Analytical and numerical studies of foilless diodes

The generation of intense annular beams by foilless diodes is studied through analytic equilibrium models and particle-in-cell simulation. In the high-voltage regime, the foilless diode operates below the space-charge limit and the impedance is nearly independent of the voltage. The current density is proportional to the current and to the square of the external magnetic field. From a kinetic theory equilibrium model, the beam scattering angle is found to be inversely proportional to the diode voltage, external magnetic field strength, and cathode radius. The predicted scaling is in good agreement with the simulation results. Criteria for adiabatic expansion and cooling of the beam, supported by simulation results, have also been considered