Abstract

Nonlinear Ion Acoustic Waves in a Magnetic Plasma

I.Molotkov (Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, IZMIRAN, Moscow Region, Troitsk, Russia)

e-mail: molotkov@izmiran.rssi.ru

We consider ion acoustic waves (IAW) in a two-component plasma with the equal density of electrons and ions in the presence of an external magnetic field and under the standard assumptions (electron inertia and ion temperature are neglected ). These waves are described by well known and sufficiently complicated nonlinear system of the three equations for the three desired function - the ions flow velocity, the electron (ion) density and the electrical field potential. In the submitted work we consider space-one-dimensional IAW of the small amplitude. The last assumption means that there is a small parameter in the investigated system of equation and a possibility of the asymptotic methods application. As a result we find for all three desired functions quasi-monochromatic wave motions with a general phase. In the frame of these motions explicit approximate formulae for all desired functions are constructed. Moreover for each function we obtain a separate evolution equation, in which other desired functions are not contained. The separate equations are nonlinear Schroedinger equations with perturbation correction terms.

Section : 1