A Numerical Study on Finite-Bandwidth Resonances of High-Order Axial Modes (HOAM) in a Gyrotron Cavity

Abstract

Many novel and prospective applications of the gyrotrons as sources of coherent radiation require a broadband and continuous frequency tunability. A promising and experimentally proven technique for the latter is based on a successive excitation of a sequence of high-order axial modes (HOAM) in the cavity resonator. Therefore, the studies on HOAM are of both theoretical and practical importance. In this paper we present and discuss the methods and the results of a numerical investigation on the resonances of HOAM in a typical open gyrotron cavity. The simulations have been performed using the existing as well as novel computational modules of the problem oriented software package GYROSIM for solution of both the homogeneous and the inhomogeneous Helmholtz equation with radiation boundary conditions, which governs the field amplitude along the axis of the resonant structure. The frequency response of the cavity is studied by analyzing several resonance curves (spectral domain analysis) obtained from the numerical solution of the boundary value problem for the inhomogeneous Helmholtz equation by the finite difference method (FDM). The approach proposed here allows finite-bandwidth resonances of HOAM to be identified and represented on the dispersion diagram of the cavity mode as bands rather than as discrete points in contrast to the frequently used physical models that neglect the finite width of these resonances. Developed numerical procedures for calculation of the field profiles for an arbitrary frequency and excitation will be embedded in the cold−cavity and self-consistent codes of the GYROSIM package in order to study the beam−wave interaction and energy transfer in gyrotron cavities.

Fundamentals of Electron Cyclotron Resonance and Cyclotron Autoresonance in Gyro-Devices: A Comprehensive Review of Theory

“…The axial field profile is described by the Helmholtz equation, which is supplemented by certain boundary conditions. The analysis of the solutions of this equation leads to a more detailed picture of the resonances with finite bandwidths and is discussed in [28]. According to this approach, the resonances should be represented by zones (bands) rather than points.…”

“…Following the same approach as before, we express the transverse magnetic field of the TM mode through the corresponding transverse electric field using ( 24) and (28). In such a way, we rewrite (32) in the following form:…”

The Gyrotrons as Promising Radiation Sources for THz Sensing and Imaging

“…The first one is step-wise, and the tunability is being achieved switching to different operating modes by varying the cyclotron frequency (see Equation 1), changing the accelerating voltage (and thus γ) or the magnetic field. The second one is a smooth continuous tunability, which is based on the excitation of a sequence of high-order axial modes (HOAM) [51]. The third possibility (which is rarely used due to the additional technical complications that it introduces) involves changing the dimensions and the shape of the cavity mechanically or by temperature control of the expansion/contraction of the resonator [52].…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…Several hundred of milliwatts are observed when operating at the second harmonic. The authors emphasize and discuss the mode competition problem.High order axial (longitudinal) mode excitation by changing the magnetic field is a proven technique for obtaining wide range frequency tuning capabilities[48]. By using high order modes, smooth change is observed, as the characteristic values of the following T E m,n,k modes, where k is changing, are closely spaced.…”