Circular polarized nonlinear Alfvén waves—a new type of nonlinear evolution in plasma physics

Abstract

A nonlinear evolution equation is derived for Alfven waves propagating along the magnetic field in a cold plasma. The equation provides new types of solitary waves. The phase of a soli­ tary wave is coupled nonlinearly with its amplitude, and the propa­ gation velocity is restricted within the range determined by the as­ ymptotic amplitude and the wave number. 1. Introduction. As early as in 1942, Alfven (1) recognized that a hydromagnetic wave propagates in an incompressible, perfectly con­ ducting fluid in the presence of a strong magnetic field. This Alfven wave is nothing but the low frequency limit of electromagnet ic waves propagating in a plasma. Generation and propagation of the Alfven waves in a gaseous plasma has been investigated experimentally (2), and has attracted renewed interest as one of the useful ways to heat a plasma (3). Alfven wave propagation in solid state plasmas provides in­ formation on the effective masses of carriers (4), Large amplitude in­ compressible magnetic field perturbation observed in the solar wind has been attributed to propagation of the Alfven wave (5). Now, turning to the studies of nonlinear wave propagation in plasmas, we have seen the remarkable success of theoretical and experi­ mental investigations of the ion acoustic solitary waves. Using reductive perturbation theory, Washimi and Taniuti (6) have predicted existence of the Korteweg-deVries type soliton for the ion acoustic mode. Their prediction has been experimentally confirmed by Ikezi et al. (7). Sys­ tematic ordering of dispersive effects and nonlinear steepening effects in the reductive perturbation theory (8) provides a rigorous procedure for reducing the hyperbolic system of nonlinear partial differential equations to a single nonlinear evolution equation; namely, the Korte­ weg-deVries equation for a weakly dispersive system and the nonlinear Schrodinger equation for a strongly dispersive system. In the case of Alfven waves, however, Kakutani and Ono (9) have noticed that it is necessary to modify the expansion scheme of the re­ ductive perturbation theory so as to be consistent with steady state soli­ tary wave solution of Kazantsev (10). Thus, they have been led to the conclusion that the Alfven wave is governed by the modified Korteweg-