Propagating Filament Solutions for Nonlinear Coupled Electromagnetic and Solitary Ion Waves

Propagating filament solutions describing an electromagnetic wave trapped by a soliton-like rarefactory ion-wave are obtained, for both homogeneous and weakly inhomogeneous plasmas. The ion wave which traps the electromagnetic field moves at subsonic speed and is assumed to travel normal to the direction of electromagnetic wave propagation. For small ion-wave amplitude, the solution for the homogeneous plasma becomes similar to the electro-acoustic wave discussed by Karpman. When the amplitude of the ion wave is large, nonlinearity and dispersion in ion dynamics become important (in a manner similar to that of K-dV soliton); this causes the propagation speed of the filament to be amplitude dependent. In the weakly inhomogeneous case, a WKB approximation is used and it is found that the filament penetrates deep into overdense regions accompanied by an adiabatic change of its shape and increase of the electromagnetic wave frequency.