Infrared Physics & Technology 54 (2011) 512–516

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Infrared Physics & Technology

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Numerical design of 120 GHz, 1 MW gyrotron interaction cavity

Nitin Kumar ⇑, Udaybir Singh, Anil Kumar, A.K. SinhaGyrotron Laboratory, Microwave Tube Area, Central Electronics Engineering Research Institute (CEERI), A Constituent Laboratory of Council of Scientific and Industrial Research,CSIR, Pilani, Rajasthan 333 031, India

a r t i c l e i n f o

Article history:Received 4 February 2011Available online 23 July 2011

Keywords:GyrotronInteraction cavityBeam–wave interactionEigenmode analysis

1350-4495/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.infrared.2011.07.001

⇑ Corresponding author. Tel.: +91 1596 252229.E-mail address: nitingkv@gmail.com (N. Kumar).

a b s t r a c t

The design and the numerical simulation of the interaction cavity for 120 GHz, 1 MW gyrotron is pre-sented. The optimizations of the cavity parameters are carried out by using the Particle-in-Cell, 3D-electromagnetic simulation code MAGIC. The co-rotating TE22,6 mode is selected by using the in-housedeveloped code GCOMS. The cold cavity and the beam–wave interaction analyses are carried out to ana-lyze the eigenmode, eigenfrequency and the output power performance. The output power more than1 MW is achieved at the magnetic field of 4.82 T. The sensitivity analyses of the output power and thefrequency with respect to the various interaction cavity parameters are also performed.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

The gyrotron is a high power, high frequency millimeter wavesource based on the phenomenon called Cyclotron Resonance Ma-ser (CRM) instability [1]. The device generates the coherent milli-meter and submillimeter wave radiation upto megawatt powerlevel by the interaction between the relativistic gyrating electronbeam and the RF [2]. The gyrotron is a signature device in theElectron Cyclotron Resonance Heating (ECRH) in the magneticallyconfined plasma fusion [3,4]. The other potential applications ofthe gyrotron at the different frequencies and the power levels areplasma diagnostics, material processing, THz spectroscopy, highdensity communication, weather monitoring, etc. [5–7]. The milli-meter wave radiation of 120 GHz frequency with 1 MW or more RFpower is used in the plasma fusion applications. For the require-ment of Indian plasma fusion system, an activity related to thedevelopment of the high power, high frequency gyrotron is initi-ated. The basic specifications of the gyrotron are given in Table 1.In this paper, the design of the interaction cavity and the resultsof the beam–wave interaction are presented.

Recently, the 120 GHz gyrotron has been designed for 1 MW ofRF power at TE24,6 mode by Choi et al. due to its requirement in theITER start-up [8]. The MAGY code was used in the interactioncavity designing. The gyrotron at the same frequency has also beendesigned and developed at TE15,2 mode by Shimozuma et al. for600 kW of RF power [9]. Here, the 120 GHz gyrotron is designedat different mode by using the different numerical technique Par-ticle-in-Cell (PIC). The gyrotron is designed to operate at the funda-mental electron cyclotron frequency due to the requirement of

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high efficiency and low mode competition. High order transverseelectric (TE) mode is selected to reduce the ohmic wall loading atthe interaction cavity. The higher order modes show high modecompetition due to the large volume of the interaction cavity andthus various high order modes are studied carefully by using thein-house developed code GCOMS [10–12]. The code is used forthe mode selection, the mode competition and the initial estima-tion of cavity dimensions. Finally the TE22,6 is selected as the oper-ating mode.

The Particle-in-Cell (PIC) numerical simulation technique is usedfor the optimization of the cavity dimensions and the beam–waveinteraction calculations [13]. The PIC approach has already beenused in the design of the low and high frequency gyrotrons[14–16] and the gyro amplifiers [17]. In this paper efforts are madeto design and simulate the interaction cavity for the high power andthe high frequency gyrotron by using PIC numerical approach. TheMAGIC code provides the powerful PIC algorithms to represent theincoming and outgoing waves, the particle emission processes, theelectromagnetic fields, relativistic particles trajectories and is usedin the simulation and analysis of the interaction cavity [13]. Thesensitivity analysis of the output power and the frequency has beenperformed with respect to the geometrical parameters of the inter-action cavity and the beam parameters. The EGUN simulations ofMIG optimize the electron beam parameters, like, electron beamvelocity ratio, and velocity spread, and these optimized values areused in the interaction cavity simulations.

