Non-perturbative analysis of space charge limited electron flow in critical regimes

摘要

The combined Eulerian-Lagrangian formalism, developed in our previous work for studying the turn on regime of a one-dimensional diode, is extended for wider versatility and better precision in the study of the time dependent space charge limited electron flow with fixed injected current. An analytical analysis is supplemented with an approximate numerical scheme which appears to be sufficiently accurate to calculate the flow evolution until the process approaches stabilization or becomes unstable. This can be compared with properties of stationary flows and showed to be in a good agreement with them. When the stabilization is impossible, the ratio of anode to cathode currents is decreasing and thus the space charge is accumulated in the diode. We discuss the limitations of our approach and give some qualitative estimates for the flow parameters when stabilization is impossible.