Two-Dimensional Thomson Model of a High-Frequency Induction Discharge of Finite Length

The paper considers the main stages of constructing a two-dimensional model of the constant conductivity of a finite-length RF induction discharge. The system of equations describing the quasi-stationary electromagnetic field of a high-pressure discharge allows only a numerical analysis of its structure. An analytical model is required to study the discharge structure in the axial region. To construct it, it is necessary to proceed to the complex form of Maxwell's equations. This approach was first used by J.J. Thomson to describe a one-dimensional RF discharge. In this case, the nonlinear differential equations of the electromagnetic field in physical variables turn into linear differential equations for complex quantities, which allow accurate solutions using special Bessel and Kelvin functions for a complex argument. The obtained relations allow us to formulate several conclusions that relate to the structure of a quasi-stationary electromagnetic field in a finite-length discharge. The results obtained in this work may be useful to specialists in the field of physics and technology of RF induction discharge.