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The current status and performance of the ALPHIE plasma thruster is discussed. This new concept was the subject of two recently granted patents and is radically different from conventional (Kauffman) gridded ion engines. Since it makes use of three DC power supplies and only one electron-emitting cathode disposed outside the plasma chamber, its power processing unit has low requisites. This electron emission is employed for both ionization and neutralization of the ion beam. Contrary to usual ion engines where only ions flow through the grids, in this case ionizing electrons and supersonic ions counterflow through the open spaces of a two-grid system. The performance of this plasma thruster was determined using both laboratory tests and particle-in-cell numerical simulations which confirmed the basic physical principles of the ion acceleration process. Laboratory experiments under realistic conditions show the ALPHIE thruster to produce supersonic Argon plasma flows with peak speeds of 37-44 km/s and therefore specific impulses in the range 3700-4400 s−1 . Additionally, ALPHIE delivers 1-3.5 mN throtteable thrusts using a maximum 325 W peak power, all of which were directly measured in the laboratory. These performances make ALPHIE suitable for station keeping, flight formation and end-of-life disposal of small and medium sized satellites.

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.