Anomalous Electron Transport from Wave-particle Interactions in Hall-effect Ion Propulsion

A first-principles model of the anomalous momentum-transfer collision frequency (ν_ea) and frictional power density (Q_ea) of electrons in ExB ion accelerators, also known as Hall-effect thrusters, is presented. The theory on which the model is based adopts a two-stage evolution of unstable waves. First, short-wavelength (k_⊥ρ_e>1), high-frequency (|ω|~ω_ce) modes that are driven by the cross-field drift (u_E=ExB/B²) grow and saturate at a level of turbulence too low to explain the observed measurements. Then the wave energy is dominated by modes of longer wavelength (k_⊥ρ_e<1) and in the range of the lower-hybrid frequency ω_LH. The lower-hybrid modes combine wave growth in the azimuthal direction that is driven by the diamagnetic drift (u_De=▽p_exB/enB²), with growth parallel to B due to a higher effective mass of electrons. The latter has been typically identified as the modified two-stream instability. The diamagnetic-driven modes are found to be important in regions of the channel where ions begin to accelerate since |u_E|~|u_De| there. The theoretical model compares extremely well with a large set of empirical profiles of ν_ea derived from laser-induced fluorescence measurements. Our model validation comparisons spanned thrusters with >10x range in discharge power, various sizes and operating conditions, in unshielded and shielded magnetic field topologies. The kinetic version of our closed-form expression yields the scaling ν_ea~ω_ceu_Tie^τ/(u_E+u_De), where τ~ω_LH/ν_i, ν_i is the sum of the ionization and charge-exchange frequencies and u_Ti is the ion thermal speed. The latter must be determined by the appropriate integration of the ion velocity distribution function and include not only random changes of the drift velocity but also ion production. The new expression for the anomalous frictional heating reported here has been derived from the same kinetic theory and shows Q_ea is a function of the lower-hybrid wave properties at maximum growth and the drifts that drive it.