A theoretical model of cathode plasma behavior in a planar, high current, space‐charge limited diode is presented. The model predicts the evolution of the cathode plasma to steady state when certain diode conditions are satisfied. This steady state corresponds to current extraction from a stationary plasma boundary with no diode impedance collapse. In order for the equilibrium to be achieved, the driving impedance of the external power supply circuit must be smaller than a critical value that depends only on diode voltage, gap spacing, and plasma electron temperature. The temporal evolution of the cathode plasma is described using both a discrete numerical simulation model and an approximate analytical solution to the transport equations. The dependence on plasma temperature, neutral gas density and composition, diode voltage, gap spacing, and extracted current density are investigated.