Danly, B.G.

Mulligan, W.J.

Sollner, T.C.

Temkin, R.J.

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PFC/JA-84-34High Power Second Harmonic Emission and FrequencyLocking in a 28 GHz GyrotronB.G. Danly, W.J. Mulligan, and R.J. TemkinPlasma FVsion CenterMassachusetts Institute of TechnologyCambridge, MA 02139andT.C.L.G. SollnerLincoln LaboratoryMassachusetts Institute of TechnologyLexington, MA 02139This work was supported by the U.S. Department of EnergyContract No. DE-AC02-78ET51013.By acceptance of this article, the publisher and/or recipientacknowledges the U.S. Government's right to retain anonexclusive royalty-free licence in and to any copyrightcovering this paper,1AbstractTwo important new results are presented from a study of secondharmonic (2wc) emission from a pulsed gyrotron designed forfundamental (wc) emission of 200 kW at 28 GHz in the TE021 mode.Mode locking between two modes of a gyrotron has been observed for thefirst time; one mode oscillates at w - wc and the other at exactlytwice that frequency. Strong, single mode 2wc emission (80 kW at50 GHz) is also observed, and such emission is shown to be characteristicof gyrotrons designed for high power emission at the fundamental.2High power, high frequency gyrotronsi-4 are of great importance tocontrolled fusion research; their applications include both electroncyclotron resonance heating (ECRH)5-8 and plasma diagnostics. 9-'1 Withthe growing demand for gyrotrons suitable for these applications, increasingthe gyrotron operating frequency becomes of primary importance. Operationat the second (w m 2wc) or higher harmonics (nwc, n > 2) of thecyclotron frequency, wc, would utilize a magnetic field smaller by n thanthat required for operation at the fundamental.12-1 4  Here, wc equalseBo/ymec, where B0 is the magnetic field, me and e the electron mass andcharge, c the speed of light, and Y = (1 + U/Mrec 2) where U is the electron energy.We report here the results of a study of second harmonic emissionfrom a gyrotron oscillator designed for high power operation at thefundamental. This study was performed on a Varian 28 GHz gyrotron, which wasdesigned to produce 200kW in the TE0 2 1 mode in long pulse operation.Although many parameters were varied in this study, such as current andvoltage, the data obtained were primarily dependent on the magneticfield at the cavity. Gyrotrons operate in circular TE modes near cutoff, thatis w/c = k = (k2 + k2) 1/2 with kg >> kj , where k± and k,, are the transverseand axial wavenumbers of the waveguide modes. In this case, we may takew/c = k kj = vmp/R for TE modes, where R is the cavity radiusand Vmp is the pth zero of J (x). The combination of this conditionand the condition w w nwc determine the oscillation mode of a gyrotron oscillatoras the magnetic field is varied. We have observed a high power second harmoniccavity mode: 80 kW at 50.38 GHz in the TE43 1 mode with 21% efficiency.This mode was not observed in previous studies of this gyrotron. Themagnetic fields corresponding to this mode and the two high powerfundamental modes in which this gyrotron also operates are shown in Table 1.3As a second result of this study, we have also observed harmonicemission at exactly twice the frequency of the emission at the fundamental.Because the frequency of the second harmonic emission we have observedis exactly twice the fundamental frequency, it is likely to result froma frequency locking or parametric effect rather than from ordinarycavity emission. Hence, we refer to it as parametric emission. Theexistence of this parametric emission is interesting both from ascientific point of view and because it could have deleterious effectsin gyrotrons designed for plasma diagnostics or communications wherespectral purity is of great importance. To our knowledge., such parametricemission has not been previously observed in a gyrotron.A diagram of the gyrotron and experimental apparatus is shown in Fig. 1.Although capable of long pulse operation (up to 1OOms), the gyrotron pulse lengthwas limited to < 300ps for this study; the pulse repetition rate was 1.4 Hz.There is a short length of output waveguide with a side hole coupled toKa-band (26.5 - 40 GHz) waveguide on the output side of the gyrotronwindow, followed by an asymmetric mode filter and the main outputwaveguide (inside diameter = 6.35 cm). The radiation is emitted fromthe open end of the output waveguide. At the side port, a Ka-band3 dB directional coupler splits the signal into two Ka-band waveguides.One waveguide is connected to a Ka-band wavemeter, attenuator, anddiode. The other waveguide was connected through a transitionto V-band (50 - 75 GHz) waveguide. The V-band cutoff occurs at 39.9GHz. A V-band wavemeter, attenuator, and diode were connected to the V-band waveguide. With this apparatus both the wc and 2 wc signalscan be detected, and only gyrotron emission at the second harmonic isdetected with the V-band diode.4Although the diodes at the side port output coupler were usefulfor locating the regions of oscillation at the second harmonic, the wcand 2Wc signals were also monitored in the far field of the outputwaveguide (Fig. 1). For direct measurement of the far-field pattern of theradiation emitted from the