Excitation of an electrostatic wave by a cold electron current sheet of finite thickness

Calculations for the threshold of current-driven instabilities and the growth rates of ion acoustic and electrostatic ion cyclotron instabilities in a magnetized plasma driven a current sheet with a finite width are presented. Maxwellian equations are employed to model the velocity distributions of electrons and ions in a direction perpendicular to the sheet. A dispersion relation is defined for the regions of instability, and boundary conditions are characterized in order to obtain a set of eigenvalue equations. Thresholds are delineated for various regions, including ducted mode solutions where only ion-acoustic waves are excited in areas where the frequency range significantly exceeds the ion cyclotron frequency. When a constant electron drift velocity is present, a thick current sheet is more unstable than a thin one. Fewer modes become unstable with a thinner sheet.