PSFC/JA-17-31

Operation of a 140 GHz Gyro-amplifier using a Dielectric-loaded, Sever-less Confocal Waveguide

Alexander V. Soane, Michael A. Shapiro, Sudheer Jawla, Richard J. Temkin

August 2017

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was supported by the National Institutes of Health (NIH), National Institute for Biomedical Imaging and Bioengineering (NIBIB) under Grants EB004866 and EB001965. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

1

Operation of a 140 GHz Gyro-amplifier using aDielectric-loaded, Sever-less Confocal Waveguide

Alexander V. Soane, Student Member, IEEE, Michael A. Shapiro, Member, IEEE,

Sudheer Jawla, Member, IEEE and Richard J. Temkin, Life Fellow, IEEE

Abstract—The design and experimental results of a 140GHz gyro-amplifier that uses a dielectric-loaded, sever-lessconfocal waveguide are presented. The gyro-traveling waveamplifier uses the HE06 mode of a confocal geometry withpower coupled in and out of the structure with Vlasov-type,quasi-optical couplers. Dielectric loading attached to theside of the confocal structure suppresses unwanted modesallowing zero-drive stable operation at 48 kV and 3A ofbeam current. The confocal gyro-amplifier demonstrated apeak circuit gain of 35 dB, a bandwidth of 1.2 GHz and apeak output power of 550 W at 140.0 GHz.

I. Introduction

There is an active interest in designing high-gain ampli-fiers for use with dynamic-nuclear-polarization-enhancednuclear magnetic resonance (DNP/NMR). Currently, gy-rotron oscillators at frequencies of 140, 250, 330, and 460GHz are in operation at the Francis Bitter Magnet Labat MIT [1–7]. These DNP/NMR systems all use contin-uous wave (CW) sources. The polarization enhancementin CW DNP/NMR spectroscopy scales inversely with in-creasing magnetic field. This means that as NMR pro-ceeds towards higher magnetic fields the enhancement isadversely affected. Pulsed DNP/NMR can help with main-taining a strong signal enhancement at high magnetic fieldstrengths [8]. Previously, pulsed DNP has been achievedusing an IMPATT diode driver [9, 10]. The pulse lengthof 50 ns at 35 mW and 140 GHz was able to excite 1% ofthe sample’s linewidth [9]. In order to capture the entirelinewidth, a shorter and more powerful pulse is needed, onthe order of 100 W to 1 kW at 1 to 10 ns, assuming a cav-ity Q of several hundred [11, 12]. For pulsed DNP/NMR,gyro-amplifiers are a good candidate for generation of therequired pulses. Additionally, the frequency scaling ofgyro-amplifiers is a useful feature for accessing various fre-quencies. To date, amplification of short pulses has beendemonstrated at 140 GHz [13], and at 250 GHz [14,15].

Contemporary gyro-amplifiers take advantage of a vari-ety of design approaches [16]. Lossy-wall gyro-amplifiershave been designed and operated at 35 GHz [17, 18] andat 95 GHz [19]. As the gyrotron frequency increases, itis advantageous for the gyrotron amplifier to operate in ahigher order mode of the interaction circuit to minimizespace charge effects and ohmic loss. One possible designfeature is a helically-corrugated interaction circuit [20,21].

A. V. Soane, M. A. Shapiro, S. Jawla, and R. J. Temkin are withthe Plasma Science and Fusion Center, Massachusetts Institute ofTechnology, Cambridge, MA. 02139. e-mail: sasha08@mit.edu

Manuscript received June XX, 2017. This work was supportedby the National Institutes of Health (NIH), National Institutefor Biomedical Imaging and Bioengineering (NIBIB) under GrantsEB004866 and EB001965.

We present a confocal interaction circuit as an alternativeto lossy-wall designs. The confocal waveguide structure isa candidate for an interaction circuit geometry that canreduce mode competition [22, 23]. Gyrotron devices withconfocal circuits continue to be studied intensively [24–28].

