RESONANT ABSORPTION OF NONLINEAR SLOW MHD WAVES IN ISOTROPIC STEADY PLASMAS - I - THEORY

This paper considers driven resonant nonlinear slow magnetohydrodynami c (MHD) waves in dissipative steady plasmas. A theory developed by Rud erman, Hollweg, and Goossens (1997) is used and extended to study the effect of steady flows on the nonlinear resonant behaviour of slow MHD waves in slow dissipative layers. The method of matched asymptotic ex pansions is used to describe the behaviour of the wave variables in th e slow dissipative layer. The nonlinear analogue of the connection for mulae for slow MHD waves obtained previously by.Goossens, Hollweg, and Sakurai (1992) and Erdelyi (1997) in linear MHD, are derived. The eff ect of an equilibrium flow results partly in a Doppler shift of the av ailable frequency for slow resonance and partly in the modification of the width of the dissipative layer.