2. Mode selection and cavity parameters optimization

A high order mode, i.e. k?Rc � 1 allows for the large cavity ra-dius and consequently reduces the ohmic loss per unit area atthe wall of the interaction cavity (k? is the perpendicular wave

Fig. 2. Starting current curves with respect to the cavity magnetic field for themodes nearing to TE22,6.

Table 1Basic specifications of the gyrotron.

Operating frequency (f) 120 GHzOutput power (Po) P1 MWInteraction efficiency (g) P35%Beam voltage (Vb) 80 kVBeam current (Ib) 40 A

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number and Rc is the cavity radius). Fig. 1 shows the mode spec-trum for 40 < k?Rc < 50 for the cylindrical waveguide cavity. Eachvertical line in Fig. 1 represents a TE mode. The complication in theselection of the high order modes is reflected from Fig. 1 as themode spectrum becomes dense at the higher values of k?Rc . Themode selection criteria depend on the several parameters de-scribed in Table 2 [18–20]. Further the mode selection has beenstudied carefully with the aim of minimizing the mode competi-tion. The start oscillation current (SOC) and the coupling coefficient(CC) are computed for the various suitable high order modes likeTE22,6, TE28,4, TE28,6 and TE24,6 [10,21]. On the basis of the modecompetition analyzed by the SOC and CC, the TE22,6 mode is se-lected as the operating mode.

The cavity radius (Rc = vmnk/2p) and the beam radius (Rb =vm±n,ik/2p) are calculated for the selected mode, where vmn is thenth root of the Bessel function derivative J0mðxÞ ¼ 0, k is the freespace wavelength (k = 2.5 mm corresponding to operating fre-quency) and for first harmonic i = 1 [22]. The mode selectionparameters are calculated for TE22,6 and shown in Table 3. The cal-culated mode selection parameters values are under the technicallimits as shown in Table 2. The electrical properties of high qualityOxygen Free High Conductivity (OFHC) copper are used in the cal-culations. The middle section length of the interaction cavity isdecided by the optimized diffractive quality factor.

From the SOC curves (Fig. 2), it is clear that the TE21,6, TE23,6,TE19,7 and TE20,7 (+ sign for co-rotating and � sign for counter-rotating modes) are the most competing modes for the operatingmode. These competing modes have approximately the similar

Table 3Calculated values of mode selection parameters for the selectedmode.

Estimated wall loss (dP/dA) 0.45 kW/cm2

Voltage depression (Vd) 5 kVLimiting current (IL) 83 ADiffractive Q value (Qd) �700Beam wall gap 7.5 mmm/vmn �0.48

50

k Rc

TE22,6

40

Fig. 1. Mode spectrum for TE mode in cylindrical waveguide cavity.

Table 2The limits of mode selection parameters.

Estimated wall loss (dP/dA) <2 kW/cm2

Voltage depression (Vd) <8 kV (10% of Vb)Limiting current (IL) >80 A (2Ib)Diffractive Q value (Qd) �700–1000Beam wall gap >2 � larmour radiusm/vmn �0.5

start-up condition and may couple with the gyrating electronbeam. Maximum interaction efficiency is achieved in the lowermagnetic field side (at the operating magnetic field 4.82 T). Sothe main competing modes for the operating mode are TE21,6 andTE19,7 in lower magnetic field side. The coupling coefficient forthe operating mode and its most competing modes is shown inFig. 3. The maximum beam–wave coupling for the operating modetakes place at the Rb/Rc = 0.508, but due to the presence of the highcoupling coefficient region of TE21,6 near to the operating mode, thebeam radius is selected slightly more than the calculated beam ra-dius for the better separation of the modes.

