly perturbs the electromagnetic ® eld. As the radius of the conductor grows,its in¯ uence on the eigenvalue of the mode remains weak until the radius belongingto the ® rst zero of the azimuthal electric ® eld of the mode is reached. Independent ofthe depth of the grooves, the change in the eigenvalue increases rapidly as the radiusof the inner conductor is enlarged further. This is becauseÐ at least for a smoothinner conductorÐ the eigenvalue of a cavity with the radius of its inner conductorcoinciding with the radius of the ® rst zero of the azimuthal component is the same asthat of the unperturbed waveguide. As described by Iatrou et al. (1996), this is notquite true for a grooved inner conductor, but the di� erence in eigenvalue will be low.As the inner conductor keeps increasing, the ® eld will be squeezed, leading to astrong increase in eigenvalue and ohmic losses on the conductor. For a taperedinner conductor, depending on the sign of the slope, the cavity quality factorincreases or decreases with growing radius of the inner conductor. In the case ofdecreasing quality factor for the strongly increased radius of the inner conductor thisdecrease will be so strong that the quality factor will come close to its minimum valueand hence the cold cavity approximation will no longer be acceptable. For gyrotronsan enlargement of the inner conductor to such values will be unreasonable, since formost practical gyrotron designs it already will be larger than the radius of theelectron beam. This might be di� erent for mode generators where these two aspectsdo not play any role.

3. Calculations

To illustrate our ideas we have taken the parameters of the cavity (see ® gure 1) ofthe German± Russian gyrotron (Flyagin et al. 1994). The output power of this gyro-tron is Pout = 1.5 MW, and the operating mode is TE28,16 at frequencyF = 139.974 GHz. The only di� erence between the original cavity and our model

412 O. Dumbrajs and A. MoÈ biusD

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Tunable coaxial gyrotron 413

Fig

ure

1.G

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cav

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.8m

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,L1

=10

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,L2

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,L3

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,µ1c

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=-0

.5ë,µ

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.5ë,µ

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cavity is the inner conductor. The neighbouring TE31,15 mode has a central frequencyof 140.87 GHz which is about 1GHz higher than the resonant frequency of thedesign mode. To have a continuously tunable gyrotron the tuning range for thedesign mode has to be 1 GHz.

Note that the angle of the taper of the inner conductor is negative, i.e. for thechosen depth of the grooves the radius of the insert decreases along the axis, whichhas the consequence that the quality factor decreases as the radius and hence theresonant frequency grows. The larger the taper angle chosen the stronger the decayin quality factor for the same change in frequency. To be able to cover a largefrequency range, with the quality factor remaining considerably larger than theminimum value for the entire range, a small taper angle would be desirable. This,however, must be balanced against the desire to keep the inner conductor as well asthe path of axial displacement reasonably short. Our study is limited to a lineartaper. Hence, the length of the axial displacement can simply be determined bythe product of the variation of the radius with the tangent of the angle. A goodcompromise between the two requirements is a taper angle of - 0.5ë . To achieve afrequency tuning range up to 1GHz for the operating TE-

26,18 mode the axial dis-placement length has to be twice the length of the cavity, leading to an overall lengthof the inner conductor of three times the cavity length.

It is well known (Iatrou et al. 1996) that in a coaxial cavity the eigenvalue c mp ofthe TEmp mode can be determined from the equation:

[NÂm( c mp

C ) + WNm( c mp

C ) ]J Âm( c mp) - [J Âm( c mp

C ) + WJm( c mp

C ) ]NÂm( c mp) = 0

where Jm and Nm are, respectively, Bessel functions of the ® rst and second kinds withprimes denoting di� erentiation with respect to the argument, C = Rcav /Rin, and W isa parameter characterizing impedance of the corrugated insert.

414 O. Dumbrajs and A. MoÈ bius

Figure 2. Eigenvalues of the modes listed in Table 1 as a function of the ratio C = Rcav /Rin.Here I, II, and III mark those mean values of C which correspond to segments I, II,and III marked in ® gure 1.