II. Principles of Operation

The gyro-amplifier works by transferring the energy as-sociated with the perpendicular velocity of a gyrating,mildly relativistic electron beam to the field of a microwavepulse. The microwave field is confined in the transverseelectric mode of a waveguide. The gyration of the electronbeam is supported by a magnetic field. The dispersion re-lations for the waveguide mode and the electron beam maybe written as follows:

ω2 − k2zc2 − k2⊥c

2 = 0 (1)

ω−Ω/γ− kzvz ≥ 0 (2)

where kz and k⊥ are the components of the wavevector,ω is the angular frequency, Ω = eBo/me is the cyclotronfrequency, and γ is the relativistic factor. In Ω, e is theelectron charge, Bo is the magnetic field, me is the electronmass. We note that the dispersion relations experimentallydepend on the magnetic field, the beam voltage, and thepitch factor α= v⊥/vz (in which v⊥ and vz are the perpen-dicular and axial velocity components of the electron beam,respectively). Gain occurs when the dispersion curves de-scribed by Eqs. 1 and 2 are near intersection. This canbe shown visually in Fig. 1. The ability to experimentallytune laboratory parameters such as beam voltage and mag-netic field, as well as the choice of a waveguide cutoff bymechanical design, allow the possibility to engineer an in-teraction circuit to amplify at a desired frequency range.The confocal geometry is a choice of interaction circuit thatsupports transverse electric modes and is amenable to thegyro-amplifier setup.

The confocal geometry is defined as a set of two curvedmirrors with radius of curvature Rc equal to their separa-tion distance, L⊥ (Rc = L⊥). This geometry is shown inFig. 2. The total width of each mirror, known as the aper-ture, is 2a. This width can be adjusted to either increaseor decrease the diffractive losses experienced by the sup-ported modes of this open geometry, which are the HEmn

modes. The mode numbers m and n denote the spatialvariations in the x and y directions, respectively. The ex-ample in Fig. 2 shows the HE06 mode, as indicated by thesix variations in the y direction.

2

-1000 -500 0 500 1000

kz

[m-1]

110

120

130

140

150F

req

uen

cy [

GH

z]

48 kV

HE06

HE15

HE05

Fig. 1. The dispersion curves, given by Eq. 1, are plotted for threemodes (HE06, HE15, HE05) of a confocal waveguide. Also plottedis the electron beam line given by Eq. 2. The parameters of the plotare typical for the present experiments with B0 = 5.087 T, beamvoltage of 48 kV, pitch factor α = 0.64, and confocal rail spacing of6.83 mm. The electron dispersion line is tangential to the waveguidemode curve around 140 GHz. The intersection of the electron beamline with the backward wave curves of the HE15 and HE05 modesindicates a potential source of parasitic oscillations that need to besuppressed.

Fig. 2. The confocal geometry including the field distribution of theHE06 mode. The dashed line represents the annular electron beam.

For a mirror radius of curvature Rc = 6.83 mm, 140 GHzradiation is supported by the HE06 mode. The dashedline in Fig. 2 shows the annular electron beam of radiusRb = 1.8 mm, which is seen to interact with the second andfifth peaks of the HE06 mode. As stated previously, theopen geometry of the confocal interaction circuit allows forradiative losses. This mechanism is directly responsible forthe mode selectivity of the system, as lower-order modesfeature a high attenuation per unit distance along the ax-ial dimension of the circuit. Figure 3 shows a compari-son of the HE06 and HE15 modes; the transverse extent(“footprint”) of the two modes is seen to be different. Inparticular, the broader extent of the HE15 mode in the xdirection is the reason for the attenuation per unit distancebeing higher than for the operating mode HE06.

An additional feature of the confocal circuit is that theabsence of lossy materials allows for, in principle, a contin-uous wave operation. Diffractive loss, as opposed to lossymaterials, avoids the heating that would prevent contin-

-4 -2 0 2 4

[mm]

-2

0

2

[mm]

HE06

-4 -2 0 2 4

[mm]

-2

0

2

[mm]

HE15

a) b)

Fig. 3. Contours of the horizontal component of the electric fielddistribution for the HE06 mode at 140 GHz (a) and HE15 modeat 126 GHz (b) are plotted. This field distribution is found for anaperture of 2a = 4 [mm] and Rc = 6.83 [mm]. These plots are on alinear scale with yellow showing the highest field values.

uous wave operation. The present experiments, however,were all conducted with 2 microsecond pulses.