The cavity is a three section structure with an input taper, a uni-form middle section and an output taper. The beam–wave interac-tion takes place at the middle uniform section where the RF field isat maximum value. The efficiency and the output power perfor-mance are considered the main goals in the optimization of thecavity parameters. On the basis of the mode selection and the ini-tially designed cavity, MAGIC simulations are performed and thecavity parameters are finalized for the 120 GHz, 1 MW gyrotron(Table 4).

The cold cavity eigenmode analysis for the weakly taperedcylindrical cavity is performed by using MAGIC code. Fig. 4 showsthe electric field pattern and the cold cavity normalized axial elec-tric field profile for the weakly tapered interaction cavity. The

Fig. 3. Coupling coefficient for various competing modes with respect to the ratio ofbeam radius to cavity radius.

Table 4Optimized cavity parameters for 120 GHz, 1 MW gyrotron.

Middle section length (L) 15 mmInput taper length (L1) 12 mmOutput taper length (L2) 20 mmCavity radius (Rc) 18.2 mmInput taper angle (h1) 2.8�Output taper angle (h2) 2.8�Beam radius (Rb) 9.25 mmVelocity ratio of electron beam (a) 1.5Operating mode TE22,6

Quality factor (Q) 700

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beam–wave interaction simulations are performed for the opti-mized cavity parameters by using MAGIC. An electron beam pos-sessing all the desired properties of the beam emitted from theMIG is launched at the input taper entrance for the beam–waveinteraction simulations. The same beam interacts with the normal-ized RF field profile at the first co-rotating radial maximum of theoperating mode (at 9.25 mm radius). The Maxwell CENTEREDalgorithm is used to run the code for the relativistic electronbeam–wave interaction. Initially, each electron with the energyof 79.86 keV enters into the input taper of the cavity, which trans-fers an amount (about 38%) of the energy to the electromagnetic

Fig. 4. (a) TE22,6 electric field pattern for the designed weakly tapere

Fig. 5. (a) Profile of electron energy in the cavity. (b) Frequency spectrum for TE22,6 movelocity ratio = 1.5, magnetic field = 4.82 T, beam radius = 9.25 mm and cavity radius = 1

wave in the midsection of the cavity. An output power of1.2 MW is achieved at 120.36 GHz frequency with the interactionefficiency of 38%. Fig. 5a clearly shows that, maximum energy istransferred from the gyrating electrons to the RF at the center ofthe cavity.

The resonant frequencies are found through Fast Fourier Trans-form (FFT) of the time history of the fields. From the frequencyspectrum (Fig. 5b), it is clear that the maximum gain is achievedat the two frequencies, 108.67 GHz and 120.36 GHz. The frequencypeak of 108.67 GHz is sufficiently far away from the operatingmagnetic field (4.82 T). The magnetic field difference between boththe frequencies is approximately 0.5 T, so there is no possibility ofthe excitation of 108.67 GHz frequency. Around the peak of120.36 GHz, there is a satisfactory suppression of the other com-peting modes. Fig. 6a and b shows that the frequency and thepower growth are stabilized at 110 ns. The figure shows the outputfrequency and power, 120.36 GHz and 1.2 MW, respectively. Forthe optimized interaction cavity parameters, the simulation resultsare quite satisfactory with the high interaction efficiency (38%).

3. Sensitivity analysis

During the fabrication and operation of an actual tube, it is dif-ficult to maintain the fixed value of the cavity geometry and the

d cylindrical cavity and (b) cold cavity axial electric field profile.

de gyrotron with peak at 120.36 GHz (beam voltage = 80 kV, beam current = 40 A,8.2 mm).

Fig. 6. (a) Frequency stability curve and (b) output power curve with respect to the time for TE22,6 mode beam voltage = 80 kV, beam current = 40 A, velocity ratio = 1.5,magnetic field = 4.82 T, beam radius = 9.25 mm and cavity radius = 18.2 mm).

