This paper presents a hybrid PIC-fluid approach to model the interaction of a plasma plume with a spacecraft and/or any nearby object. Ions and neutrals are modeled with a particle-in-cell approach, while electrons are treated as a fluid. After a first iteration of the code, the domain is split into quasineutral and non-neutral regions, based on nonneutrality criteria, such as the relative charge density and the Debye length to cell size ratio. At the material boundaries of the former quasineutral region, a dedicated algorithm ensures that the Bohm condition is met. In the latter non-neutral regions, the electron density and the electric potential are obtained by solving the coupled electron momentum balance and Poisson equations. Boundary conditions for both the electric current and potential are finally obtained with a plasma sheath sub-code and an equivalent circuit model. The hybrid code is validated by applying it to a typical plasma plume-spacecraft interaction scenario, and the physics and capabilities of the model are finally discussed.

An improved radial particle-in-cell model of an annular Hall effect thruster discharge with secondary-electron emission from the walls and a radial magnetic field is presented. New algorithms are implemented: first, to adjust the mean neutral density to the desired mean plasma density; second, to avoid the refreshing of axially accelerated particles; and third, to correctly weigh lowdensity populations (such as secondary electrons). The high-energy tails of the velocity distribution functions of primary and secondary electrons from each wall are largely depleted, leading to temperature anisotropies for each species. The secondary-electron populations are found to be partially recollected by the walls and partially transferred to the primary population. The replenishment ratio of the primary high-energy tail is determined based on the sheath potential fall. Significant asymmetries at the inner and outer walls are found for the collected currents, the mean impact energy, and the wall and sheath potentials. Radial profiles in the plasma bulk are asymmetric too, due to a combination of the geometric expansion, the magnetic mirror effect, and the centrifugal force (emanating from the E × B drift). The temperature anisotropy and non-uniformity, and the centrifugal force modify the classical Boltzmann relation on electrons along the magnetic lines.

The expansion of a rarefied axisymmetric plume emitted by a plasma thruster is analyzed and compared with a 3D Cartesian-type and a 2D cylindrical-type simulation code, both based on a particle-in-cell formulation for the heavy species and a simple Boltzmann-type model for the electrons. The first part of the paper discusses the 2D code numerical challenges in the moving of particles, their generation within the cells, and the weighting to the nodes, caused by the radial non-uniformity and the singular and boundary character of the symmetry axis. The second part benchmarks the 2D code against the 3D one for a high-energy, unmagnetized plume with three major species populations (injected neutrals, singly-charged and doubly-charged ions) and three minor species populations (constituted by particles coming from collisional processes, such as the charge-exchange reactions). The excellent agreement found in the results proves that both plume codes are capable of simulating, with a reasonable noise level, heavy particle populations differing by several orders of magnitude in number density. For simulations with a comparable level of accuracy, the 2D code presents a ten-fold gain in computational cost, although the symmetry axis remains its weakest point, due to particle depletion there and the related weighting noise.

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.

An investigation on the influence of relevant parameters on an annular Hall effect thruster plasma discharge is performed using a radial particle-in-cell simulation code with secondary electron emission from the walls and prescribed axial electric and radial magnetic fields. A simulation with true-secondary electrons only is taken as reference. First, the near-wall conductivity effects on the magnetized secondary electrons are illustrated by doubling the E × B, allowing a further code validation. Second, when secondary backscattered electrons are included, the enhanced secondary emission yields lower sheath potential drops and primary electron temperature. Moreover, the dominant backscattered electrons increase the average secondary electrons emission energy, greatly affecting its temperature anisotropy ratio and increasing the replenishment level of the wall collectable tails of the primary electrons velocity distribution function. Third, the effect of the truesecondary electrons emission energy on the potential profile is shown to be negligible, the latter being mainly set by the dominant magnetic mirror effect. Finally, a planar case featuring symmetric plasma profiles permits to confirm the validity of the large cylindrical asymmetries present in the reference case, induced by the combined effects of the geometric expansion, the magnetic mirror and the centrifugal force (due to the E × B drift). A smaller deviation of the primary electron momentum equation from the Boltzmann relation along the magnetic lines is still found in the planar case, induced by the parallel temperature non-uniformity.