Elementary Scaling Relations for Hall Effect Thrusters

Various sizing methodologies are currently available to get a first estimate of the required Hall effect thruster dimensions for a given input power and a corresponding thrust and specific impulse level. In this work, a semiempirical approach to compute the three characteristic thruster dimensions, i.e., the channel length, the channel width, and the channel mean diameter, is introduced. The magnetic field strength is also considered. The determination of the scaling relations is based onanalytical relationships deduced from the physicalmechanisms that govern the properties of a Hall thruster discharge. A set of simplifying assumptions naturally specifies the validity domain of the relationships. The existence of a critical propellant atom density inside the channel, which warrants a high-efficiency thruster operation, is revealed and commented. The proportionality coefficients of the scaling relations are assessed by way of a vast database that comprises 33 single-stage Hall effect thrusters covering a power range from 10W up to 50 kW. The sizing method is employed to access the geometry and the operating parameters for a 20 kW-class Hall thruster operating with xenon. Results obtained with two different series of simplifying assumptions are compared. The first set forms a very restrictive frame. The second set offers a more realistic description of the physics at work as the electron temperature, the energy losses andmultiply charged ion species are taken into account.