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Three detachment mechanisms proposed in the literature (via resistivity, via electron inertia, and via induced magnetic field) are analyzed with an axisymmetric model of the expansion of a small-beta, weakly collisional, near-sonic plasma in a diverging magnetic nozzle. The model assumes cold, partially magnetized ions and hot, isothermal, fully magnetized electrons. Different conditions of the plasma beam at the nozzle throat are considered. A central feature is that a positive thrust gain in the nozzle of a plasma thruster is intimately related to the azimuthal current in the plasma being diamagnetic. Then, and contrary to existing expectations, the three aforementioned detachment mechanisms are divergent, that is, the plasma beam diverges outwards of the guide nozzle, further hindering its axial expansion and the thrust efficiency. The rate of divergent detachment is quantified for the small-parameter range of the three mechanisms. Alternative mechanisms for a convergent detachment of the plasma beam are suggested.

This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These "E×B" plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research.

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.

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.

A kinetic paraxial model of a collisionless plasma stationary expansion in a convergent-divergent magnetic nozzle is analyzed. Monoenergetic and Maxwellian velocity distribution functions of upstream ions are compared, leading to differences in the expansion only on second and higher-order velocity moments. Individual and collective magnetic mirror effects are analyzed. Collective ones are small on the electron population since only a weak temperature anisotropy develops, but they are significant on the ions all over the nozzle. Momentum and energy equations for ions and electrons are assessed based on the kinetic solution. The ion response is different in the hot and cold limits, with the anisotropic pressure tensor being relevant in the first case. Heat fluxes of parallel and perpendicular energies have a dominant role in the electron energy equations. They do not fulfill a Fourier-type law; they are large even when electrons are near isothermal. A crude electron fluid closure based on a constant diffusion-to-convective thermal energy ratio is shown equivalent to the much invoked polytropic law. Analytical dimensionless parameter laws are derived for the nozzle total electric potential fall and the downstream residual electron temperature. Electron confinement and related current control by a thin Debye sheath and a the semi-infinite divergent magnetic nozzle are compared.

The collisionless, steady state expansion into vacuum of a warm electron, cold ion plasma thruster plume is studied with a set of new electrostatic particle-in-cell model and globally-consistent boundary conditions that discriminate between reflected and escaping electrons. As a proof of concept, several simulations are analyzed. Results from both two-dimensional planar and axisymmetric plasma plumes are discussed. In particular, the electrons' anisothermal and anisotropic behavior in the plume is recovered.

Plasma detachment in propulsive magnetic nozzles is shown to be a robust phenomenon caused by the inability of the internal electric fields to bend the supersonic ions along the magnetic streamtubes. As a result, most of the plasma momentum is effectively ejected to produce thrust, and only a marginal fraction of the beam mass flows back. Detachment takes place even if electrons are fully-magnetized and is intimately linked to the formation of local electric currents. The divergence angle of the 95%-mass flow tube is used as a quantitative detachment performance figure.