A two-fluid model of the unmagnetized, collisionless far region expansion of the plasma plume for gridded ion thrusters and Hall effect thrusters is presented. The model is integrated into two semi-analytical solutions valid in the hypersonic case. These solutions are discussed and compared against the results from the (exact) method of characteristics; the relative errors in density and velocity increase slowly axially and radially and are of the order of 10 −2 -10 −3 in the cases studied. The plasma density, ion flux and ambipolar electric field are investigated. A sensitivity analysis of the problem parameters and initial conditions is carried out in order to characterize the far plume divergence angle in the range of interest for space electric propulsion. A qualitative discussion of the physics of the secondary plasma plume is also provided.

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.

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.

Modeling the far region expansion into vacuum of a plume from an electric thruster is crucial in engineering fields such as spacecraft platform design or mission analysis of a novel contactless orbital object relocator technique, known as Ion Beam Shepherd (IBS). In this context, a two-fluid model for the collisionless, quasi-neutral far region plume expansion is presented and two innovative semi-analytical solution methods introduced. A first solution is based on the perturbation method about the hypersonic expansion limit. A second solution, based on the self-similarity assumption, generalizes and contextualizes existing plume models of that kind. The validity and limitations of each approximation are discussed in detail and their accuracy is evaluated by comparing them with the exact solution obtained numerically with the method of characteristics. Lastly, the development plans for an advanced Hybrid/PIC plasma plume simulator, EP2-Plus, are presented.

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