2-D Vlasov simulations and kinetic theory of sheared two-stream electron instabilities in strongly magnetized plasmas

In this work, we present new 2-D Vlasov simulations with periodic boundary conditions together with a new supporting linear analytic theory for the kinetic instability of equal and opposite electron streams parallel and anti-parallel to a strong background magnetic field B. The magnitude of the initially equal and opposite electron stream velocities is taken to vary sinusoidally with position across magnetic field lines. The neutralizing ions are static and the plasma is current-free. We shall refer to this as a sheared symmetric two-stream instability . A linear stability analysis is based on the eigenvalues and eigenfunctions of Poisson's equation for the electrostatic potential. Poisson's equation is shown to be a Mathieu equation in the limit of weak shear. This study is relevant to space and laboratory plasmas.