Nonlinear Investigation and 3-D Particle Simulation of Second ...

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 5, MAY 2015

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Nonlinear Investigation and 3-D Particle Simulation of Second-Harmonic Gyro-TWT With a Mode Selective Circuit Muthiah Thottappan, Member, IEEE, and Pradip Kumar Jain, Senior Member, IEEE

Abstract— The beam–wave interaction behavior of a second-harmonic Ku-band high-power gyro-TWT comprising a mode selective RF interaction circuit has been investigated using a 3-D particle simulation code. The mode-selective RF circuit has been cut axially into four slices to restrain the electromagnetic modes not having m = 2 symmetry. A self-consistent nonlinear large signal code has been developed to compute the field amplitude, power, energy, and phase of the gyrating beam. The amplifier gives a saturated peak power of ∼230 kW at 15.8 GHz for beam parameters of 80 kV and 20 A having a pitch of 1.1. The large signal gain of the device has been calculated as ∼16 dB for the beam spread of 14%. Further, the nonlinear findings have been validated against the Particle-in-Cell code that predicts the saturated output power of ∼193 kW in a circular TE21 mode at the desired operating frequency. Index Terms— Beam spread, gyro-TWT, Ku-band, large signal regime, Particle-in-Cell (PIC) code, pitch.

I. I NTRODUCTION

T

HE gyro-TWT works on the principle of cyclotron resonance maser instability in which helically moving electrons interact with a transverse circular waveguide mode. In gyro-TWTs, the RF amplification is obtained by the phase bunching of the relativistic electrons gyrating in their Larmor orbits around the guiding center [1]. Since the gyro-TWT provides a broader bandwidth and high power at millimeterwave frequencies, it has always been preferred in radar and high-density communications. When the interaction involves the gyrating motion of electrons in a static magnetic field B0 , the synchronism requires that ω − k z vz − sc ≈ 0

(1)

where ω is the angular frequency, k z is the axial propagation constant, vz is the axial velocity of electrons, s is the cyclotron harmonic number, and c is the relativistic electron cyclotron frequency. The RF interaction mechanism in a gyroTWT is limited by the gyrating characteristics and the dc magnetic field; therefore, research interest has been focused on the high-frequency RF circuit. The novelty in the RF Manuscript received August 22, 2014; accepted March 10, 2015. Date of publication March 27, 2015; date of current version April 20, 2015. The review of this paper was arranged by Editor M. Thumm. The authors are with the Centre of Research in Microwave Tubes, Department of Electronics Engineering, IIT Varanasi, Varanasi 221005, India (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2015.2412777

circuits of gyro-TWTs has been coming up since last three decades and that helps to improve the performance of the gyro-TWT [2]. The utilization of a nonresonant RF circuit enhances the output power and bandwidth of amplifier in millimeter/submillimeter wave region [3]. However, high gain, broad bandwidth, and stability of fundamental gyro-TWT have been affected by the following limitations. First, the frequency of operation of gyro-TWT is directly proportional to the externally applied magnetic field. Hence, the maximum frequency at which fundamental operation of gyro-TWT is determined by the availability of high-field magnets [4]. Second, fundamental gyro-TWTs have intense interactions, so they are susceptible to spontaneous oscillations, where internal feedback mechanism is provided by a backward wave at a frequency near the cutoff frequency of the operating mode [4]. Harmonic gyro-TWTs are having weak interactions compared with fundamental gyro-TWTs, so they are very stable to oscillations and can be operated at higher power levels [5]. The possibility of gyrotron backward-wave oscillations at various harmonics also limits the performance of fundamental gyro-TWT. For stable operation of gyro-TWT, beam current must be reduced below threshold value at which amplifier breaks into oscillations. Interaction length should also be kept less than the start oscillation length for the strongest competing interaction [4]. Marginal stability theory and design criteria were introduced to maximize the output power and stability of gyro-TWTs [6]. A three-stage second-harmonic gyro-TWT operating at TE31 mode has been reported to provide an output of 533 kW for 100 kV, 25-A beam input with 20% efficiency at 35 GHz [7]. Third-harmonic gyro-TWT operating in TE31 mode at a frequency of 140 GHz has been demonstrated to provide an output of 937 kW with 18.7% efficiency [8]. Sirigiri et al. [2] have reported an experimental work on quasi-optical gyro TWT operating at a frequency of 140 GHz, providing an output power of 100 kW and a saturated gain of 38 dB. The modeling of 16-GHz TE21 second-harmonic Ku-band gyro-TWT was performed in [4] and obtained an output power of 207 kW with large-signal gain of 16 dB. A similar technique was used in second-harmonic TE31 gyro-TWT, where the RF circuit was cut into six slices and azimuthally separated by 600 to improve the stability by interrupting the wall currents of the waveguide circuit [9]. Guo et al. [10] have designed a 35-GHz second-harmonic TE02 gyro-TWT with an efficiency of 25% and peak