III. Gyro-amplifier Experimental Setup

The 140 GHz gyro-amplifier experiment is centeredaround a 6.2 T Magnex Scientific magnet, which has a±1% flat field of 20 cm. Shielding in the magnet designcauses the axial magnetic field B0 to fall off as z−4 near theelectron gun’s cathode. A 12.7 mm diameter corrugatedwaveguide acts as a transmission line that brings powerfrom the RF input drive sources. A cutaway view of the1.5 m, 11.4 cm diameter stainless steel gyro-amplifier tubeis shown in Fig. 4.

a)

b)

c)

d)

f)e)

150 cm

g)

h)

Fig. 4. A cross section schematic of the confocal system setup isshown, in which a) location of electron gun, b) the gun coil magnet,c) confocal circuit, d) input waveguide, e) output waveguide, f) theoutput window, g) the ion pump, and h) the location of the inputwindow (axis normal to the page). The tube is housed inside of the6.2 T superconducting magnet.

As part of the setup to transport microwave power to thecircuit, individual sections of 20 cm corrugated waveguidewere manufactured. These were clamped together to createa length of corrugated waveguide over 2.5 m in length. Mi-crowaves are introduced into the vacuum chamber througha 3.28 mm Corning 7940 fused quartz window. This ex-tensive input transmission line setup introduces a loss tothe transported microwave power, which in the frequencyrange of interest (137 to 143 GHz) is about 6 dB in total.

It is important that the mechanical and magnetic fieldaxes are aligned because a misalignment would result inthe electron beam missing the interaction with the confo-

3

cal mode. The meter-long system that supports the con-focal circuit as well as the input and output corrugatedwaveguide is inserted horizontally into the vacuum tubeand is secured by a taper and clamp arrangement. In or-der to maintain a straight alignment to the vacuum tubemechanical axis, this meter-long system is supported bystainless steel bracers that are compressed with a springwasher when the tube is assembled.

The interaction circuit is a 20 cm set of copper railsarranged with the confocal geometry described. Their ra-dius of curvature, equal to their separation, is 6.83 mm.The aperture (2a) of these rails is 4.3 mm, which at 140GHz provides about 4 dB/cm of attenuation due to diffrac-tive losses. A cutaway schematic showing the detailed ar-rangement of the confocal rails along with the reciprocalinput/output mode converters is shown in Fig. 5

Fig. 5. The confocal circuit was fabricated with integral in-put/output mode converters. The launchers were machined fromthe same bar of copper that was used to cut the confocal rails, adesign feature that improves mechanical alignment.

The electron gun used is a CPI triode configuration,non-laminar VUW-8140 MIG gun, with nominal operat-ing parameters of 65 kV and 5.0 A of beam current. Theseconditions were designed to operate at 5.6 T to produce apitch factor α of 1.5 and a perpendicular velocity spreadof 2.7%. For use as a gyro-amplifier at 140 GHz, the gunwas ultimately run at a different operating point of 5.087T, 48 kV beam voltage, 34 kV mod-anode voltage, a pitchfactor of 0.64, and beam current up to 3 A.

The small signal gain of the gyro-amplifier is studied byusing a solid state RF driver as an input source to thesystem. This Virginia Diodes amplifier multiplier chain(AMC) has an output power of about 50 mW over a band-width of 138 to 144 GHz. The AMC is able to function aseither a continuous wave or as a pulsed source. Saturatedgain behavior is studied by using an extended interactionoscillator manufactured by CPI. This source is operated ina pulsed capacity with a pulse width of 2 microseconds overa tunable band of 139.5 to 142 GHz. The output powerinto the transmission line is about 50 W at its peak andmay be varied with an attenuator.

IV. Mode Converter Cold Test

The gyro-amplifier experiment features a 12.7 mm di-ameter corrugated waveguide for transmitting RF powerinto the vacuum tube. It is necessary to couple powerfrom the HE11 mode of the corrugated waveguide into theHE06 mode of the confocal circuit. This is accomplished

by using a quasi-optical mode converter with a Vlasov-style design [29]. A scale model of the Vlasov-style modeconverter, shown as a cutaway CAD figure in Fig. 6, wasfabricated and cold tested using a vector network analyzer(VNA). The scale model is identical to the complete struc-ture except that the length of the confocal rails is 3 cmversus 20 cm in the full structure.

Fig. 6. A CAD rendering of the cold test mode converter. Thismodel includes integrated parabolic mirrors that were machined aspart of the short confocal rail section.

The scale cold test model mode converter was fully simu-lated with the commercial software CST Microwave Studio.A comparison of both the measured (VNA) and simulated(CST) S21 parameters is shown in Fig. 7. The S21 param-eter shown is for the entire scale model, calibrated at thewaveguide input to the quasi-optical launcher, and there-fore includes the losses from both sets of launchers. Goodagreement between simulation and measurement indicatesa successful fabrication of a quasi-optical mode converterfor the confocal HE06 mode.

