Freak waves in laboratory and space plasmas
Freak waves in plasmas
School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield S3 7RH, UK
a e-mail: M.S.Ruderman@sheffield.ac.uk
Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.
© EDP Sciences, Springer-Verlag, 2010