Fig. 7. Output power and frequency as a function of (a) input taper angle and (b) output taper angle for TE22,6 mode gyrotron (beam voltage = 80 kV, beam current = 40 A,velocity ratio = 1.5, magnetic field = 4.82 T, beam radius = 9.25 mm and cavity radius = 18.2 mm).

Fig. 8. Output power and frequency as a function of (a) beam current and (b) beam voltage for TE22,6 mode gyrotron (beam voltage = 80 kV, velocity ratio = 1.5, magneticfield = 4.82 T, beam radius = 9.25 mm and cavity radius = 18.2 mm).

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beam parameters. The sensitivity analyses are carried out in viewof fabrication tolerance of the tapered interaction structure. Thesmall deviation of the cavity geometry parameters and the beamparameters affects the beam–wave interaction and consequently

leads to change in the output power. The sensitivity analyses ofthe output power and the frequency with respect to the geometri-cal parameters of the interaction cavity and the beam parametersare carried out (Figs. 7–9).

Fig. 9. Output power and frequency as a function of (a) middle section length and (b) magnetic field for TE22,6 mode gyrotron (beam voltage = 80 kV, beam current = 40 A,velocity ratio = 1.5, magnetic field = 4.82 T, beam radius = 9.25 mm and cavity radius = 18.2 mm).

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From the figures, it is clear that the output power dependsstrongly on the various beam parameters and cavity geometrywhile the frequency response is approximately constant. Fig. 7aand b shows the eigenfrequency and the output power behaviorwith respect to the input and the output taper angle. Again the out-put power is very sensitive to the input and the output taper anglesup to a certain value of 2.5�. Fig. 8 shows the effect of beam param-eters on the output power and the frequency. With the increase inthe beam current and the beam voltage, the output power growswith a constant rate. The start-up scenario of a particular modealso depends on the beam parameters and thus imposes a restric-tion on the beam parameters values. So the fixed values of thebeam current and the beam voltage, i.e. 40 A and 80 kV respec-tively, have been chosen. Fig. 9a shows the strong dependency ofthe output power on the middle section length (Qd = 700–1100).The output power decreases with increase in the length of middlesection. Fig. 9b shows the critical dependency of the output poweron the guiding magnetic field. At the magnetic field of 4.81 T, themaximum power is achieved. Below and above to this field, theoutput power decreases rapidly. A thorough sensitivity analysisof various interaction cavity and beam parameters provides a safelimit for the required output power and frequency.

4. Conclusion

The detail design of the interaction cavity for the 120 GHz,1 MW gyrotron operating at TE22,6 mode is described. The simu-lated results show the output power of 1.2 MW at the frequencyof 120.36 GHz with the interaction efficiency 38%. The results ob-tained by the PIC simulations show the feasibility of 1 MW of RFpower at 120 GHz frequency. The simulated results show thedependence of the output power on the cavity geometry parame-ters and the beam parameters. The sensitivity analyses of the cav-ity dimensions are also carried out to decide the fabricationtolerance of the tapered interaction structure.

Acknowledgments

The authors are pleased to acknowledge the support ofDr. Chandra Shekhar, Director, CEERI Pilani and Dr. S.N. Joshi,National Coordinator of Gyrotron project. The authors also wishto thank to the team members of gyrotron for helpful discussions.Thanks are also due to CSIR for funding this project and awardingthe Senior Research Fellowship (SRF) to the corresponding author.

References

[1] V.A. Flyagin, A.V. Gaponov, I. Petelin, V.K. Yulpatov, The gyrotron, IEEETransactions on Microwave Theory and Techniques 25 (1977) 514–521.

[2] M. Thumm, State-of-the-art of high power gyro-devices and free electronmasers update 2006, Forschungszentrum Karlsruhe, Karlsruhe, Germany,Scientific Report FZKA 7289, February 2007.

[3] M. Thumm, High power gyro-devices for plasma heating and otherapplications, International Journal of Infrared and Millimeter Waves 26(April) (2005) 483–503.

