KdV dynamics in the plasma-sheath transition

A mathematical model is formulated to catch the dynamics hidden in the plasma-sheath transition layer and the inner sheath layer for planar motion of a plasma. It is shown that the rescaled potential in the plasma-sheath transition layer and inner layer is governed by a perturbed KdV equation, through which some of the complex interactions and couplings among physical mechanisms acting in the plasma-sheath formation process are elucidated. This model is analyzed and compared with the model used by Fokas in his study of nonlinear dispersive initial boundary value problems [1].

[1]  M. Slemrod.  Shadowing and the Plasma-Sheath Transition Layer , 2001, J. Nonlinear Sci..

[2]  K. Riemann,et al.  The influence of collisions on the plasma sheath transition , 1997 .

[3]  A. Lichtenberg,et al.  Principles of Plasma Discharges and Materials Processing , 1994 .

[4]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[5]  C. S. Gardner,et al.  Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion , 1968 .

[6]  Valery Godyak,et al.  Smooth plasma-sheath transition in a hydrodynamic model , 1990 .

[7]  Paul Ernest,et al.  The mathematics department , 1988 .

[8]  J. R. Ockendon,et al.  Asymptotic matching of plasma and sheath in an active low pressure discharge , 1970, Journal of Plasma Physics.

[9]  M. Slemrod.  Monotone increasing solutions of the Painlevé 1 equation y″ = y2+x and their role in the stability of the plasma-sheath transition , 2002, European Journal of Applied Mathematics.

[10]  Athanassios S. Fokas,et al.  Integrable Nonlinear Evolution Equations on the Half-Line , 2002 .

[11]  K. Riemann,et al.  The Bohm criterion and sheath formation , 1991 .

[12]  Robert M. Miura,et al.  Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation , 1968 .

[13]  Valery Godyak,et al.  Approximation of the bounded plasma problem by the plasma and the sheath models , 1996 .

[14]  Marshall Slemrod,et al.  Quasi-Neutral Limit for Euler-Poisson System , 2001, J. Nonlinear Sci..