The quasi-optical design furthermore reduces backwardreflections in the corrugated transmission line as it avoidsthe downtaper that a fundamental waveguide WR8 in-put section would require. Additionally, the integratedparabolic mirrors, cut from the same copper section thatforms a confocal rail, helps to ensure the inline mechanicalalignment of the confocal circuit.

V. Suppression of Vacuum Pipe Modes

Numerical studies performed in CST Microwave Studioshowed that the interior wall of the vacuum chamber thathouses the confocal circuit supported vacuum pipe modesthat coupled back into the interaction region of the con-focal geometry. In order to suppress these vacuum pipemodes, the dielectric ceramic Macor was added into the

4

137 138 139 140 141 142 143

Frequency [GHz]

-15

-10

-5

0S

21 [

dB

]

CSTVNA

Fig. 7. The S21 parameter shown for both the measured (VNA) andsimulated (CST) results. Good agreement is seen between measure-ment and numerical simulation.

vacuum tube on the flanks of the confocal structure. Fig.8 shows the computed spatial mode pattern for a 126.5GHz eigenmode of the entire cross section of the vacuumtube, including the vacuum tube inner walls and the confo-cal structure, with and without the inclusion of the Macordielectric.

Confocal Rails

Fig. 8. a) 126.5 GHz mode of the entire volume of the vacuum pipewithout Macor bars. The vacuum pipe wall supports a mode that hasstrong fields at the confocal interaction region (located at the centerof the simulation and as indicated by the arrows). b) The 126.5GHz mode is seen to be suppressed by the addition of Macor bars(shown in red). These plots are on a linear scale with red showingthe location of the highest E field values.

The addition of Macor bars creates an absorptive loss,which supplements the diffractive loss mechanism of theconfocal geometry. A Q factor was computed by CST Mi-crowave Studio for the vacuum pipe modes with and with-out the Macor bars. As shown in Table I, the Macor barssignificantly dampen the quality factor of the vacuum pipemodes and help to prevent these parasitic oscillations atunwanted frequencies.

The inclusion of these Macor bars led to zero-drive sta-ble operation at beam currents above 2 A and operatingvoltages above 30 kV. This is a requirement for successfulamplifier operation at 140 GHz and for application to DNPNMR systems.

Frequency Q no Macor Q with Macor126.1 GHz 2.9e4 450126.2 GHz 4e4 480126.5 GHz 3e6 170

TABLE I

Quality factors computed for several spatial modes of the

vacuum pipe.

VI. Experimental Results

The application to DNP/NMR sets the experimental de-sign goals, which are shown in Table II. These values allowcoherent excitation of the sample linewidth [11,12].

Frequency 140.0 GHzPower > 500 W

Bandwidth > 1 GHz

TABLE II

Design goals of the 140 GHz confocal gyro-TWT

Losses in the gyro-amplifier system mean that the actualconfocal circuit interaction needs to produce a high gain inorder to achieve a high power for small signal amplification.The main sources of loss are the transmission waveguideand window setup as well as the reciprocal input/outputquasi-optical mode converters. At 140 GHz, the total lossdue to the sum of input and output coupling is about 12dB, which is the offset when comparing device and circuitgain, the latter of which may be predicted using numericalsimulations.

The numerical code MAGY was used to simulate gainin the confocal circuit [30]. At 5.08 T, 46 kV, 3 A ofbeam current and a pitch factor α of 0.8, a circuit gainof about 50 dB is predicted, provided that perpendicularvelocity spread is low at 3%. Figure 9 shows the effect ofan increase in perpendicular velocity spread from 3 to 5%.A drop in the simulated peak circuit gain from 50 to 40dB due to an increase in the velocity spread illustrates thesensitivity of amplifiers to electron beam quality.

