KdV Equations for High- and Low-Frequency Magnetosonic Waves in a Multi-Ion Plasma

Abstract

Investigations are made of nonlinear magnetosonic waves propagating perpendicular to a magnetic field in a multi-ion plasma. The magnetosonic wave is split into two modes in a two-ion plasma; low- and high-frequency modes. The frequency of the low-frequency mode tends to zero as the wave number k goes to zero. A KdV equation is derived for this mode by the conventional reductive perturbation method. The frequency of the high-frequency mode does not tend to zero as k→ 0. Using a new expansion scheme in which the amplitude ε is assumed to be much larger than (m_e/m_i)^1/2, where m_e/m_i is a measure of electron-to-ion mass ratios, it is found that the nonlinear high-frequency mode can also be described by a KdV equation, although it has a finite cut-off frequency. This shows that KdV equations are not limited to the waves whose frequencies tend to zero as k→ 0.