Simple Model Analysis of Hysteresis Phenomenon of Gas Discharge Plasma

The hysteresis and multiple-steady states of gas discharge plasma are analyzed by a simple model of chemical-reaction system. In our analysis the emergence of multiple-steady states is explained by using a fact that a function describing the energy balance has three different real roots. The condition that the function has three roots depends on the ratio of the bulk energy increase to the surface energy loss of plasma. The criterion of taking place of the jump between two steady states is examined in a similar manner to order-disorder transition. The critical parameter contains the non-thermodynamic variables such as conductivity and surface quantities. Stabilities of three obtained solutions are discussed by using linear analysis of differential equations and we find that a root represents a saddle point and other two roots represent stable points. The first step to explain the hysteresis phenomenon in Ar gas discharge plasma is found.