During initial hot tests of the gyro-amplifier, parasiticoscillations in the range of 126.5 GHz were observed atoperating voltages around 45 kV and beam current of 1 A.In order to achieve high gain, operation around this voltageand a higher current of 3 A are desirable. The addition ofMacor bars allowed for zero-drive stable operation at thetarget voltage and beam current, in which the parasiticoscillations were suppressed by the mechanism described inSection V. The electron gun code MICHELLE calculatesa pitch factor α of 0.60 at the design operating point at5.08 T. The experimental data and numerical calculationare shown in Fig. 10 for the operating point of 5.08 T,46 kV, 3 A, and α of 0.60. The peak gain is measuredat 139.4 GHz and is about 35 dB of circuit gain or 23 dBdevice gain. Agreement between experiment and numericalsimulation using MAGY is achieved when perpendicular

5

Fig. 9. Simulated gain bandwidth results from the numerical codeMAGY for the case of two different velocity spreads. A drop insimulated peak circuit gain due to a slight increase in velocity spreaddemonstrates the importance of good electron beam quality. Thesesimulation results are for an operating point of 5.08 T, 46 kV, 3 A,and α= 0.8.

velocity spread is at 6%.

138.5 139 139.5 140 140.5

Frequency [GHz]

24

26

28

30

32

34

36

Cir

cuit

Gai

n [

dB

]

ExpMAGY

Fig. 10. Zero-drive stable gain bandwidth is shown as the blue linewith a peak of about 35 dB at 139.4 GHz. Good agreement is seenwith a MAGY simulation at a velocity spread of 6%. These are theexperimental results for the operating point at 5.08 T, 46 kV, 3 A,and α= 0.60.

The results in Fig. 10 were optimized for 139.4 GHz.For optimization at 140.0 GHz, the operating point wasadjusted slightly to 5.087 T, 48 kV, and 3A of beam cur-rent. At this operating point, a peak circuit gain of about35 dB (or 23 dB device gain) was measured at 140 GHzwith a 3 dB bandwidth of 1.2 GHz. This measured gainbandwidth is shown in Fig. 11. At this operating point, thenumerical electron gun code MICHELLE predicts a pitchfactor α of 0.64. Given a perpendicular velocity spread of6%, MAGY predicts a good agreement with the measuredgain.

139 139.2 139.4 139.6 139.8 140 140.2 140.4 140.6

Frequency [GHz]

27

28

29

30

31

32

33

34

35

Cir

cuit

Gai

n [

dB

]

ExpMAGY

Fig. 11. Zero-drive stable gain bandwidth is shown as the blueline with a peak of 35 dB at 140.0 GHz. Good agreement is seenwith a MAGY simulation at a velocity spread of 6%. These are theexperimental results for the operating point at 5.087 T, 48 kV, 3 A,and α= 0.64.

The saturated gain characteristics of this high gain oper-ating point were also explored. Figure 12 shows a compar-ison of measured to simulated saturated gain behavior. Atthe high gain operating point the output saturated powerreaches about 550 W at 140.0 GHz.

10-1 100 101 102

EIO Power [W]

24

26

28

30

32

34

Cir

cuit

Gai

n [

dB

]

ExpMAGY

Fig. 12. The measured saturated gain at 140.0 GHz is shown com-pared to numerical simulation using MAGY. These are the saturationresults for the operating point at 5.087 T, 48 kV, 3 A, and α= 0.64.

VII. Discussion and Conclusion

Using a newly designed set of reciprocal input/outputquasi-optical mode converters, the confocal gyro-amplifierhas demonstrated a peak circuit gain of 35 dB at 140 GHzwith a bandwidth of 1.2 GHz. At this same operatingpoint, the saturated output power at 140 GHz was mea-sured at about 550 W. The measurements were performedunder zero-drive stable conditions, necessary for applica-

6

tion to DNP/NMR. Vacuum pipe modes were identifiedand simulated successfully using CST Microwave Studio.The inclusion of dielectric Macor bars in the vacuum tubereduced parasitic oscillations, which enabled this zero-drivestability. Following the successful demonstration of zero-drive stable, high power operation, research will now com-mence on pulsed DNP/NMR experiments at MIT.

The efficiency of the gyro-TWT is limited by the largenumber N (= 270) of gyro-orbits along the 20 cm interac-tion space. In the case of no velocity spread, simple esti-mates of the amplifier efficiency predict about 4% [16,31].This efficiency agrees well with our MAGY calculations fora lossless circuit with no velocity spread. The observed re-duced efficiency of ∼ 0.4% arises primarily from velocityspread.

References

[1] L. R. Becerra, G. J. Gerfen, B. F. Bellew, et al., “A spectrome-ter for dynamic nuclear polarization and electron paramagneticresonance at high frequencies,” Journal of Magnetic Resonance,Series A, vol. 117, no. 1, pp. 28 – 40, 1995.

