Analysis of collisional and facility effects in a magnetic nozzle plasma expansion

An axisymmetric, quasineutral three-fluid model is proposed to study plasma expansion in a magnetic nozzle in the presence of neutrals coming either from the plasma source or as a homogeneous background. Electron cooling in the plume is achieved by treating the electron heat flux as convective rather than conductive, eliminating the need to postulate anomalous cross field or parallel diffusion of momentum or energy. Solutions are presented for the high electron magnetization limit, in which the main electron flow variables can be integrated along magnetic field lines. Ionization, elastic, and charge-exchange collisions with neutrals do not alter the main qualitative features of the plasma expansion established in previous collisionless models. Ionization enhances the plasma flow in the nozzle and leads to additional electron cooling, which reduces the potential drop along the nozzle. Nozzle efficiency is quantified in terms of magnetic thrust gain and plume divergence angle. Two types of boundary conditions for the electron flow are evaluated: local throat current-ambipolarity conditions and global current-free conditions at the outer boundary (i.e., metallic vacuum chamber walls). The latter are shown to be physically more realistic: they incorporate the effect of the chamber walls on plasma expansion by shaping the ambipolar electric field and align better with experimental trends regarding background pressure.