An Approach to Thermal Analysis of Helically Corrugated Waveguide Elements of Vacuum Electron Devices

Metallic helically corrugated structures play an important role in microwave vacuum electron devices serving as wave converters, wave compressors, and interaction circuits. Thermal analysis of such structures operating in a high-power regime is important for their design and development. In this paper, an algorithm for an efficient analysis of temperature distribution in helically corrugated metallic structures caused by Ohmic losses in their walls is presented. The algorithm is based on the coordinates transformation with the subsequent expansion of the equations to the Fourier series with respect to the longitudinal coordinate. The advantages and limitations of the algorithm are discussed. Comparison with a 3-D finite-element simulation was performed, and a sufficiently good agreement was demonstrated.

I. Introduction

Metallic structures having helical corrugation of the inner wall have found numerous applications in vacuum microwave electronics devices, such as wave converters [1], wave compressors [2], interaction circuits for electron tubes [3], particle accelerators [4], and undulators [5]. Apart from other factors, such as the electrical break down, the maximum operating power of vacuum electron devices and components is limited by the overheating caused by the dissipation of a fraction of the propagating wave power due to Ohmic losses in their walls [6]–[8]. It should be noted that along with an electromagnetic properties evaluation, the thermal analysis often becomes an inseparable part of studies of various objects and devices in the medical [9]–[11] and industrial [12]–[15] domains. For the high-power vacuum electron devices, such as gyrotron traveling-wave tubes (Gyro-TWTs) [3], [16], [17], the thermal limitation becomes increasingly severe at higher operating frequencies due to the increase of the reactive part of the surface impedance and miniaturization of the device, so a correct prediction of the heating load on such devices becomes an important task. Since the geometry of helically corrugated structures has a form that does not allow the use of analytical methods [12], a numerical method has to be employed. A general approach consists in using of a numerical method based on the first-principles equations, such as the finite-element, finite-difference, or boundary-element methods [9], [10], [18]–[21], which, however, would require a considerable amount of computer resources. It should also be noted that due to the dependence of the wall’s electric conductivity on the temperature, the problem becomes nonlinear and, consequently, even more computationally involved.