Virtual Cathode in a Stationary Spherical Inertial Electrostatic Confinement

"Double-well" potential structure (virtual cathode formation) is studied in a stationary spherical inertial electrostatic confinement (SIEC) using the nonlinear Poisson's equation and particle densities derived from kinetic theory. A novel method to obtain a spherically symmetric stationary distribution function is introduced and an integral-differential equation is simplified by applying a relevant approximated formula for an integral. Electron and ion beams are collision-free, and their velocities are roughly aligned toward the spherical center, but with a slight divergence. Analyses show that the angular momentum of ions and the smaller one of electrons create a virtual cathode, i.e., a double-well structure, of the electrostatic potential on a potential hill near the center. The density limit of an SIEC is exhibited, and the condition relevant to form a deep potential well is presented.