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In ® gure 2 we show eigenvalues of all the relevant modes as a function of C,where W = 10. In table 1 we list the corresponding frequencies and quality factors.Figure 1 depicts the cavity and the inner conductor. The radius Rin is de® ned to bethe radius of the inner conductor at the cavity entrance when the correspondingsection is moved into the cavity. Figures 3 and 4 show respectively the variation ofthe resonant frequency and the quality factor as the radius of the inner conductorgrows due to its axial displacement. Three modes of the entire mode chart have beenconsidered. As desired, for the design mode TE28,16 the 1GHz tuning range is almostachieved. This is di� erent for the other two modes which is due to the strongperturbation of the TE26,27 mode and the extremely weak perturbation of theTE31,15 mode caused by the inner conductor. In ® gure 5 we show ohmic losses onthe inner conductor. Figure 6 shows the mode chart for the case when segment I ofthe inner conductor is inside the cavity. Figure 7 shows starting currents for case IIwhich corresponds to having the inner conductor axially displaced by one cavitylength. As one can see, the design mode can still be reached, with some of theneighbouring modes almost disappearing. The situation arising after the displace-ment of the inner conductor by two cavity lengths, i.e. having segment III inside thecavity, is shown in ® gure 8. The starting currents all have increased since the quality

Tunable coaxial gyrotron 415

No. Mode FI (GHz) QI FII (GHz) QII FIII (GHz) QIII

1 TE-29,16 142.07 2622 142.18 2090 142.68 1299

2 TE-31,15 140.87 2678 140.89 2590 141.00 2052

3 TE+26,17 141.23 1785 141.91 1080

4 TE-28,16 139.98 2473 140.16 1800 140.83 1105

5 TE-30,15 138.80 2609 138.82 2454 139.00 1817

6 TE+25,17 139.23 1488 140.12 915

7 TE-27,16 137.90 2275 138.18 1525 139.03 964

Table 1. Frequencies and quality factors.

Figure 3. Frequency of the selected modes as a function of the radius of the inner conductorat the cavity entrance.

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factor is lowered for all modes. Here in all calculations the external magnetic ® eldhas been optimized for the design mode.

Here it should be emphasized that calculations performed in the single modeapproximation predict, for the operating TE28,16 mode, an e� ciency h = 40%(Bopt = 5.64 T) for case I, h = 37% (Bopt = 5.67 T) for case II, and h = 27%(Bopt = 5.725 T) for case III, for V = 90 kV, a = 1.3, and Rel = 10.1 mm.

Regarding these charts and seeing the number of competing modes reduced asthe inner conductor radius grows, the question may arise whether additional modes,

416 O. Dumbrajs and A. MoÈ bius

Figure 4. Quality factors of selected modes as a function of the radius of the inner conductorat the cavity entrance.

Figure 5. Ohmic losses in the inner conductor as a function of the radius of the inner con-ductor at the cavity entrance. Here Pout = 1.5 MW.

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that have not played a role for the parameters corresponding to ® gure 6, may for theparameters corresponding to ® gures 7 and 8 become of importance. The answer isno, as long the electron beam radius does not considerably change its size. Of course,there are several modes that have not been considered and that have resonant frequen-cies even closer to the design mode than the modes considered. However, since theydo not e� ectively couple to the electron beam, they will not compete. Anotherquestion is whether in cases II and III it will be possible to operate at voltages as

Tunable coaxial gyrotron 417

Figure 6. Starting currents of the modes listed in table 1 as a function of the acceleratingvoltage in the case when segment I of the inner conductor is inside the cavity. Here B = 5.64 T.

Figure 7. Starting currents of the modes listed in table 1 as a function of the acceleratingvoltage in the case when segment II of the inner conductor is inside the cavity. HereB = 5.67 T.

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high as 90 kV without exciting the parasitic modes TE25,17 or TE27,16 . All this can bechecked only be means of calculations performed on the basis of the non-stationarymultimode formalism. Such a study is beyond the scope of the present work.

