Space-charge limited current with a finite injection velocity revisited
Trevor Lafleur
Abstract
Abstract The problem of space-charge limited current flow between two electrodes with a finite particle injection velocity is revisited theoretically, and numerically with particle-in-cell (PIC) simulations. Using an Eulerian approach, we obtain a complete analytical solution for both the space-charge limited (SCL) current (which agrees with previously derived expressions), as well as the spatial profiles of all physical quantities. These analytical solutions are unique in that they apply to both fluid, and kinetic particle descriptions of the system, and we demonstrate how they can be used to verify the accuracy and correctness of certain aspects of numerical simulation codes. For injection currents above the SCL limit, the PIC simulations show that the system becomes unstable, and self-excited space charge oscillations are generated with a period of the order of the particle transit time between the electrodes. In this oscillatory regime, the maximum time-averaged current that can be transmitted depends on the ratio of the particle injection energy to the applied potential difference across the electrodes, and is always less than the SCL current. By considering a finite particle injection temperature, these oscillations can be damped for sufficiently high temperatures, and we show that a new non-oscillatory steady-state solution can be obtained.