The Electron Cyclotron Drift Instability (ECDI) 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.

In this paper we propose a representative simulation test-case of E × B discharges accounting for plasma wall interactions with the presence of both the Electron Cyclotron Drift Instability (ECDI) and the Modified-Two-Stream-Instability (MTSI). Seven independently developed Particle-In-Cell (PIC) codes have simulated this benchmark case, with the same specified conditions. The characteristics of the different codes and computing times are given. Results show that both instabilities were captured in a similar fashion and good agreement between the different PIC codes is reported as main plasma parameters were closely related within a 5% interval. The number of macroparticles per cell was also varied and statistical convergence was reached. Detailed outputs are given in the supplementary data, to be used by other similar groups in the perspective of code verification.

The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the Buneman instability in unmagnetized plasmas are studied. It is found that, in the regime of low drift velocity, the linear stage of the instability in PIC simulations differs significantly from the theoretical predictions, whereas in the Vlasov simulations it does not. A series of highly resolved PIC simulations with increasingly large numbers of macroparticles per cell is performed using a number of different PIC codes. All the simulations predict highly similar growth rates that are several times larger than those calculated from the linear theory. As a result, we find that the true convergence of the PIC simulations in the linear regime is elusive to achieve in practice and can easily be misidentified. The discrepancy between the theoretical and the observed growth rates is attributed to the initial noise inherently present in PIC simulations, but not in Vlasov simulations, that causes particle trapping even though the fraction of trapped particles is low. We show analytically that even weak distortions of the electron velocity distribution function (such as flattening due to particle trapping) result in significant modifications of the growth rates. It is also found that the common quiet-start method for PIC simulations leads to more accurate growth rates but only if the maximum growth rate mode is perturbed initially. We demonstrate that the quiet-start method does not completely remedy the noise problem because the simulations generally exhibit inconsistencies with the linear theory.

Kinetic effects in plasma flow due to a finite ion temperature and ion reflections in a converging–diverging magnetic nozzle are investigated with collisionless quasineutral hybrid simulations with kinetic ions and isothermal Boltzmann electrons. It is shown that in the cold ions limit, the velocity profile of the particles agrees well with the analytical theory, predicting the formation of the global accelerating potential due to the magnetic mirror with the maximum of the magnetic field and resulting in the transonic ion velocity profile. The global transonic ion velocity profile is also obtained for warm ions with isotropic and anisotropic distributions. Partial ion reflections are observed due to a combined effect of the magnetic mirror and time-dependent fluctuations of the potential as a result of the wave breaking and instabilities in the regions when the fluid solutions become multi-valued. Despite partial reflections, the flow of the passing ions still follows the global accelerating profile defined by the magnetic field profile. In simulations with reflecting boundary condition imitating the plasma source and allowing the transitions between trapped and passing ions, the global nature of the transonic accelerating solution is revealed as a constrain on the plasma exhaust velocity that ultimately defines plasma density in the source region.