An analytical model for the flow of collisionless plasma along magnetic fields

Abstract

ow-averaged plasma parameters from their spatial non-uniformities. The result gives analytical solutions for the spatial variation of the potential, plasma density, and ion Mach number. Application of the model to the problem of supersonic plasma expansion from a magnetic nozzle shows good agreement with both numerical simulations and experimental measurements. Notably, the development of a downstream radial electric eld to preserve quasi-neutrality is the main factor that drives non-uniformities within the plasma. This result is used to explain experimentally observed focusing of the plasma exhaust with respect to the applied magnetic eld. Finally, the competition in the expansion process, between the conversion of thermal energy into kinetic energy and the loss to plume divergence of the kinetic energy useful for propulsion yields an expression for the maximum thrust coecient of a magnetic nozzle in terms of the parameters of the plasma source.