High-Frequency Breakdown of Nonuniform Gases in Spatially Varying Fields

Abstract

A method is described for predicting the field strength required to produce continuous wave breakdown of gases with spatially varying properties subjected to electric fields of nonuniform intensity. The proposed method is based on a variational principle derived from the electron continuity equation. A Ritz method is used to generate solutions of the variational problem. The approximate solutions are evaluated by comparing them with several exact solutions which are also developed. The use of a one-term trial function in the Ritz method is found to give very good agreement with the exact solutions. A two-term approximation provides greater accuracy than is presently available from experimental data.

Gas breakdown in inhomogeneous microwave electric fields

“…However, in the general case when ν a = 0 and/or γ = 0, analytical solutions cannot be found. However, it should be possible to obtain good approximate solutions using direct variational methods [4,5,7,[11][12][13]. To this end we reformulate the eigenvalue problem as the variational problem δλ[n] = 0, where λ[n] is defined by…”

“…However, when the electric field in a gas-filled microwave device is inhomogeneous in space, the interplay between the concomitant inhomogeneous ionization, which tends to create free electrons, and the diffusion and attachment mechanisms, which tend to decrease the free electron density, becomes complicated and depends significantly on the field inhomogeneity and on the gas pressure. Electrical breakdown in gas-filled microwave devices has been analysed for a number of designs and microwave mode structures [1][2][3][4][5][6][7][8][9][10][11][12][13], including situations involving field singularities, e.g. sharp corners or edges where the electric field strength (and the ionization) becomes locally very high [14].…”

Theoretical Studies of the Breakdown Characteristics at Microwave Frequencies

“…[1][2][3][4] Microwave breakdown in gases under various physical and technical conditions is a well-known and intensively studied problem from the early days of gaseous electronics. [5][6][7][8][9][10][11] More recently, interest in microwave-induced breakdown has shifted to studies of microwave breakdown at atmospheric pressures due to its relevance both for industrial applications [12][13][14][15] and for a deeper understanding of fundamental plasma behavior. [16][17][18][19] The microwave breakdown phenomenon provides both problems and opportunities that are reflected in the applications of the microwave breakdown theory.…”