[4] S. Albertia et al., European high power CW gyrotron development for ECRHsystems, Fusion Engineering and Design 53 (2001) 387–397.

[5] N. Kumar, U. Singh, T.P. Singh, A.K. Sinha, A review on the applications of highpower, high frequency microwave source – gyrotron, Journal of Fusion Energy30 (2011) 257–276.

[6] M. Thumm, Novel applications of millimeter and submillimeter wave gyro-devices, International Journal of Infrared, Millimeter and Terahertz Wave 22(2001) 377–386.

[7] Andrei V. Gaponov-Grekhov, Victor L. Granatstein, Application of High PowerMicrowaves, Artech House Publication, London, 1994.

[8] E.M. Choi, C. Marchewka, I. Mastovsky, M.A. Shapiro, J.R. Sirigiri, R.J. Temkin,Megawatt power level 120 GHz gyrotrons for ITER start-up, Journal of Physics:Conference Series 25 (2005) 1–7.

[9] T. Shimozuma, T. Kikunaga, H. Asano, Y. Yasojima, K. Miyamoto, T. Tsukamoto,A 120 GHz high-power whispering-gallery mode gyrotron, InternationalJournal of Electronics 74 (1993) 137–151.

[10] D.R. Whaley, M.Q. Tran, T.M. Tran, T.M. Antonsen Jr., Mode competition andstarup in cylindrical cavity gyrotrons using high-order operating modes, IEEETransactions on Plasma Science 22 (1994) 850–860.

[11] N. Kumar, U. Singh, T.P. Singh, A.K. Sinha, Design of 95 GHz, 2 MW gyrotron forcommunication and security applications, International Journal of Infrared,Millimeter Wave and Terahertz wave 32 (2011) 186–195.

[12] N. Kumar, U. Singh, A. Kumar, H. Khatun, T.P. Singh, A.K. Sinha, Design of35 GHz gyrotron for material processing applications, Progress inElectromagnetic Research B (PIER B) 27 (2011) 273–288.

[13] MAGIC User Mannual: 2007 Version of Magic 3D, ATK Mission Research,Washington.

[14] J.J. Barroso, K.G. Kostov, R.A. Correa, Electromagnetic simulation of a 32 GHz,TE021 gyrotron, IEEE Transactions on Plasma Science 27 (1999) 384–390.

[15] N. Kumar, U. Singh, A. Kumar, H. Khatun, T.P. Singh, A.K. Sinha, Numericalanalysis of interaction cavity for 1.5 MW/127.5 GHz gyrotron, Journal ofFusion Energy 30 (2011) 1–6.

[16] N. Kumar, U. Singh, A. Kumar, A.K. Sinha, Design and misalignment analysis of140 GHz, 1.5 MW gyrotron interaction cavity for plasma heating applications,Journal of Fusion Energy 30 (2011) 169–175.

[17] E. Nicholas Comfoltey, Michael A. Shapiro, J.R. Srigiri, R.J. Temkin, Design of anovermoded W-band TWT, in: IVEC-2009, Rome, Italy, pp. 127–128.

[18] M.V. Kartikeyan, E. Borie, M.K.A. Thumm, Gyrotrons-High Power Microwaveand Millimeter Wave Technology, Springer Verlag, Berlin, Germany, 2004.

[19] A.K. Sinha, S.N. Joshi, Progress report for design review meeting: design anddevelopment of 200 kW CW/long pulse 42 GHz gyrotron, Technical Reports,MTRDC, Bangalore, India, February 2008.

[20] C.J. Edgcombe (Ed.), Gyrotron Oscillators: Their Principles and Practice, Taylor& Francis, London, 1993.

[21] B.G. Danly, R.J. Temkin, Generalized nonlinear harmonic gyrotron theory,Physics of Fluids 29 (1986) 561–567.

[22] M.V. Kartikeyan, E. Borie, O. Drumm, S. Illy, B. Piosczyk, M. Thumm, Design of a42 GHz 200 kW gyrotron operating at the second harmonics, IEEE Transactionson Microwave Theory and Techniques 52 (2004) 686–692.