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

An analytical model is derived to study the two-dimensional character of axisymmetric, collisionless plasma flow along a guiding magnetic field. This is accomplished using a transformation from cylindrical to magnetic coordinates, which enables the separate treatment of the flow-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 field 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 field. 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 coefficient of a magnetic nozzle in terms of the parameters of the plasma source.