Relativistic electron-fluid model of an applied-B ion diode

A one-dimensional model of an applied-B ion diode filled with magnetized electrons is considered. The screening length rB≅B/4πene of the electric field is assumed to be on the order of the collisionless electron skin depth c/ωpe. The electrons are described in cold relativistic hydrodynamics. It is assumed that equalizing the Lagrange invariant I=Ω/ne, where Ω is the electron vorticity and ne is the electron density, leads to an equilibrium state in which I=const. Under this assumption, an additional relation between the magnetic field and electric potential is derived, which allows one to reduce the problem of calculating the ion-diode current to solving a set of algebraic equations for the introduced constants. The results of calculations are compared with the experimental results obtained in the KALIF device (Forschungszentrum Karlsruhe, Germany). The theory proposed predicts a peak of the electron density profile in the vicinity of the anode surface, which is in excellent agreement with recent measurements