Modeling of Field Emission Cathodes for Space Propulsion

Abstract

An approximate one-dimensional analytical model was developed to predict the potential distribution and space charge limited current for a field emission (FE) cathode in a triode configuration which consists of the field emitter, gate and an anode. The emitter could be carbon nanotubes, diamond like carbon or Spindt type metallic cones provided that the cones are recessed below the gate surface more than about one gate hole radius. The gate is a highly perforated metal in close proximity to the emitter. The electrons enter the region between the gate and the anode with an energy proportional to the electron extraction voltage Vo approximately given by the potential difference between the emitter and the gate and are assumed to be monoenergetic. Depending on the anode potential and the cathode current a space charge barrier may be created in the gate-to-anode region that limits the anode current and diverts the cathode current into the gate. Understanding the parameters that govern the anode current is the objective of this analytical effort which is relevant to all electric propulsion (EP) including the electrodynamic (ED) tethers and ion type thrusters. For the ED tether, the edge of the space plasma sheath can be viewed as the anode in our triode model. Previously developed model for predicting the space charge limited anode current was shown to have limited scope of validity. The expressions developed herein predict about 50% lower anode current limit than the previously developed model and show that for a typical ED tether conditions the near optimum FE cathode current density is of the order of 10 mA/cm 2