4. Mode excitation units

When designing a cold test mode generator the cold cavity calculation for theresonant frequency and the quality factor are the same as for gyrotrons, however, themode selectivity by means of an electron beam does not exist. Here the modes areselected by the proper design of the caustic mirror, leading to a given phase variationalong the caustic of the mode. However, it should be emphasized that for the designof a mode generator more modes have to be taken into account than for the designof a cavity for a gyrotron. As shown in ® gure 5, the ohmic losses strongly rise as theinner conductor exceeds a given radius. However, this is irrelevant if the proposedtuning is used for testing mode exciters.

For a prototype already built (Pereyaslavets et al. 1997) one problem was thatdespite the high quality of the fabrication neither the resonant frequency nor has thequality factor has been exactly hit. For the quality factor the discrepancy betweendesign and experiment was large which led to a poor coupling e� ciency. Again theaxial displacement of the inner conductor can help to overcome these problems.

5. Conclusions

We have shown that by using a - 0.5ë tapered 240 mm long insert it should bepossible to vary the frequency of the operating TE28,16 mode continuously between

418 O. Dumbrajs and A. MoÈ bius

Figure 8. Starting currents of the modes listed in table 1 as a function of the acceleratingvoltage in the case when segment III of the inner conductor is inside the cavity. HereB = 5.725 T.

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139.98 GHz and 140.83 GHz. Such a possibility could be useful for various applica-tions mentioned in the Introduction. It should be emphasized, however, that wediscussed in detail only the operation in the TE28,16 mode. One can envisage also acombination of step-tunability by jumping from one mode to the other by changingthe magnetic ® eld and ® ne tuning of the respective operating mode by moving theinner conductor. Here our calculations for the design mode have to be repeated forall other modes.

ACKNOWLEDGMENTS

This work was supported by the European Community as part of the EuropeanFusion Technology Programme under the auspices of the Fusion Project at theHelsinki University of Technology. We express our gratitude to Ch.T. Iatrou forvaluable discussions.

References

Alexandrov, N. L., Denisov, G. G., Tran, M. Q., and Whaley, D. R., 1995, InternationalJournal of Electronics, 79, 215.

Brand, G. F., 1985, Infrared and Millimeter Waves, 14, 371.Dumbrajs, O., Moï bius, A., and Muï hleisen, M., 1995, Design study of a tunable coaxial

gyrotron. Digest of the 20th International Conference on Infrared and MillimeterWaves, Orlando, Florida, USA, 11± 14 December 1995, p. 419.

Dumbrajs, O., and Nusinovich, G. S., 1992, IEEE Transactions on Plasma Science, 20, 452.Flyagin, V. A., Khizhnyak, V. I., Manuilov, V. N., Pavelyev, A. B., Pavelyev, V. G.,

Piosczyk, B., Dammertz , G., Hoï chtl, O., Iatrou, C., Kern, S., Nickel, H.-U.,Thumm, M., Wien, A., and Dumbrajs, O., 1994, Development of a 1.5 MW coaxialgyrotron at 140 GHz. Digest of the 19th International Conference on Infrared andMillimeter Waves, Sendai, Japan, 17± 20 October 1994, p. 75.

Iatrou, C.T., Kern, S., and Pavelyev, A. B., 1996, IEEE Transactions on Microwave Theoryand Techniques, 44, 56.

Idehara, T., Shimizu, Y., Makino, S., Ichikava, K., Tatsukawa, T., Ogava, I., andBrand, G. F., 1994, Physics Plasmas, 1, 233.

Pereyaslavets, M., Braz, O., Kern, S., Losert, M., Moï bius, A., and Thumm, M., 1997,International Journal of Electronics, 82, 107.

Piosczyk, B., Braz, O., Dammertz , G., Iatrou, C. T., Kern, S., Kuntze, M., Moï bius, A.,Thumm, M., Flyagin, V. A., Khizhnyak, V. I., Kuftin, A. N., Malygin, V. I.,Pavelyev, A. B., and Zapevalov, V. E., 1996, A 140 GHz, 1.5MW, TE28,16 coaxialcavity gyrotron. Digest of the 21th International Conference on Infrared and MillimeterWaves, Berlin, Germany, 14± 19 July 1996, p. AM2.

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