Calculation of conditions for maintaining an ICRF-plasma using a self-consistent model

Abstract

The article proposes a new approach to calculating the strength of the magnetic field on the inner wall of the discharge chamber, which is necessary to maintain a steady state of a low-pressure ICRF discharge. The model is treate as a nonlinear eigenproblem. The influence of the third type boundary conditions for electron density as well as and the nonlinear boundary conditions for electrical strength is considered. This approach makes it possible solving two problems of designing ICRF plasma torches: for a given electron density in the discharge find the magnetic field strength that ensures the maintenance of the discharge, or, conversely, at a given magnetic field strength, determine the value of the electron density that can be created in the discharge. In addition, the radial distributions of the electric and magnetic fields and the electron concentration can be determined.

Frequency dependencies of the characteristics of an inductively coupled radiofrequency discharge at reduced pressure

“…Also it is important to note examples of numerical models: an one-dimensional model in which the system of ICP equations is solved as an eigenvalue problem [30]; RF plasma simulation with chamber using OpenFOAM [31][32][33]. These works consider the model of a plasma jet.…”

A mathematical model of an inductively coupled radio-frequency discharge at low pressure as nonlinear partial eigenproblem

“…It was proved [3] that the boundary value problem (1), ( 4) is an eigenvalue problem, the minimum eigenvalue of which is ER, electron concentration in plasma bunch ne0 is a free parameter. The free parameter ne0 is defined as for a given inductor current…”

“…We propose a new approach to the formulation of the problem and study the 1D model in detail in order to use it in the future as an initial approximation for 2D and 3D problems [3].…”