A New Method for the Development of a Nonlinear Equivalent Circuit for a Gas Discharge

Abstract

The behaviour of gas discharges can be modelled by equivalent circuits built on the basis of a theoretical description of the plasma. This paper introduces a method to develop a nonlinear equivalent circuit directly by means of the balance equations of the column plasma and by the help of the knowledge obtained from the design of the linear equivalent circuit. The linear network theory was used for the derivation. The circuit found in this way is similar to a derived linear equivalent circuit of the column plasma with two inertial factors (delayed effects) for a neon gas discharge described in previous papers.

The Influence of the Gas‐Temperature on the Behaviour of the Positive Column of a Neon Glow Discharge and its Description by a Nonlinear Equivalent Circuit

“…Because of the changed parameters due to higher gas-temperature another continued fraction expansion must be applied. Neglecting all nonlinearities in (4) we found the following continued fraction expansion for the application of the plasma in the oscillating regime at higher pressure and at higher temperature (for the definition of the Ai, see [4]):…”

“…. 6) contain the plasma quantities (for definition see [4]): X , and x1 represent ill, and u/Eo respectively, x2 and x~~ are proportional to the density of electrons N , and of metastable atoms M , respectively.…”

“…For the derivation of linear equivalent circuits representing some aspects of the plasma behaviour in [9, 101 the linearized eq. (4) was used, here we prefer another way using the method developed in [4,5]. Because of the changed parameters due to higher gas-temperature another continued fraction expansion must be applied.…”

“…The dependence of the collision rates on the field strength (zpv as functions of E / p ) can be approximated from known curves [7l or can be taken from [8] or rewritten like in [4].…”