The paraxial expansion of a collisionless plasma jet into vacuum, guided by a magnetic nozzle, is studied with an Eulerian and non-stationary Vlasov-Poisson solver. Parametric analyses varying the magnetic field expansion rate, the size of the simulation box, and the electrostatic potential fall are presented. After choosing the potential fall leading to a zero net current beam, the steady states of the simulations exhibit a quasi-neutral region followed by a downstream sheath. The latter, an unavoidable consequence of the finite size of the computational domain, does not affect the quasi-neutral region if the box size is chosen appropriately. The steady state presents a strong decay of the perpendicular temperature of the electrons, whose profile versus the inverse of the magnetic field does not depend on the expansion rate within the quasi-neutral region. As a consequence, the electron distribution function is highly anisotropic downstream. The simulations revealed that the ions reach a higher velocity during the transient than in the steady state and their distribution functions are not far from mono-energetic. The density percentage of the population of electrons trapped during the transient, which is computed self-consistently by the code, is up to 25% of the total electron density in the quasi-neutral region. It is demonstrated that the exact amount depends on the history of the system and the steady state is not unique. Nevertheless, the amount of trapped electrons is smaller than the one assumed heuristically by kinetic stationary theories.

An electron-cyclotron resonance thruster (ECRT) prototype is simulated numerically, using two coupled models: a hybrid particle-in-cell/fluid model for the integration of the plasma transport and a frequency-domain full-wave finite-element model for the computation of the fast electromagnetic (EM) fields. The quasi-stationary plasma response, fast EM fields, power deposition, particle and energy fluxes to the walls, and thruster performance figures at the nominal operating point are discussed, showing good agreement with the available experimental data. The ECRT plasma discharge contains multiple EM field propagation/evanescence regimes that depend on the plasma density and applied magnetic field that determine the flow and absorption of power in the device. The power absorption is found to be mainly driven by radial fast electric fields at the electron-cyclotron resonance region, and specifically close to the inner rod. Large cross-field electron temperature gradients are observed, with maxima close to the inner rod. This, in turn, results in large localized particle and energy fluxes to this component.

An axisymmetric fluid model for weakly-collisional, magnetized electrons is introduced and coupled to a particle-in-cell model for heavy species to simulate electrodeless plasma thrusters. The numerical treatment of the model is based on a semi-implicit time scheme, and specific algorithms for solving on a magnetic field aligned mesh. Simulation results of the plasma transport are obtained for a virtual electrodeless thruster. The particle and energy fluxes of electrons are discussed. A first phenomenological model is included for the anomalous cross-field electron transport, and a second one for the anomalous parallel-field electron cooling in the plume. The balances of the plasma properties reveal that wall losses are the crucial reason for the poor thrust efficiency of these thrusters. The magnetic thrust inside the source could be negative and largely depending on the location of the magnetic throat, which is found uncoupled from the location of the plasma beam sonic surface. Furthermore, a sensitivity analysis of the results against the simulated plume extension shows that finite plumes imply an incomplete electron expansion, which leads to underestimating the performances.

Plasma discharges in electromagnetic thrusters often operate with weakly-collisional, magnetized electrons. Macroscopic models of electrons provide affordable simulation times but require to be solved in magnetically aligned meshes so that large numerical diffusion does not ruin the solution. This works discusses suitable numerical schemes to solve the axisymmetric equations for the electric current continuity and the tensorial Ohm's law in such meshes, when bounded by the thruster cylindrical or annular chamber. A finite volume method is appropriate for the current continuity equation, even when meshes present singular magnetic points. Finite differences and weighted least squares methods are compared for the Ohm's law. The last method is more prone to producing numerical diffusion and should be used only in the boundary cells and requires a special formulation in the boundary faces. In addition, the use of the thermalized potential is suggested for an accurate computation of parallel electron current densities for very high conductivity. The numerical algorithms are tested in a hybrid (particle/fluid) simulation code of a helicon plasma thruster, for different magnetic fields, mesh refinement, and plume lengths. The different contributions to the electric current density are assessed and the formation and relevance of longitudinal electric current loops is discussed.1

The transient and steady-state expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle is studied with a kinetic Boltzmann–Poisson model. Only intraspecies collisions involving electrons are considered and these are modeled with a Bhatnagar–Gross–Krook operator. Simulations show that occasional collisions progressively populate the phase-space region of isolated trapped electrons until a steady state is reached, which is independent of transient history. The steady state is characterized by a partial occupancy of that region increasing with the collisionality rate but far away from the full occupancy postulated by an alternative steady-state kinetic model. The changes on the amount of trapped electrons with the collisionality rate explain, in turn, the changes on the spatial profiles of main plasma magnitudes. Conclusions on the momentum and energy balances of ions and electrons agree, in terms of general trends, with those of the steady-state kinetic model. In the downstream region of the expansion, ions and electrons lose all their perpendicular energy but they still keep part of their parallel thermal energy. Electron heat fluxes of parallel energy are not negligible and are approximately proportional to enthalpy fluxes.

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