Helicity-Aware Design of Hall-Type MHD Thrusters

We study thrust production in a single-fluid magnetohydrodynamic (MHD) thruster with Hall-type coaxial geometry and show how velocity–field alignment and magnetic topology set the operating regime. Starting from the momentum equation with anisotropic conductivity, the axial Lorentz force density reduces to fz=σθzEzBr(χ−1), with the motional-field ratio χ≡(uBr)/Ez. Hence, net accelerating force (fz>0) is achieved if and only if the motional electric field Em=uBr exceeds the applied axial bias Ez (χ>1), providing a compact, testable design rule. We separate alignment diagnostics (cross-helicity hc=u·B) from the thrust criterion (χ) and generate equation-only axial profiles for χ(z), jθ(z), and fz(z) for representative parameters. In a baseline case (Ez=150Vm−1,σθz=50Sm−1,u0=12kms−1,Br0=0.02T,L=0.10m), the χ>1 band spans ≈21.2% of the channel; a lagged correlation peaks at Δz★≈8.82mm(CHU=0.979), and ∫0Lfzdz is slightly negative—indicating that enlarging the χ>1 region or raising σθz are effective levers. We propose a reproducible validation pathway (finite-volume MHD simulations and laboratory measurements: PIV, Hall probes, and thrust stand) to map fz versus χ and verify the response length. The framework yields concrete design strategies—Br(z) shaping where u is high, conductivity control, and modest Ez tuning—supporting applications from station-keeping to deep-space cruise.