Ionization and current sheet formation in inductive pulsed plasma thrusters

Current sheet formation in inductive pulsed plasma thrusters (IPPTs) is investigated theoretically to determine how non-equilibrium ionization processes influence plasma impermeability to inductive electromagnetic fields and downstream propellant mass. Plasma impermeability to both electromagnetic fields and downstream mass is a prerequisite for efficient IPPT operation. A lumped-element circuit model of an IPPT plasma is modified to include propellant ionization and the electron energy balance under non-equilibrium conditions, neutral gas entrainment via charge exchange collisions, and electromagnetic coupling to a finite skin depth plasma. It is found that current sheets impermeable to both the accelerating fields and downstream mass-presumed to exist in all prior circuit modeling efforts-form only under specific conditions. The dynamics of electron heating during the early portion of the inductive current cycle are identified as the dominant contributors to current sheet formation. A new dimensionless scaling parameter is derived to characterize electron heating relative to inelastic ionization losses, from which it is found that impermeable current sheet formation requires Ohmic heating in the early formation phase to offset ionization losses associated with the entire propellant mass bit. This finding provides a physical explanation and generalization of the semi-empirical requirement on coil current rise rate that is commonly used in the early design phase of IPPTs to ensure current sheet formation.