Collisional effects in non-stationary plasma expansions along convergent-divergent magnetic nozzles

Abstract

The electron-electron collisional effect on the nonstationary expansion of a plasma in a convergentdivergent magnetic nozzle is studied. Under paraxial and fully magnetized plasmas approximations, an Eulerian code has been adapted to solve Poisson's equation coupled with the kinetic transport equations for plasma species, i.e. a Vlasov equation for singly-charged ions and a Boltzmann equation with a Bhatnagar-Gross-Kook operator for electrons. The study is focused on weakly collisional plasma plumes, which have a collisional time scale larger than the transit time in the nozzle of typical electrons. A kinetic analysis shows that phasespace regions of isolated, doubly-trapped electrons that are nearly empty in the collisionless case are progressively populated due to the electron-electron collisions. Such a higher density of trapped electrons modifies the profile of the electrostatic potential, which keeps almost unaltered the density of free electrons and decreases the density of the reflected ones. As compared with the collisionless case, the collisions decrease the length of the downstream sheath and the parallel electron temperature while increasing the normal one. Therefore the steady plasma state is more isotropic. The simulations show that collisions erase the time history of the system and, unlike the collisionless case, the steady state is unique.