This paper presents a comprehensive theory of the cyclotron resonance maser (CRM) interaction in a circular waveguide. The kinetic theory is used to derive the dispersion relationships for both TE and TM modes. The TE mode case has been investigated by several authors, but there has been comparatively little work on the TM mode case. However, the TM mode interaction competes effectively with the TE mode interaction at relativistic electron energies. The conditions for maximum temporal and spatial growth rates are shown. The TM mode growth rates are found to vanish when the RF wave group velocity equals the beam axial velocity (‘grazing incidence’). The single particle theory is used to derive a compact set of self-consistent non-linear equations for the TE and TM mode interactions. These equations are particularly appropriate for the cyclotron auto-resonance maser (CARM) regime but applicability extends to other regimes as well. The conditions for optimum efficiency are investigated for oscillator and amp...

Linear and nonlinear theory of the Doppler-shifted cyclotron resonance maser based on TE and TM waveguide modes

This paper presents linear and self-consistent nonlinear theories to describe the beam-wave interaction in a gyrotron traveling wave amplifier (gyro-TWA) with a misaligned electron beam. A linear theory based on the linearized Vlasov equations is developed by using Laplace transforms. By setting appropriate initial values of the electron guiding center, the nonlinear theory without misalignment can be used to study the misalignment effect. The two theories are in good agreement in the small-signal region for the gyro-TWA. The effects of beam misalignment on the TE01 mode gyro-TWA operating at the fundamental are discussed and the corresponding physical mechanism is analyzed.

Linear and nonlinear analysis of a gyrotron traveling wave amplifier with misaligned electron beam

A linear theory for a rectangular waveguide cyclotron maser with a sheet electron beam is developed by using the Laplace transformation approach. This theory can be applied to any TEmn rectangular waveguide mode. The corresponding equations for the TMmn mode in the rectangular waveguide are also derived as a useful reference. Especially, the effect from the coupling between degenerate modes, which is induced by the nonideal rectangular waveguide walls, on the dispersion relation is considered in order to provide a more accurate model for the real devices. Through numerical calculations, the linear growth rate, launching loss, and spontaneous oscillations (caused by the absolute instability and backward wave oscillation) of this new structure can be analyzed in detail. It is worthwhile to point out that the operation at higher power levels of the rectangular waveguide sheet beam system is possible.

Linear analysis of a rectangular waveguide cyclotron maser with a sheet electron beam

In the fast-wave devices like gyrotron, gyro-peniotron and cyclotron autoresonance maser (CARM) that generate millimeter and sub-millimeter waves, the transverse dimensions of the resonator and the output cylindrical waveguide become small. In order to prevent loss of electrons and thermal loading of the rf structure, the electron beam must be kept relatively far from the walls. The latter requirement demands smaller transverse dimensions of the helical electron beam as well. In this paper linear formulation of a CARM operating in a general transverse-magnetic (TM) mode is derived, and a detailed analysis of the influences of the parameters is presented for the TM1,1 mode CARM. It is found that, compared to the TE1,1 mode which is often employed in gyrotron traveling wave tube (gyro-TWT) and CARM experiments, the TM1,1 mode has a greater eigen value and consequently leads to a greater waveguide radius for a given cutoff wave number, and also, allows the electron beam to be settled close to the waveguide axis to have a small transverse dimension. Results show that a TM-mode CARM can reach high power and ultrahigh gain, just as a TE-mode CARM or a TE-mode gyro-TWT does.

Linear Analysis of a Cyclotron Autoresonance Maser (CARM) Operating in a Transverse Magnetic Mode

In the fast-wave devices like gyrotron, gyro-peniotron and cyclotron autoresonance maser (CARM) that generate millimeter and sub-millimeter waves, the transverse dimensions of the resonator and the output cylindrical waveguide become small. In order to prevent loss of electrons and thermal loading of the rf structure, the electron beam must be kept relatively far from the walls. The latter requirement demands smaller transverse dimensions of the helical electron beam as well. In this paper linear formulation of a CARM operating in a general transverse-magnetic (TM) mode is derived, and a detailed analysis of the influences of the parameters is presented for the TM 1,1 mode CARM. It is found that, compared to the TE 1,1 mode which is often employed in gyrotron traveling wave tube (gyro-TWT) and CARM experiments, the TM 1,1 mode has a greater eigen value and consequently leads to a greater waveguide radius for a given cutoff wave number, and also, allows the electron beam to be settled close to the waveguide axis to have a small transverse dimension. Results show that a TM-mode CARM can reach high power and ultrahigh gain, just as a TE-mode CARM or a TE-mode gyro-TWT does.

A linear theory of the electron cyclotron maser, which is applicable to any TM circular waveguide mode, is developed by using Laplace transforms. This theory can be used to analyze the linear behaviors of both the TM mode gyrotron traveling wave tube (gyro-TWT) and the TM mode gyrotron backward wave oscillator (gyro-BWO). Numerical results show that, although the TM mode is less effective than the TE mode for the gyro-TWT interaction, the TM mode may be as effective as the TE mode for the gyro-BWO interaction, even in the case of weak relativistic electron energy.

Jirun Luo

Papers

Linear theory of the electron cyclotron maser based on TM circular waveguide mode