Supersonic Constricted Plasma Flows

Abstract

The Pocket Rocket electrothermal microthruster is a miniaturised electric propulsion system designed for nanosatellites operating in space. A weakly ionised capacitively coupled plasma is ignited in the flowing Ar gas propellant within a constricted discharge chamber at 1 Torr using less than 10 W of radiofrequency power. The discharge can operate either continuously or in rapid pulsed mode since plasma breakdown initiates almost instantaneously on a μs time scale. The propellant is heated to temperatures approaching 1000 K and is expanded through a converging-diverging nozzle into vacuum at supersonic velocities. Thrust on the order of 1 mN is generated as a reactionary force to the linear momentum of the expelled neutral gas propellant.

This thesis presents a comprehensive model of Pocket Rocket developed with computational fluid dynamics and plasma simulations.

Boundary layer effects are significant in the rarefied flow within the constricted discharge chamber. A slip boundary condition with the appropriate tangential momentum and thermal accommodation coefficients must be used to produce results that precisely match experimental measurements. The problem of including vacuum regions within a fluid simulation domain is unconventionally circumvented by taking advantage of the flow velocity choking. The computed sonic surface, thrust force, and specific impulse are in good agreement with theoretical predictions.

Volumetric plasma-induced heating of the background neutral gas is primarily due to ion-neutral charge exchange collisions, with very little contribution from electron-neutral elastic collisions. The propellant temperature is described by two local models based on the different ion transport behaviour in the plasma bulk and plasma sheath. The most dominant process is surface bombardment by ions accelerated through the plasma sheath, which heats the discharge chamber wall and is responsible for the creation of secondary electrons that sustain the gamma mode discharge.

The geometrical area asymmetry of the grounded and powered electrodes results in a self-bias that manifests as a spatially nonuniform negative charging within the dielectric discharge chamber wall. In the thin sheath regime, the self-biased waveform has a diminished trailing edge at each positive peak, and asymmetrically displaced negative peaks due to the extraneous impedance of the dielectric wall. This leads to a redefinition of the self-bias voltage that uses the maxima envelope of the self-biased waveform instead of the mean, which maintains consistency with different extraneous impedances.

The performance of Pocket Rocket is improved by optimising the physical and electrical geometry for thrust and boundary layer effects, and plasma confinement is achieved through the formation of a conical plasma sheath at the nozzle throat. Enhanced recombination in the supersonic expanding plume creates a neutral exhaust, thereby avoiding contamination of externally mounted solar panels and interference with sensitive instruments. Most importantly, the combination of flow velocity choking and plasma confinement results in a convergent plasma simulation that accurately models plasma expansion into vacuum.

The computational fluid dynamics and plasma modelling technique and analysis presented in this thesis are not restricted to the Pocket Rocket discharge and may be adapted for other discharges at different pressure regimes and physical scales.