Low-frequency electromagnetic instabilities in a collisionless current sheet: magnetohydrodynamic model

Low-frequency electromagnetic instabilities in a collisionless current sheet are discussed by using the 3-dimensional, collisionless and compressible magnetohydrodynamic model with the isotropic pressure. The linear dispersion relations are numerically solved at the middle plane (z = 0) and edges (z = 1) of the current sheet for modes of 2-and 3-dimensional propagation. The main results are as follows. (1) For 2-dimensional disturbed propagation (kz = 0), at the middle plane (z = 0), the growth rate of Alfven waves is maximum, and the frequency and the wavenumber region of unstable waves are widest. The farther the distance from the middle plane, the smaller the growth rate and the wavenumber region. As the ion-inertial length becomes longer, the growth rate of Alfven waves becomes larger. (2) For 3-dimensional disturbed propagation (kz does not equal 0), whistler waves are unstable. At the current sheet middle plane, whistler waves have an obvious growth rate. Outside the ion-inertial region, the growth rate of whistler waves becomes larger. (3) At the middle plane (z = 0), low-frequency waves are mainly excited by the current-driven instabilities. At places far from the middle plane, the gradient instabilities of the current, density and pressure become more important.