gyrotron, a large box, lined with microwaveabsorbing foam, was constructed. The Ka- and V-band diodes were placedon movable arms in this box for far-field measurements.The frequency of the observed emission was measured by two independentmethods. The first method was the use of wavemeters in Ka- and V-bandwaveguide. This method has reasonable accuracy and has the advantage of onlybeing sensitive to the radiation in the designated band. The second method wasa harmonic mixing technique with an accuracy of ± 5 MHz for a single pulse.A diagram of the harmonic mixing apparatus is shown in Fig. 2 and describedin detail elsewhere.4 For the strong wc and 2wc modes, powermeasurement was obtained by calorimetry with a modified Varian modelVLA-8050C water calorimeter. Estimates for the power of the weaker2wc modes were obtained from a calibration of the diode responsivityand an integration over the far field pattern.The theoretical efficiency of a gyrotron at the nth harmonic canbe obtained by a numerical integration of the equation of motion for anelectron moving in combined axial magnetic and rf electric fields.Numerical results have been presented by Nusinovich and Erm15 for n=1and n=2 in the form of a contour plot of efficiency as a function oftwo parameters, the normalized beam current,2(3-n) 5-2n 2I0 = (0.24 x 103 3. J~0 (( TA 2nn) [V2 -m2 J 2(viimp m mp5and the normalized cavity length, 4 = *L/O11X In these equations,I, QT, L, Re, 0j, Ou, and X are the current, total cavity Q, effectivecavity length, electron beam radius, transverse and axial electronvelocity divided by c, and the wavelength (2wc/w), respectively.The efficiency of operation at 2wc in a gyrotron designed foroperation at wc can be obtained from a scaling of 10 and p.14 Thevalues of Io and P for the fundamental correspond to gyrotron operationin the high efficiency zone (0.4 < n < 0.7, n.= transverse efficiency).At nearby values of the magnetic field, there exist cavity modes resonantat w - 2wc. We have found that the values of Io and ii.for thesesecond harmonic modes often fall in a high efficiency zone (0.2 < n <0.4) [see Ref. 14 for a detailed analysis]. This implies that gyrotronoscillators designed for high efficiency operation at the fundamentalwill in general have efficient 2wc modes nearby. It is theobservation of a correlation of high efficiency between wc and 2wcmodes that is demonstrated by the present results.Experimental evidence of strong second harmonic emission in a gyrotrondesigned for operation at the fundamental is provided by the observationof the TE43 1 cavity mode at 50.38 GHz. The mode was identified byan accurate measurement of the frequency and confirmed by a measurement ofthe far-field radiation pattern which is in reasonable agreement with theory.The voltage and current for which this mode was excited are 77.5 kVand - 5A. An output power of 80kW was observed with a water calorimeter;this corresponds to a total efficiency of 21%. The theoretical totalefficiency was calculated from a nonlinear theory and is approximately40%.15 A scan of calorimeter power versus magnetic field shows thatthe TE43 1 2wc mode is well separated from the TE22 1 fundamentalmode, which occurs at a slightly higher magnetic field.6In addition to the observation of high power, 2wc cavity emissionin the TE4 3 1 mode, frequency-locked, parametric emission was also observed.Under certain operating conditions, and present simultaneously withfundamental emission in either the TE0 2 1 or TE22 1 modes, harmonicemission at exactly twice the frequency of the fundamental mode was observed.We have observed this parametric emission during operation in both theTE02 1 and TE22 1 modes; however, the parametric emission associatedwith the TE2 2 1 mode is much stronger than that associated with theTE021 mode.For operation in the TE2 2 1 mode, the measured frequency of thefundamental emission was 26.78 GHz; the frequency of the 2wc emissionassociated with the TE2 2 1 mode is 53.56 GHz, which is exactly twice thefundamental frequency. At a slightly higher value of the magnetic field, thefundamental emission frequency is pulled by dispersion to a value of 26.81 GHzand the 2wc emission is found at 53.62 GHz. The harmonic frequencyis thus observed to track the wc frequency as the magnetic field isvaried, further evidence of a frequency locking phenomenon. Observation ofthe relative powers indicates that the fundamental and second harmonicpowers also show a positive correlation. In addition, this parametricemission is only observed when strong fundamental emission is alsooccuring. This contrasts with the previously described cavity 2wcemission which is suppressed by emission at the fundamental and thushas a negative power correlation with the fundamental.An estimate of the power at the harmonic was made with a calibrateddiode and an integration over the far field pattern. For an outputpower of - 150 kW in the TE2 2 1 mode, the harmonic power level7was - 100 W. While harmonic content of this magnitude is negligiblefor gyrotron applications such as plasma heating, it is potentiallydetrimental for applications such as communications and plasma diagnostics.For operation in the fundamental TE0 2 1 mode at a frequency of28.04 GHz, very