[2] S. Han, R. Griffin, K. Hu, C. Joo, C. Joye, J. Sirigiri, R. Temkin,A. Torrezan, and P. Woskov, “Spectral characteristics of a 140-GHz long-pulsed gyrotron,” IEEE Transactions on Plasma Sci-ence, vol. 35, no. 3, pp. 559–564, June 2007.

[3] A. C. Torrezan, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, andR. G. Griffin, “Operation of a continuously frequency-tunablesecond-harmonic CW 330-GHz gyrotron for dynamic nuclearpolarization,” IEEE Transactions on Electron Devices, vol. 58,no. 8, pp. 2777–2783, Aug 2011.

[4] V. S. Bajaj, M. K. Hornstein, K. E. Kreischer, J. R. Sirigiri, P. P.Woskov, M. L. Mak-Jurkauskas, J. Herzfeld, R. J. Temkin, andR. G. Griffin, “250 GHz CW gyrotron oscillator for dynamicnuclear polarization in biological solid state NMR,” J. Magn.Reson., vol. 189, no. 2, pp. 251–279, Dec 2007.

[5] K. E. Kreischer, C. Farrar, R. Griffin, and R. Temkin, “The useof a 250 GHz gyrotron in a DNP/NMR spectrometer,” in 23rdInternational Conference on Infrared, Millimeter and TerahertzWaves, 1998, pp. 341–357.

[6] A. C. Torrezan, S. T. Han, M. A. Shapiro, J. R. Sirigiri, and R.J. Temkin, “CW operation of a tunable 330/460 GHz gyrotronfor enhanced nuclear magnetic resonance,” in 33rd InternationalConference on Infrared, Millimeter and Terahertz Waves, Sept.2008.

[7] M. K. Hornstein, V. S. Bajaj, R. G. Griffin, and R. J. Temkin,“Continuous-wave operation of a 460-GHz second harmonicgyrotron oscillator,” IEEE Transactions on Plasma Science,vol. 34, no. 3, pp. 524–533, June 2006.

[8] T.V. Can, Q.Z. Ni, and R.G. Griffin, “Mechanisms of dynamicnuclear polarization in insulating solids,” Journal of MagneticResonance, vol. 253, pp. 23 – 35, 2015, special Issue: RecentAchievements and New Directions in Biomolecular Solid StateNMR.

[9] M. Bennati, C. T. Farrar, J. A. Bryant, S. J. Inati, V. Weis, G. J.Gerfen, P. Riggs-Gelasco, J. Stubbe, and R. G. Griffin, “Pulsedelectron-nuclear double resonance (ENDOR) at 140 GHz,” J.Magn. Reson., vol. 138, no. 2, pp. 232–243, June 1999.

[10] R. G. Griffin and V. Weis, “Electron-nuclear cross polarization,”Solid State Nucl. Magn. Reson. (USA), vol. 29, no. 1-3, pp. 66–78, Feb. 2006.

[11] E. A. Nanni, A. B. Barnes, Y. Matsuki, P. P. Woskov, B. Corzil-ius, R. G. Griffin, R. J. Temkin, “Microwave field distributionin a magic angle spinning dynamic nuclear polarization NMRprobe.” Journal of magnetic resonance, vol. 210 1, pp. 16–23,2011.

[12] T. V. Can, J. J. Walish, T. M. Swager, and R. G. Griffin, “Timedomain dnp with the novel sequence,” The Journal of ChemicalPhysics, vol. 143, no. 5, p. 054201, 2015.

[13] H. J. Kim, E. A. Nanni, M. A. Shapiro, J. R. Sirigiri, P. P.Woskov, and R. J. Temkin, “Amplification of picosecond pulsesin a 140-GHz gyrotron-traveling wave tube,” Phys. Rev. Lett.,vol. 105, 135101, Sept. 2010.

[14] E. A. Nanni, S. M. Lewis, M. A. Shapiro, R. G. Griffin, and R.J. Temkin, “Photonic-band-gap traveling-wave gyrotron ampli-fier,” Phys. Rev. Lett., vol. 111, 235101, Dec 2013.

[15] E. A. Nanni, S. Jawla, S. M. Lewis, M. Shapiro, and R. J.Temkin, “Amplification of picosecond pulses with a photonic-band-gap gyro-TWT,” in 2016 IEEE International VacuumElectronics Conference (IVEC), April 2016.

[16] G. S. Nusinovich, Introduction to the Physics of Gyrotrons. TheJohns Hopkins University Press, 2004.

