Analysis of filamentation instability in a current-carrying plasma using meshless method of lines coupled with radial basis functions

Abstract

The filamentation instability and the nonlinear dynamics of the magnetic field produced in a current-carrying plasma are investigated in the diffusion regime. Starting the coupled fluid equations for electrons and ions and using the Ampere-Maxwell equation, a nonlinear partial differential equation for the magnetic field diffusion is obtained. This paper presents an efficient meshless method of lines using radial basis functions to approximate this equation and consequently to analyze the magnetic field diffusion and the electron density distribution in the plasma. For this purpose, we applied the multi-quadric radial basis functions on some points and found appropriate approximations. Our method provides an expansion which is smooth enough for applying on high order differential equations. This method does not depend on any meshing procedure and has good accuracy, but is seriously parameter dependent. Finally, we have compared our results with two previously well-established finite difference and Adomian decomposition methods.