Equilibria for Magnetic Insulation

We have studied fully-relativistic, self-consistent theoretical equilibria for the electron sheath near a magnetically insulated cathode. Such equilibria exist at stresses of 3 MV/cm for applied magnetic fields of ≥13 kG and at stresses of 5 MV/cm for applied magnetic fields of ≥20 kG in an 0.5 cm gap. The equilibrium solutions are obtained analytically as elliptic integrals, which are then evaluated numerically for special cases of interest to obtain quantitative results for the breakdown stress at various field levels.