Nonlinear theory of resonant slow MHD waves in twisted magnetic flux tubes

Abstract

The nonlinear dynamics of resonant slow MHD waves in weakly dissipative plasmas is investigated in cylindrical geometry with a twisted equilibrium magnetic field. Linear theory has shown that the wave motion is governed by conservation laws and jump conditions across the resonant surface considered as a singularity – first derived in linear ideal MHD theory by Sakurai, Goossens and Hollweg [Solar Phys.133, 227 (1991)]. By means of the simplified method of matched asymptotic expansions, we obtain the generalized connection formulae for the variables across the dissipative layer, and we derive a non-homogeneous nonlinear partial differential equation for the wave dynamics in the dissipative layer.