[17] K. R. Chu, H. Y. Chen, C. L. Hung, T. H. Chang, L. R. Barnett,S. H. Chen, and T. T. Yang, “Ultrahigh gain gyrotron travelingwave amplifier,” Phys. Rev. Lett., vol. 81, pp. 4760–4763, Nov.1998.

[18] K. R. Chu, H. Y. Chen, C. L. Hung, et al, “Theory and ex-periment of ultrahigh-gain gyrotron traveling wave amplifier,”IEEE Transactions on Plasma Science, vol. 27, no. 2, pp. 391–404, April 1999.

[19] L. R. Barnett, W. C. Tsai, H. L. Hsu, N. C. Luhmann, C. C.Chiu, K. F. Pao, and K. R. Chu, “140 kW W-band TE01 ultrahigh gain gyro-TWT amplifier,” in IEEE International VacuumElectronics Conference held Jointly with 2006 IEEE Interna-tional Vacuum Electron Sources, 2006, pp. 461–462.

[20] G. G. Denisov, V. L. Bratman, A. D. R. Phelps, et al., “Gyro-TWT with a helical operating waveguide: new possibilities toenhance efficiency and frequency bandwidth,” IEEE Transac-tions on Plasma Science, vol. 26, no. 3, pp. 508–518, June 1998.

[21] V. L. Bratman, G. G. Denisov, S. V. Samsonov, A. W. Cross,A. D. R. Phelps, and W. Xe, “High-efficiency wideband gyro-TWTs and gyro-BWOs with helically corrugated waveguides,”Radiophysics and Quantum Electronics, vol. 50, no. 2, pp. 95–107, 2007.

[22] J. R. Sirigiri, M. A. Shapiro, and R. J. Temkin, “High-power140-GHz quasioptical gyrotron traveling-wave amplifier,” Phys.Rev. Lett., vol. 90, 258302, June 2003.

[23] C. D. Joye, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin,“Demonstration of a 140-GHz 1-kW confocal gyro-traveling-wave amplifier,” IEEE Transactions on Electron Devices,vol. 56, no. 5, pp. 818–827, May 2009.

[24] Y. Yang, S. Yu, T. Z. Zhang, Y. Zhang, and Q. Zhao,“Study of beam-wave interaction in a 170-GHz confocal gyrotrontraveling-wave tube,” IEEE Transactions on Plasma Science,vol. 43, no. 3, pp. 791–795, March 2015.

[25] Y. Yang, S. Yu, Y. Liu, T. Zhang, Y. Zhang, and Q. Zhao,“Efficiency enhancement of a 170 GHz confocal gyrotron trav-eling wave tube,” Journal of Fusion Energy, vol. 34, no. 4, pp.721–726, 2015.

[26] G. S. Nusinovich, S. Chainani, and V. L. Granatstein, “Effect ofthe transverse nonuniformity of the radiofrequency field on thestart current and efficiency of gyrodevices with confocal mir-rors,” Physics of Plasmas, vol. 15, 103106, 2008.

[27] W. Fu, X. Guan, and Y. Yan, “High harmonic terahertz confocalgyrotron with nonuniform electron beam,” Physics of Plasmas,vol. 23, 013301, 2016.

[28] W. Hu, M. A. Shapiro, K. E. Kreischer, and R. J. Temkin, “140-GHz gyrotron experiments based on a confocal cavity,” IEEETransactions on Plasma Science, vol. 26, no. 3, pp. 366–374,Jun 1998.

[29] S. N. Vlasov, L. I. Zagryadskaya, and M. I. Petelin, “Transfor-mation of a whispering gallery mode, propagating in a circularwaveguide, into a beam of waves,” Radiotekhnika i Elektronika,vol. 20, pp. 2026–2030, Oct. 1975.

[30] M. Botton, T. M. Antonsen, B. Levush, K. T. Nguyen, andA. N. Vlasov, “MAGY: a time-dependent code for simulationof slow and fast microwave sources,” IEEE Transactions onPlasma Science, vol. 26, no. 3, pp. 882–892, June 1998.

[31] V. L. Bratman, N. S. Ginzburg, G. S. Nusinovich, M. I. Pe-telin, and P. S. Strelkov, “Relativistic gyrotrons and cyclotronautoresonance masers,” International Journal of Electronics,vol. 51, no. 4, pp. 541–567, 1981.