Particle-In-Cell modelling of magnetized plasma flux collection by spherical bodies

Charge collection by perfectly absorbing bodies (probes, dust particles, satellites) immersed in magnetized plasmas is usually addressed in a simplified manner by approximating particle transport as 2D and employing the cross-section of the body as the collecting area. One of the most rigorous analytical solutions, for fully ionized plasmas in the regime of equal ion and electron temperatures (directly relevant for fusion plasmas), has been developed back in 1970 by J. R. Sanmartin. His kinetic theory solution revealed that when the body is close to the plasma potential, the potential distribution along the B-field becomes non-monotonic and a so-called potential ‘overshoot’ emerges. Fluid models, both for weakly ionized and for fully ionized plasmas, were later proposed whose solutions for the electron current at repulsive potential were constructed by relating particle fluxes to the nonmonotonic potential structure of Sanmartin’s model, i.e. using his potential solution as an a-priori postulation. However, up to now, no numerical tests have succeeded in simulating this particle collection regime due to the prohibitively high computational cost associated with the length scale separation of the problem. Namely, for electrons, the collection perpendicular to B-field is strongly suppressed, and flux conservation results in the formation of an extremely extended collection area along it. Simultaneously, it is necessary to resolve length scales of the order of the Debye length. Capitalizing on the state-of-the-art tool, Curvilinear-Particle-In-Cell (CPIC) and frontier computational facilities at Los Alamos National Laboratory, in this work we have simulated this previously inaccessible collection regime. For the first time, the emergence of the non-monotonic potential profile has been confirmed. Moreover, the electron current was shown to be reasonably close to the model predictions and drastically suppressed compared to the typically employed unmagnetized Orbital Motion Limited model. The results of this work have direct implications for applications to probes in magnetized plasmas as well as modelling of dust and droplet survival in fusion environments.