Alfvén Solitons

Abstract

The theory of MHD soliton formation parallel to the magnetic field, as described by the DNLS equation and related models, is reviewed. The known results on the physical relevance, solutions and mathematical properties of the DNLS equation, are briefly described. New results on the extension of the theory to finite beta and three space dimensions are presented. A hybrid fluid and kinetic treatment of the case of finite temperature based on the guiding center plasma model, leads to an additional nonlocal term due to resonant particles. The combination of modulational instability and resonant particle damping leads to the conclusion that parallel weakly dispersive Alfvén waves are nonlinearly damped in a finite beta plasma.