Electron cyclotron drift instability and anomalous transport: two-fluid moment theory and modeling

Abstract

In the presence of a strong electric field perpendicular to the magnetic field, the electron crossfield (E × B) flow relative to the unmagnetized ions can cause the so-called Electron Cyclotron Drift Instability (ECDI) due to resonances of the ion acoustic mode and the electron cyclotron harmonics. This occurs in, for example, collisionless shock ramps in space, and in E × B discharge devices such as Hall thrusters. A prominent feature of ECDI is its capability to induce an electron flow parallel to the background E field at a speed greatly exceeding predictions by classical collision theory. Such anomalous transport is heavily researched due to its role in particle thermalization at space shocks, and in causing plasma flows towards the walls of E × B devices, leading to unfavorable erosion and performance degradation, etc. The development of ECDI and anomalous transport is often considered to require a fully kinetic treatment. In this work, however, we demonstrate that a reduced variant of this instability, and more importantly, the associated anomalous transport, can be treated self-consistently in a collisionless two-fluid framework without any adjustable collision parameter. By treating both electron and ion species on an equal footing, the free energy due to the inter-species velocity shear allows the growth of an anomalous electron flow parallel to the background E field. We will first present linear analyses of the instability in the two-fluid five-and ten-moment models, and compare them against the fully-kinetic theory. At low temperatures, the two-fluid models predict the fastest-growing mode in good agreement with the kinetic result. Also, by including more (>= 10) moments, secondary (and possibly higher) unstable branches can be recovered. The dependence of the instability on ion-to-electron mass ratio, plasma temperature, and background B field strength is also thoroughly explored. We then carry out direct numerical simulations of the cross-field setup using the five-moment model. The development of the instability, as well as the anomalous transport, is confirmed and in excellent agreement with theoretical predictions. The force balance properties are also studied using the five-moment simulation data. This work casts new insights into the nature of ECDI and the associated anomalous transport and demonstrates the potential of the two-fluid moment model in efficient modeling of E × B plasmas.

Two-dimensional effects on electrostatic instabilities in Hall thrusters. I. Insights from particle-in-cell simulations and two-point power spectral density reconstruction techniques

“…Several instabilities have been identified and studied in HTs. These instabilities cover a large range of frequencies, including: (1) the so-called Breathing Mode (BM) [17][18][19][20] at ≈ 10 kHz, (2) the Ion Transit-Time Instability (ITTI) [21][22][23][24] at ≈ 500 kHz, (3) the Modified Two-Streams Instability (MTSI) [25][26][27][28] at ≈ 1 MHz, (4) the Electron Cyclotron Drift Instability (ECDI) 6,8,15,25,[29][30][31][32][33] and (5) the evolution of the ECDI towards an Ion Acoustic Wave (IAW) 16,27,34 , at ≈ 8 MHz. However, the origin, the growth and the saturation mechanisms of some of the above instabilities remain unclear (see for instance the different theories proposed for the BM 18,19 , or the partial theoretical treatment of the IAW 16 or the ITTI 21 ).…”

Two-dimensional effects on electrostatic instabilities in Hall thrusters. II. Comparison of particle-in-cell simulation results with linear theory dispersion relations

“…The Electron Cyclotron Drift Instability (ECDI) is a short-wavelength (λ ∼ 1 mm) highfrequency (ω ∼ 7 MHz) electrostatic instability that develops mainly along the E × B drift direction. This instability has been studied during the last 20 years 6,15,21,22,24,32,[36][37][38] and has shown to have a significant impact on the electron transport in axial direction. PIC simulations 16,25,39 Two-dimensional effects on electrostatic instabilities II have revealed that this instability evolves towards the Ion Acoustic Wave (IAW) after some tens of microseconds.…”