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output power of 200 kW at the University of Maryland. Li et al. [11] have designed and modeled 390-GHz TE721 harmonic gyrotron using a cusp electron gun with an output power of 600 W. Liu et al. [12] have experimentally studied a Ka-band gyro-TWT in TE01 circular mode and this gave an output power of 86 kW with saturated gain of 33 dB with an efficiency of 21.3% using a mode-selective technique. The behavior of 95-GHz slotted third-harmonic gyro-TWT was studied and simulated in [13] at the University of Electronic Science and Technology of China and was found that the saturated bandwidth decreases from 10.3% for a harmonic number of 2%–5.7% for 4. The effect of absolute instability in 94-GHz TE01 mode and also for higher order modes of gyro-TWT was studied in [14] at the Department of Physics, NTHU, Taiwan, in 2004. The concept of harmonic multiplying was studied for mode-selective circuit at the University of Maryland using the frequency trippler and thirdharmonic gyro-TWT, and obtained an output power of 1 MW and gain of 40 dB with an efficiency of 25% [15]. A peak power of 465 kW with a gain of 49 dB at 91 GHz was obtained for W -band TE02 mode gyro-TWT at second harmonics at Vacuum Electronics National Laboratory, Beijing, China, in [16]. In [17], an experimental study on electron cyclotron maser instability was performed, and the structure was modeled at 35 GHz and an output power of 10 kW with 9% bandwidth along with a gain of 20 dB was obtained. The main objective of this paper is to realize the beam–wave interaction behavior of gyro-TWT using sliced RF interaction circuit along with small orbit gyrating electron beam. The modeling and simulation has been carried out using a 3-D Particle-in-Cell (PIC) code CST Particle Studio. Further, its response has been validated with a self-consistent nonlinear code. The simulation studies show the EM and transient behavior of gyro-TWT. The transient analysis is important to understand the saturation phenomenon in the beam–wave interaction process of gyro-TWT. In Section II, the nonlinear self-consistent theory has been revisited to study the beam–wave interaction mechanism in the amplifier, comprising a mode-selective interaction circuit. Section III gives the stability analysis of the harmonic TE21 mode gyro-TWT. In Section IV, the nonlinear findings have been elaborated in terms of energy, phase of electrons, and the saturated power output of amplifier. In Section V, the 3-D modeling and simulation of beam–wave interaction behavior has been discussed and the conclusion is drawn in Section VI. II. N ONLINEAR C OMPUTATIONAL T HEORY In this approach, we study the beam–wave interaction mechanism by tracking the behavior of each electron separately, as the beam drifts through the RF circuit. The equations showing the field amplitude of RF wave, energy, and phase of electrons can be used to determine the net energy exchange in the interaction mechanism. The interaction between the electrons and the RF field occurs over many cycles, and in one such cycle, we assume that the variables pt , pz , ψ, X  , and Y  vary slightly. This time scale of variation over one cyclotron period is called the fast-time scale, contrary to the slow-time scale

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 5, MAY 2015

variation corresponding to the transit time in the interaction region. With the above assumptions in place, we obtain the following [3]: p˙ t = −

1 βt Re{A G sθ eiϑs } + g βz k

1 β2 Re{A G sz eiϑs } + g t βz kβz   μ 1 s p˙ z s  − − v˙ s + h = − Re{A G sr eiϑs } pz βz βz p˙ z = −

(2) (3) (4)

 is the Lorentz force, which is given by G  = ( E s + where G  v × Bs ). The electric and magnetic fields in the waveguide can be expressed in terms of the so-called membrane function , the Eigen function of the Helmholtz equation L l (X, Y ) = (1/kt )(∂/∂ X + i ∂/∂Y )l (X, Y ).

(5)

L l can be identified to be the form factor of the interaction structure and decides the coupling of the cyclotron wave to the resonant waveguide mode. The radial component of the Lorentz force is given by Gr =

l=∞ 

J l (ξ )L l (X ,Y )μ0 c

l=−∞

  ξ × ((1−hβz )/s)−k/(kt2 )l/r (1−hβz ) . κ

(6)

To obtain the resonant component of G r we substitute l = s and r = r1 and is given by     1−hβz d d G s,r =μ0 c ξ Jl (ξ ) L l (X,Y). (7) sκ dξ dξ Similarly, we can obtain other components of the Lorentz force as   1−hβz  Jl (ξ )L l (X,Y) (8) G s,θ = −i μ0 c κ   hβz  Jl (ξ )L l (X,Y) (9) G s,z = −i μ0 c κ where ξ = kt r L = κkr L = κ(ω/c)(vt /) = κβt (ω/), κ = kt /k, μ0 is the permeability of the free space, c is the velocity of light, and Jl is the Bessel function. It would be expedient to describe the interaction in terms of only two quantities, namely, the electron energy and phase along the interaction circuit length. We start by evaluating the derivative of normalized energy parameter ω with respect to the normalized distance as [3] (1 − ω)s/2 dω Re{F eivs } = 2i  dz (1 − bω)

(10)

where F is a field amplitude, which is given by   s−1 κ pt 0 μ0 c (1 − hβz0 ) 1 F= A L s (X, Y ) (11) s κ γ0 βt 0 βz0 2 (s − 1)! μ where b = hβt20 /2βz0 (1 − hβz0 ) is the parameter corresponding to the changes in the longitudinal momentum of the electron by emitting or absorbing photons,

THOTTAPPAN AND JAIN: NONLINEAR INVESTIGATION AND 3-D PARTICLE SIMULATION OF SECOND-HARMONIC GYRO-TWT

Fig. 1.

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Dispersion of second harmonic of gyro-TWT with TE21 mode. TABLE I D ESIGN PARAMETERS OF H ARMONIC G YRO -TWT [4]

Fig. 2. Start oscillation current plot with respect to (a) interaction length and (b) velocity spread.

= 1 − sμ/γ − hβz0 and vs = sθ − ωt − k z z and its derivative with respect to z  is given by [3]   s 1

. −1 ivs 2 vs = μω − + s(1 − ω) Re{F e } . (12) (1 − bω) βz0 Derivative of F with respect to z is given by [2]  2π (1 − ω)s/2 −ivs dF  1 = −i I0 e dv0 dz 2π 0 (1 − bω)

(13)

where I0 is the normalized beam current I0 and ν0 = ωt0 . The coupling between electrons and EM fields is decided by the coupling factor L s (X, Y ). The whole interaction process can now be represented by (5), (11), and (12) connecting the electron energy, phase, and the RF field amplitude in a selfconsistent setup. The total efficiency of gyro-TWT is given by [3] 2

β ⊥0 η⊥ . η= −1 2(1 − γ )(1 − hβ z0 )

(14)

III. D ESIGN PARAMETERS AND S TABILITY A NALYSIS The dispersion relation of second-harmonic Ku-band gyro-TWT is shown in Fig. 1 for TE21 mode and its competing modes. The optimized design parameters of K u-band gyroTWT have been listed in Table I. For gyro-TWT amplifier’s stability, it is desirable to suppress as many unnecessary competing modes as possible near the desired mode. To boost up the amplifier gain, it was required that the gyro-backwardwave oscillator (BWO) modes have to be suppressed. In this

paper, the device employs a sliced mode-selective RF circuit to suppress odd-order azimuthal modes by interrupting their wall currents. Further, to avoid the propagation of an odd-m in TEmn modes, a lossy dielectric cylinder with graphite around the RF circuit has been used. Furthermore, the interaction between the beam and RF signal occurs only when the mode number of the cyclotron harmonic is equal to the azimuthal mode number of the RF circuit. This leaves the TE41 gyroBWO mode as the strongest threat. It is shown that gyroBWO can be suppressed by adding loss to the RF circuit. To study the amplifier’s stability, the effect of start current on various parameters has been investigated. The dependence of start current with length, and velocity spread for harmonic interactions of TE21 mode and its competing modes are shown in Fig. 2(a) and (b), respectively. The second-harmonic TE21 (1) (3) gyro-TWT is more susceptible to TE11 and TE31 modes. The start current decreases with the increase in circuit length of oscillating modes and becomes almost constant after 150 mm of circuit length [Fig. 2(a)], and for velocity spreads ≥14% [Fig. 2(b)]. As a result, no oscillations are produced in the amplifier that leads to its stable operation. Evidently, the increase in velocity spread would reduce the output power and efficiency of gyrotron devices. Gyrotrons are classified by the magnitude of the axial wave number. The operating mode is formed with waves propagating across the dc magnetic field and having very small axial wave numbers, hence resulting in weak sensitivity to the velocity spread, which is one of the merits of gyrotron devices. To enhance the efficiency, the coupling between the second-harmonic cyclotron mode of a gyrating electron beam and the radiation field in the region of very large value of phase velocity over a broad bandwidth is chosen. Therefore, a 14% spread does not seem to be too

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Fig. 3.

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 5, MAY 2015

Schematic of gyro-TWT amplifier.

Fig. 5. (a) Variation of normalized energy of electrons along interaction length. (b) Normalized phase along interaction length.

Fig. 4. (a) Normalized field amplitude along the interaction length. (b) Output power and efficiency along interaction length.

large for any gyrotron devices. The schematic of gyro-TWT is shown in Fig. 3. IV. N UMERICAL R ESULTS AND D ISCUSSION The normalized field amplitude along the length of the RF circuit is shown in Fig. 4(a). The variation of power and efficiency with circuit length is shown in Fig. 4(b). The saturated power was obtained as 230 kW at 65 cm, and the efficiency as ∼15%. The energy and the phase of gyrating electrons are shown in Fig. 5(a) and (b), respectively. As the electrons move axially along the RF circuit, some electrons give energy to RF wave, while others take up energy from RF wave. Hence, some of the gyrating electrons have higher energy than their initial energy and the rest of the electrons have lower. This mechanism is evident in normalized energy plot shown in Fig. 5(a). For gyro-TWT to act as an amplifier, the electrons receiving energy from the wave should be less than the electrons giving energy to the wave. As electrons move along the RF circuit, their phase changes because of Doppler shift and interaction with RF wave, as shown in Fig. 5(b). The performance of the amplifier is basically

Fig. 6. (a) Output power for different velocity spread at different magnetic fields. (b) Variation of output power with input power for different beam currents.

studied by varying the various parameters characterizing the beam–wave mechanism. Likewise, initially the velocity spread of the electron has been considered for a fixed magnetic field, as shown in Fig. 6(a). Similarly, the input drive power has been varied for different constant dc operating currents, as shown in Fig. 6(b). V. PIC S IMULATION In PIC simulation, we assume that the electric and magnetic fields are confined to the space within the RF

THOTTAPPAN AND JAIN: NONLINEAR INVESTIGATION AND 3-D PARTICLE SIMULATION OF SECOND-HARMONIC GYRO-TWT

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Fig. 7. (a) Cross-sectional view of the sliced RF interaction circuit. (b) Cut view of RF circuit in CST environment. Fig. 9. (a) Electric field contour distribution in desired TE21 mode. (b) Vector plot.

Fig. 10. View of (a) electron beam and (b) momentum before bunching (at 2 ns).

Fig. 8. (a) Sliced view along the axial direction on horizontal plane. (b) Vertical plane.

interaction circuit. Since the circuit is air-filled, no power is lost throughout the circuit and dielectric loss is also being negligible. But some power is lost in the form of heat at circuit boundaries and which is also negligible. It has been noted that several modes of EM waves can propagate within the circuit and for each mode; there exists a definite cutoff frequency. In addition, it is required that the frequency of the given signal be kept above the cutoff in such a way that the cutoff frequency is being kept 3%–5% lesser than that of operating frequency of given signal that avoids gain reduction while increasing bandwidth. Further, EM energy could be transmitted through RF circuit without attenuation. A. Modeling of RF Interaction Circuit To study and analyze the interaction of electrons with RF wave, the sliced interaction circuit has been modeled, as shown in Fig. 7, in CST Particle Studio. This interaction circuit has been axially cut into four slices, i.e., along the two planes (vertical and horizontal plane) through the axis and separated azimuthally by 90°, as shown in Fig. 8. The innermost section in Fig. 7 is called the RF interaction circuit, which is air-filled. This is surrounded by loss-free Teflon Polytetrafluoroethylene (PTFE), a dielectric cylinder of outer

radius 21.5 mm and an inner radius 20 mm. This cylinder was then coated with graphite at inner walls with an outer radius of 20 mm and inner radius of 19.9 mm to suppress the odd-m modes in TEmn and absorb any wave energy leaking through the slices. The mode selective sliced RF circuit has been modeled using Teflon (PTFE) loss-free dielectric material having the permeability and permittivity of 1 and 2.1, respectively, and its thermal conductivity is 0.2 W/K/m. The graphite coating have the unity permeability and the permittivity of 12 and its electrical conductivity is 105 S/m. The Teflon cylinder was then covered with a vacuum jacket. B. Cold Simulation To ensure the desired mode and frequency of operation, cold simulation or beam-absent simulation was performed using CST Microwave Studio. Like transient solver, the main task of frequency domain solver is to calculate transmission and reflection coefficients. In the cases of strong resonant loss-free structures, where the fields (modes) are to be calculated, for which eigenmode solver is very efficient. Both electric and magnetic fields must satisfy the boundary conditions imposed by the walls of RF circuit. The eigenmode solver confines the desired TE21 mode inside the RF circuit and that was propagating along the circuit axially. Fig. 9(a) shows the electric field contour distribution of the desired TE21 mode, which was obtained at the output port of the RF circuit. The RF circuit length was set at 650 mm. The vector plot of the field pattern of the desired mode is shown in Fig. 9(b), which gives a clear view of the region where electric field is maximum. This is identified by the intensity as shown in Fig. 9.

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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 62, NO. 5, MAY 2015

Fig. 11. View of (a) electron beam orbital momentum and (b) axial momentum after bunching (at 100 ns).

Fig. 13. Electric field intensity plot with respect to frequency at (a) 1 mm and (b) 650 mm.

Fig. 12. Temporal (a) output signal response and (b) output power growth observed at output end of the interaction circuit for TE21 mode.

C. Bunching Mechanism The electron beam was observed before and after the bunching mechanism. The nature of bunching in terms of orbital and axial momentum of gyrating electrons has been shown in Figs. 10 and 11 before and after bunching, respectively. Fig. 10(a) and (b) shows the beamlets at the initial bunching process (at 2 ns). Similarly, Fig. 11(a) and (b) shows the bunching at 100 ns. The gyrating electrons move with high angular velocity under the influence of magnetic field. When a beam of gyrating electrons interact with a fast RF wave in the presence of a magnetic field, it leads to an extraction of transverse kinetic energy of electrons. As a result, under the influence of magnetic field, the electrons pass through the RF circuit, providing a strong coupling between electron beam and RF wave. The electrons tend to gyrate along the axial length and possess kinetic energy associated with the transverse motion of electrons, which is then converted to RF power. After bunching occurs, the electrons transfer a part of their kinetic energy to RF energy. At resonance, the number of electrons gaining energy becomes equal to the number of electrons loosing energy, and hence no net transfer of energy.

Fig. 14. (a) Frequency spectrum of probe signal. (b) Comparison of output power with measured and simulated results.

D. 3-D Simulation Results and Discussion To observe the growth of the field, we have set the number of electric field probes. Accordingly, the field amplitude at the output port was obtained as 440 V/m as shown in Fig. 12(a). Fig. 12(b) shows the peak output power as ∼193 kW at 16 GHz in TE21 mode. This was calculated based on the template-based postprocessing feature of the CST Particle Studio in which the output power is obtained by squaring the developed electric field at the output port. Therefore, it

THOTTAPPAN AND JAIN: NONLINEAR INVESTIGATION AND 3-D PARTICLE SIMULATION OF SECOND-HARMONIC GYRO-TWT

directly represents an output power or the E-field is the square root of a power [18]. It was observed that field amplitudes of competing modes were less compared with the desired mode and that confirms the stability of amplifier. The field probe was placed at different positions of RF circuit to confirm the frequency of operation of amplifier. It was noticed that the electric field intensity was maximum at 16 GHz as shown in Fig. 13(a) (input) and (b) (output). Fig. 14(a) shows the spectrum of TE21 mode at the output, which is obtained by the Fourier transform of electric field, which shows the desired frequency of operation, i.e., 16 GHz. Further, the simulation procedure was repeated for different input frequencies in the Ku-band to observe the bandwidth of gyro-TWT using modeselective RF interaction circuit as shown in Fig. 14(b). VI. C ONCLUSION We have investigated the beam–wave interaction behavior of a harmonic gyro-TWT using a mode selective interaction circuit. The effect of unwanted oscillations on amplifier’s stability was investigated. The developed nonlinear code has been benchmarked by investigating an experimental Ku-band gyro-TWT. A peak power of ∼230 kW at 15.8 GHz has been obtained for 80 kV, 20 A, with a pitch of 1.1, and a spread of ∼14%. Further, the sliced interaction structure was modeled using a 3-D particle code in order to validate our nonlinear findings. By optimizing beam parameters, the effect of output power with even lesser variation of magnetic field was observed. A peak power of ∼193 kW has been obtained for a magnetic field of 2.89 kG along with a large signal gain of ∼15 dB and an efficiency of ∼12%. However, the discrepancy between the PIC and nonlinear calculation seems to be high. The reasons are: 1) beam loading in the PIC (hot) simulation—it is a physical process in which the energetic gyrating electron beam and the RF electric field are interacting, whereas the nonlinear results were simply obtained by numerical calculations that do not have any loading and 2) in PIC simulation, the computational area has to be meshed with finer size (more number of meshes) which is very important for better optimization of output power. This will consume more memory space during the simulation, i.e., due to the limitation of hardware of our computational machine, we were unable to increase the number of meshes; therefore, we have been restricted to report 193 kW only. Nevertheless, this PIC simulation output power is in close agreement with the experimental 207-kW gyro-TWT at the University of California by 6%.

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[5] Y. Y. Lau, K. R. Chu, L. R. Barnett, and V. L. Granatstein, “Gyrotron travelling wave amplifier: I. Analysis of oscillations,” Int. J. Infr. Millim. Waves, vol. 2, no. 3, pp. 373–393, 1981. [6] A. T. Lin, K. R. Chu, C. C. Lin, C. S. Kou, D. B. McDermott, and N. C. Luhmann, Jr., “Marginal stability design criterion for gyro-TWTs and comparison of fundamental with second harmonic operation,” Int. J. Electron., vol. 72, nos. 5–6, pp. 873–885, 1992. [7] Q. S. Wang, C. S. Kou, D. B. McDermott, A. T. Lin, K. R. Chu, and N. C. Luhmann, Jr., “High-power harmonic gyro-TWT’s. II. Nonlinear theory and design,” IEEE Trans. Plasma Sci., vol. 20, no. 3, pp. 163–169, Jun. 1992. [8] Q. S. Wang, D. B. McDermott, C. K. Chong, C. S. Kou, K. R. Chu, and N. C. Luhmann, Jr., “Stable 1 MW, third-harmonic gyro-TWT amplifier,” IEEE Trans. Plasma Sci., vol. 22, no. 5, pp. 608–615, Oct. 1994. [9] D. B. McDermott, A. T. Lin, Y. Hirata, S. B. Harriet, Q. S. Wang, and N. C. Luhmann, Jr., “High power harmonic gyro-TWT amplifiers in mode-selective circuits,” in Proc. AIP Conf., vol. 474. 1999, pp. 172–177. [10] H. Guo et al., “Design and development of a high performance gyroTWT-amplifier operating at a cyclotron harmonic frequency,” in Proc. IEEE Int. Conf. IEDM, vol. 91. Dec. 1991, pp. 783–785. [11] F. Li et al., “Design and simulation of a ∼390 GHz seventh harmonic gyrotron using a large orbit electron beam,” J. Phys. D, Appl. Phys., vol. 43, no. 15, p. 155204, 2010. [12] B. Liu, E. Wang, L. Qian, Z. Li, and J. Feng, “Experimental study of a Ka band gyro-TWT with the mode-selective circuits,” J. Infr., Millim. Terahertz Waves, vol. 31, no. 12, pp. 1463–1468, 2010. [13] Z. Hongbing, L. Hongfu, W. Huajun, Z. Xiaolan, and D. P. Zhong, “Selfconsistent nonlinear simulation of a slotted third-harmonic gyro-TWT amplifier,” in Proc. IEEE Int. Conf. Microw. Millim. Wave Technol., Aug. 1998, pp. 524–527. [14] W. C. Tsai, T. H. Chang, N. C. Chen, K. R. Chu, and N. C. Luhmann, Jr., “Absolute instabilities in a high-order-mode gyrotron traveling-wave amplifier,” Phys. Rev. E, vol. 70, no. 5, p. 056402, 2004. [15] W. Chen, H. Guo, J. Rodgers, V. L. Granatstein, and T. M. Antonsen, “Design of a frequency tripling, third harmonic gyro-TWT,” in Proc. IEEE Int. Conf. Plasma Sci., Jun. 1999, p. 163. [16] Z. Li, J. Feng, E. Wang, and B. Liu, “Study of a W-band secondharmonic gyro-TWT amplifier,” in Proc. IEEE Int. Conf. IVEC, Feb. 2011, pp. 335–336. [17] J. Seftor, V. L. Granatstein, K. R. Chu, P. Sprangle, and M. E. Read, “The electron cyclotron maser as a high-power traveling wave amplifier of millimeter waves,” IEEE J. Quantum Electron., vol. 15, no. 9, pp. 848–853, Sep. 1979. [18] M. C. Balk, “3D Magnetron simulation with CST STUDIO SUITE,” in Proc. IEEE Int. Vac. Electron. Conf., Feb. 2011, pp. 443–444. [19] User’s Manual, CST-Particle Studio, Darmstadt, Germany, 2013.

Muthiah Thottappan (M’14) received the Ph.D. degree in microwave engineering from IIT Varanasi, Varanasi, India, in 2013. He is currently an Assistant Professor with the Department of Electronics Engineering, IIT Varanasi. His current research interests include highpower microwave and millimeter wave electron beam devices (gyrotron oscillators and amplifiers), RF and microwave computer-aided engineering.

R EFERENCES [1] K. R. Chu, “The electron cyclotron maser,” Rev. Modern Phys., vol. 76, no. 2, pp. 489–540, 2004. [2] J. R. Sirigiri, M. A. Shapiro, and R. J. Temkin, “Experimental results from the MIT 140 GHz quasioptical gyro-TWT,” in Proc. IEEE 27th Int. Conf. Infr. Millim. Waves, Sep. 2002, pp. 235–236. [3] O. V. Sinitsyn, K. T. Nguyen, G. S. Nusinovich, and V. L. Granatstein, “Nonlinear theory of the gyro-TWT: Comparison of analytical method and numerical code data for the NRL gyro-TWT,” IEEE Trans. Plasma Sci., vol. 30, no. 3, pp. 915–921, Jun. 2002. [4] Q. S. Wang, D. B. McDermott, and N. C. Luhmann, Jr., “Operation of a stable 200-kW second-harmonic gyro-TWT amplifier,” IEEE Trans. Plasma Sci., vol. 24, no. 3, pp. 700–706, Jun. 1996.

Pradip Kumar Jain (SM’05) received the B.Tech. degree in electronics engineering, and the M.Tech. and Ph.D. degrees in microwave engineering from IIT Varanasi, Varanasi, India, in 1979, 1981, and 1988, respectively. He is currently a Professor with the Department of Electronics Engineering, IIT Varanasi. His current areas of research includes CAD/CAM, modeling and simulation of microwave tubes and their subassemblies, including broadbanding of helix TWTs, and cyclotron resonance measuring devices including gyrotrons and gyro-TWTs and their performance improvement