The vortex-like self-consistent electron fluid model by the applied-B ion diode: Equilibrium and instability

The electron inertia effects in the one-dimensional model of the applied-B ion diode for the relativistic diode potential eU/mec² ≥ 1 are investigated, when the magnetic Debye length rB is of the order of the collisionless electron skin depth c/wpe. For this, an analytical relation between the magnetic field and the electric potential is discovered that makes it possible to reduce the second order eigenvalue problem to the system of algebraic equations. Instabilities inside the vacuum gap and in the near-anode emitting plasma are considered. In the near-anode Hall plasma the instability with two ion species is obtained that can give contribution to the ion angle divergence.