Expansion Method For solving the Nonlinear Dynamics of an Elliptic Magnetic Stagnation line

Abstract

This study to nd the solution for nonlinear dynamic equations by Expansion method and depending on the nonlinear evolution of the kink instability of a plasma with an elliptic magnetic stagnation line. Hence we applied the Expansion method which used to solve dynamic equation. Expansion method is the easiest method and applicable one to solve Nonlinear Dynamic Partial Di erential Equations. A cylindrically symmetric plasma with circular eld lines is used to model the magnetic eld geometry close to the stagnation line. An example for the second order is given to illustrate the general case by using to potential energy representation equation. Some considerations concerning solar laments and lament bands (circular or straight) are indicated as possible besides graphical representation with cusp geometry corresponding to the stagnation line