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High power gyrotrons, including both CW and high peak power configurations, are increasingly designed to operate in high mode density regimes. It has been observed that operation is often single-moded even for cavities with dense mode spectra, but the mode density does affect the gyrotron efficiency and the available operating modes. Multimode effects have been studied extensively for the quasi-optical gyrotron but there has been less progress on fully nonlinear formulations for conventional waveguide cavity gyrotrons which involve different transverse modes with irregularly spaced frequencies and unequal coupling impedances. A time-dependent, nonlinear, multimode theory of gyrotrons has been recently developed along with a computer code to carry out the numerical calculations. The code has been used to simulate the operation of a CW-relevant 140 GHz gyrotron experiment carried out at MIT and the 750 kV, 35 GHz intense-beam gyrotron experiment at NRL. The MIT gyrotron involves competition between two transverse modes: the TE03 and TE23 modes. The NRL gyrotron involves competition between TEm2 modes and is an example of a three-mode interaction.

High power gyrotrons, including both CW and high peak power configurations, are increasingly designed to operate in high mode density regimes. It has been observed that operation is often single-moded even for cavities with dense mode spectra, but the mode density does affect the gyrotron efficiency and the available operating modes. Multimode effects have been studied extensively for the quasi-optical gyrotron but there has been less progress on fully nonlinear formulations for conventional waveguide cavity gyrotrons which involve different transverse modes with irregularly spaced frequencies and unequal coupling impedances. A time-dependent, nonlinear, multimode theory of gyrotrons has been recently developed along with a computer code to carry out the numerical calculations. The code has been used to simulate the operation of a CW-relevant 140 GHz gyrotron experiment carried out at MIT and the 750 kV, 35 GHz intense-beam gyrotron experiment at NRL. The MIT gyrotron involves competition between two transverse modes: the TE03 and TE23 modes. The NRL gyrotron involves competition between TEm2 modes and is an example of a three-mode interaction.

The gyrotron (or, electron cyclotron maser) operates on the interaction of a TE cavity mode with the relativistic electron cyclotron beam mode. This instability has been seen both theoretically and experimentally to be a very efficient source for microwave generation, useful for the heating of tokamak plasmas at the electron cyclotron frequency. The next generation of tokamaks involves high confining fields and accordingly the gyrotron must produce short (approx. 2mm) wavelength radiation, which can be realized only by a highly overmoded operation of the gyrotron. This work presents the groundwork for the study of such an overmoded operation. The self-consistent nonlinear equations have been obtained for the evolution of the electron distribution and of the power spectrum for multimode gyrotron interactions in a rectangular cavity or waveguide. The time step of the resulting algorithm is limited only by the nonlinearities and nonuniformities, and therefore yields very efficient simulations. The equations have been applied to the following cases: (a) in a waveguide, analytically, to obtain the dispersion relation and saturation behavior of a monochromatic wave with two-dimensional transverse structure; (b) in a waveguide, numerically, to test the correctness and accuracy of the computer code; (c) in a waveguide with external field (or equivalent) nonuniformities, to interpret the associated efficiency enhancement; and (d) in a two-mode cavity, to study the evolution and saturation of the eigenmodes. (Author)

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Experimental and theoretical results are presented for the second harmonic emission from a pulsed, high power gyroton designed for high frequency fundamental operation. This present study indicates that second harmonic emission can achieve high power levels at very high frequencies with reasonable efficiencies. Using available superconducting magnets and second harmonic operation, high power emission well into the submillimeter appears feasible.

A time-dependent slow-time-scale theory is developed for gyrotron oscillators driven by an external signal. The signal is introduced either directly into the cavity output or via a beam prebunching cavity. The theory is applied to a high voltage gyrotron configuration and the numerical, nonlinear calculations are compared with simple analytical estimates of the frequency bandwidth for phase-locked operation. For the case of direct injection, the non- linear slow-time-scale calculations are in good agreement with Adler's relation. Two approaches are investigated for the case of phase-locking with a prebunching cavity. In the first the induced as current density due to the prebunching cavity is treated as a small perturbation of the ac current density in the oscillator. In this approach the equations for the time-dependent wave amplitude and phase are similar in structure to the equations for gyrotrons driven by direct injection and lead to a simple analytical estimate of the locking bandwidth. The accuracy of the perturbation approach is investigated by comparing it with the results of an alternate approach used in the analysis of gyro-klystrons. The maximum phase-locking bandwidth obtainable with the prebunching cavity approach is discussed.

The objective of this research program was to explore tapering of interaction tubes and magnetic fields as techniques for enhancing the performance of high power microwave gyrotron-backward-wave- oscillators (gyro-BWOs). Experiments were performed on the Michigan Electron Long-Beam Accelerator, (MELBA), which operated with parameters: voltage=O.7-O.9 MV, diode current = 1-10 kA, injected current = 1-4 kA, and pulselengths of 0.5-i microsecond. Microwave emission frequency was in the range from 4.5-6 GHz. Experiments on the fundamental cyclotron wave showed peak microwave tube power up to 40-55 MW over shortened pulselengths (<100 ns). Longer pulse microwave emission was obtained at lower powers (multi-MW). The second harmonic gyro-BWO emission spectrum was also measured at MW power levels. The microwave spectral width was < 200 MHz (<3.7%) for uniform B field with uniform or tapered tubes. Widened spectra of 200-400 MHz (<7.4%) were measured for tapered magnetic fields with uniform or tapered tubes. Modeling was performed with the MAGIC code to guide the experiments. Results showed qualitative agreement between TE11 mode experiments and TE01 MAGIC Code simulations, regarding microwave power versus tapering direction and scaling. (KAR) P. 3

A time dependent slow time scale theory is developed for the analysis of high power, pulsed gyrotrons. Calculations are carried out to simulate the operation of a 35 GHz hig voltage gyrotron. Both free running and phase locked oscillator configurations are examined, and the effect of a voltage ripple is shown. Keywords: High power; Phase locked gyrotron oscillators; Intense relativistic electron beams; Pulse line accelerator; Interacting modes; Short pulse length; Voltage risetime.