Modulational Instability of Ion Wave in Plasma with Negative Ion

Abstract

A modulational instability of an ion wave in a plasma composed of electron, positive ion and negative ion has been investigated theoretically. We derive a nonlinear Schrödinger equation for ion wave and examine the signs of nonlinear and dispersion coefficients. The dispersion coefficient is negative irrespective of the wavenumber. The sign of the nonlinear coefficient changes at a critical wavenumber k_c, above which the coefficient becomes negative and the ion wave is modulationally unstable. The critical wavenumber k_c depends strongly on the negative ion density. At the critical density of negative ion where the nonlinear coefficient of the Korteweg-de Vries equation for ion wave vanishes, the critical wavenumber k_c is reduced to zero and the wave of any wavenumber is modulationally unstable.