weak emission at 56.07 GHz was also detected.Varying the magnetic field changes the frequency at the fundamental(by up to 1%) due to dispersion in the cavity resonance. Emission atthe second harmonic was observed to remain locked at exactly twice thefundamental frequency. We estimate that the power of this harmonicemission is about 1 W.The origin of this parametric harmonic emission associated withthe TE221 and TE0 2 1 modes is not known. Because the eigenmodesof a right circular cylinder do not form an equidistant spectrum, thereare in general no cavity eigenmodes at exactly twice the value of kfor the fundamental. Consequently, the generation of radiation atharmonics of the cyclotron frequency does not occur at an exact multipleof the fundamental frequency. The parametric emission data has beenanalysed using the waveguide and cyclotron resonance conditions, but weare unable to identify with certainty any likely cavity modes responsiblefor the 2wc emission associated with either the TE2 2 1 or TE02 1fundamental modes. To our knowledge, this is the first experimentalevidence of the locking of two modes in a gyrotron. Although a theoryof mode locking and parasitic mode excitation has been developed byNusinovich, that theory is not directly applicable to the locking oftwo modes at different harmonics observed here.1 6 It is possiblethat the parametric harmonic emission observed here results from emission8at the second harmonic component of the beam which is modulated by thestrong field at the fundamental. A similar phenomenon is observed inklystrons. The emission could occur in the cavity or uptaper/collectorregion of the gyrotron; strong frequency pulling and a low Q couldaccount for the difficulty of identifying the emission as a particularcavity mode. Ergakov and MoiseevI7 have described a theory of harmonicemission from a premodulated beam in a gyroklystron, a phenomenonsimilar to the present result.In summary, two important results concerning harmonic emission in gyrotronshave been described. One result, observation of parametric secondharmonic generation, is of scientific interest and has important implicationsfor gyrotrons designed for plasma diagnostics and communications. Theexploitation of mode locking in gyroklystrons may also prove useful.The second result, the generation of high power, high efficiency secondharmonic cavity emission, supports the theoretical argument that ingyrotrons designed for low Q operation at the fundamental, emission atthe second harmonic will be strong and efficient. This is a potentialproblem for high power gyrotrons, but it is also a potential technologicalbenefit, allowing the study of ECRH in plasmas at higher frequenciesthan are available from a fundamental gyrotron.We are grateful to M. Mauel and M. Dunham for allowing us theopportunity to perform the above experiments with their gyrotron. Wethank R. Shefer for loan of the Ka-band microwave equipment, K.Kreischer for many helpful discussions, and J. Byerly for assistancewith the experiment. The Plasma Fusion Center research was conductedunder U.S.D.O.E. Contract DE-AC02-78ET51013; the Lincoln Laboratory portionof this work was sponsored by the Department of the Air Force.9References1) Carmel, Y., et al., Phys. Rev. Lett. 50, 112 (1983).2) Gaponov, A.V., et al., Int. J. Electron. 51, 277 (1981).3) Felch, K., et al., Eighth Int. Conf. Infrared and Millimeter Waves (1983).4) Kreischer, K.E., et al., Int. J. Electron. (to be published, 1984).5) Hsuan, H., et al., Fourth Int. Symp. on Heating in Toroidal Plasmas,Rome (1984).6) Prater, R., et al., General Atomic report GA-A17026 (1983).7) Alikaev, V.V., et al., Sov. J. Plasma Phys. 9, 196 (1983).8) Gilgenbach, R.M., et al., Phys. Rev. Lett. 44, 647 (1980).9) Woskoboinikow, P., Cohn, D.R., and Temkin, R.J., Int. J. Infraredand Millimeter Waves 4, 205 (1983).10) Fiks, A. Sh., et al., Fourth Int. Symp. on Heating in ToroidalPlasmas, Rome (1984).11) Cohn, D.R., et al., Bull. American Phys. Soc. 28, 1181 (1983).12) Zaytsev, N.E., et al., Radio Eng. and Electron. Phys. 19, 103 (1974).13) Zapevalov, V.E., et al., Radiophys. and Quantum Electron. 22, 254 (1979).14) Byerly, J.L., et al., Int. J. Electron. (to be published, 1984).15) Nusinovich, G.S., and Erm, R.E., Elektronnaia Tekhnika 8, 55 (1972).16) Nusinovich, G.S., Int. J. Electron. 51, 457 (1981).17) Ergakov, V.S., and Moiseev, M.A., Radio Eng. and Electron. Phys. 22,88 (1977).-10-Figure CaptionsFig. 1 Diagram of Experiment. M: Mode filter, 0: Output Waveguide,A: Attentuator, WM: Wavemeter. Dka and Dv are detectors for theKa- and V-bands.Fig. 2 Diagram of Harmonic Mixing System. AMP: Amplifier, S: Switch,IF: intermediate frequency, S.A.W. filter: Surface acoustic wavefilter.-11-Table 1. High Power Oscillation ModesMode Harmonic Freq.[GHzI Magnetic Field [T]TE4 3 1TE221TE0212wcWe50.3826.7828.041.001.061.10JIDAp 4DVV bandAI3UBW Ka band'Im L28 GHzGYROTRONRNPUT MIXER F T R .9 ONTRDELAY APLOCALIiosc. . -GYROTRONTRIG. --

High power second harmonic emission and frequency locking in a 28 GHz gyrotron

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High power second harmonic emission and frequency locking in a 28 GHz gyrotron

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