Spacecraft-charging mitigation of a high-power electron beam emitted by a magnetospheric spacecraft: Simple theoretical model for the transient of the spacecraft potential
A spacecraft-charging mitigation scheme necessary for the operation of a high-power electron beam in the low-density magnetosphere is analyzed. The scheme is based on a plasma contactor, i.e. a high-density charge-neutral plasma emitted prior to and during beam emission, and its ability to emit high ion currents without strong space-charge limitations. A simple theoretical model for the transient of the spacecraft potential and contactor expansion during beam emission is presented. The model focuses on the contactor ion dynamics and is valid in the limit when the ion contactor current is equal to the beam current. The model is found in very good agreement with Particle-In-Cell simulations over a large parametric study that varies the initial expansion time of the contactor, the contactor current and the ion mass. The model highlights the physics of the spacecraft-charging mitigation scheme, indicating that the most important part of the dynamics is the evolution of the outermost ion front which is pushed away by the charge accumulated in the system by the beam. The model can be also used to estimate the long-time evolution of the spacecraft potential. For a short contactor expansion (0.3 or 0.6 ms Helium plasma or 0.8 ms Argon plasma, both with 1 mA current) it yields a peak spacecraft potential of the order of 1-3 kV. This implies that a 1-mA relativistic electron beam would be easily emitted by the spacecraft.