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

The increasing need to demonstrate the correctness of computer simulations has highlighted the importance of benchmarks. We define in this paper a representative simulation case to study low-temperature partially-magnetized plasmas. Seven independently developed particle-in-cell codes have simulated this benchmark case, with the same specified conditions. The characteristics of the codes used, such as implementation details or computing times and resources, are given. First, we compare at steady-state the time-averaged axial profiles of three main discharge parameters (axial electric field, ion density and electron temperature). We show that the results obtained exhibit a very good agreement within 5% between all the codes. As E × B discharges are known to cause instabilities propagating in the direction of electron drift, an analysis of these instabilities is then performed and a similar behaviour is retrieved between all the codes. A particular attention has been paid to the numerical convergence by varying the number of macroparticles per cell and we show that the chosen benchmark case displays a good convergence. Detailed outputs are given in the supplementary data, to be used by other similar codes in the perspective of code verification.

The Electron Cyclotron Drift Instability driven by the electron E × B drift in partially magnetized plasmas is investigated with highly resolved particle-in-cell simulations. The emphasis is on two-dimensional effects involving the parallel dynamics along the magnetic field in a finite length plasma with dielectric walls. It is found that the instability develops as a sequence of growing cyclotron harmonics demonstrating wave breaking and complex nonlinear interactions, being particularly pronounced in ion density fluctuations at short wavelengths. At the same time, nonlinear evolution of fluctuations of the ion and electron density, as well as the anomalous electron current, shows cascade toward long wavelengths. Tendency to generate long wavelength components is most clearly observed in the spectra of the electron density and the anomalous current fluctuations. An intense but slowly growing mode with a distinct eigen-mode structure along the magnetic field develops at a later nonlinear stage enhancing the tendency toward long wavelength condensation. The latter mode having a finite wavelength along the magnetic field is identified as the Modified Two-Stream Instability (MTSI). It is shown that the MTSI mode results in strong parallel heating of electrons.

A rotating plasma spoke is shown to develop in two-dimensional full-sized kinetic simulations of a Penning discharge cross-section. Electron cross-field transport within the discharge is highly anomalous and correlates strongly with the spoke phase. Similarity between collisional and collisionless simulations demonstrates that ionization is not necessary for spoke formation. Parameter scans with discharge current I_d, applied magnetic field strength B, and ion mass m_i show that the spoke frequency scales with $\sqrt{e{E}_r{L}_n/m_i}$ , where E_r is the radial electric field, L_n is the gradient length scale, and e is the fundamental charge. This scaling suggests that the spoke may develop as a non-linear phase of the collisionless Simon-Hoh instability.

The atmospheric pressure arcs have recently found application in the production of nanoparticles. The distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed a one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play an important role in the operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable to the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. The Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. The anode voltage is negative. In the case of strong anode cooling (water-cooled anode) when the anode is cold, temperature and plasma density gradients increase with current density, resulting in a decrease of the anode voltage (the absolute value increases). Falling VAC of the near-anode region suggests the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with the current density, leading to a drastic increase in the thermionic emission current from the anode. Correspondingly, the anode voltage increases to suppress the emission, and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions.