New approach to the theoretical modeling of applied-B ion diodes

The one-dimensional hydrodynamic electron fluid model in applied-B ion diodes is investigated. For the relativistic potential the electron inertia effect is considered, when the magnetic Debye length is of the order of the collisionless electron skin depth. By the account of the electron inertia an analytical relation between the magnetic field and the electric potential is discovered that essentially simplifies the analysis of the ion diode equilibrium. The extremum energy principle makes it possible to calculate the ion current density for a given magnetic flux in the diode gap