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Recent analytical studies and particle-in-cell simulations suggested that the electron velocity distribution function in a Hall thruster plasma is non-Maxwellian and anisotropic. 1,2 The electron average kinetic energy in the direction parallel to walls is several times larger than the electron average kinetic energy in direction normal to the walls. Electrons are stratified into several groups depending on their origin (e.g., plasma discharge or thruster channel walls) and confinement (e.g., lost on the walls or trapped in the plasma). Practical analytical formulas are derived for wall fluxes, secondary electron fluxes, plasma parameters, and conductivity. The calculations based on analytical formulas agree well with the results of numerical simulations. The self-consistent analysis demonstrates that elastic electron scattering on collisions with atoms and ions plays a key role in formation of the electron energy distribution function and plasma-wall interaction. The fluxes of electrons from the plasma bulk are shown to be proportional to the rate of scattering to loss cone, thus collision frequency determines the wall potential and secondary electron fluxes. Secondary electron emission from the walls is shown to enhance the electron conductivity across the magnetic field, while having almost no effect on insulating properties of the near-wall sheaths. Such a self-consistent decoupling between secondary electron emission effects on electron energy losses and electron crossed-field transport is currently not captured by the existing fluid and hybrid models of the Hall thrusters.

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 ExB 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. 2D axial-azimuthal Particle-In-Cell benchmark for low-temperature partially ...

Fluid theory and simulations of instabilities, turbulent transport and coherent structures in partially-magnetized plasmas of discharges To cite this article: A I Smolyakov et al 2017 Plasma Phys. Control. Fusion 59 014041 View the article online for updates and enhancements. Related content Anomalous transport in high-temperature plasmas with applications to solenoidal fusion systems R.C. Davidson and N.A. Krall-Modelling electron transport in magnetized low-temperature discharge plasmas G J M Hagelaar-Physics, simulation and diagnostics of Hall effect thrusters J C Adam, J P Boeuf, N Dubuit et al.-Recent citations Nonlinear structures and anomalous transport in partially magnetized E×B plasmas Salomon Janhunen et al-Centrifugal instability in the regime of fast rotation R.

Macroscopic models for the equilibrium of a three-component electronegative gas discharge are developed. Assuming the electrons and the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is derived. Such a discharge can consist of an electronegative core and may have electropositive edge regions, but the electropositive regions become small for the highly electronegative plasma considered here. In the parameter range for which the negative ions are Boltzmann, the electron density in the core is nearly uniform, allowing the nonlinear diffusion equation to be solved in terms of elliptic integrals. If the loss of positive ions to the walls dominates the recombination loss, a simpler parabolic solution can be obtained. If recombination loss dominates the loss to the walls, the assumption that the negative ions are in Boltzmann equilibrium is not justified, requiring coupled differential equations for positive and negative ions. Three parameter ranges are distinguished corresponding to a range in which a parabolic approximation is appropriate, a range for which the recombination significantly modifies the ion profiles, but the electron profile is essentially flat, and a range where the electron density variation influences the solution. The more complete solution of the coupled ion equations with the electrons in Boltzmann equilibrium, but not at constant density, is numerically obtained and compared with the more approximate solutions. The theoretical considerations are illustrated using a plane parallel discharge with chlorine feedstock gas of p = 30, 300 and 2000 mTorr and n e0 = 10 10 cm −3 , corresponding to the three parameter regimes. A heuristic model is constructed which gives reasonably accurate values of the plasma parameters in regimes for which the parabolic profile is not adequate.

The propagation of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam pulse by the background plasma. The electric and magnetic fields generated by the ion beam are studied analytically for the nonlinear case where the plasma density is comparable in size with the beam density. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been performed for parameters relevant to heavy ion fusion assuming long, dense beams with length lb≫Vb/ωb, where Vb is the beam velocity, and ωb is the electron plasma frequency evaluated with the ion beam density. An important conclusion is that for long, nonrelativistic ion beams, charge neutralization is, for all practical purposes, complete even for very tenuous background plasmas. As a result, the self-magnetic force dominates the electric force and the beam ions are always pinched during beam propagation in a background plasma.

The major emissive probe techniques are compared to better understand the floating potential of an electron emitting surface in a plasma. An overview of the separation point technique, floating point technique, and inflection point in the limit of zero emission technique is given, addressing how each method works as well as the theoretical basis and limitations of each. It is shown that while the floating point method is the most popular, it is expected to yield a value ∼1.5Te/e below the plasma potential due to a virtual cathode forming around the probe. The theoretical predictions were checked with experiments performed in a 2 kW annular Hall thruster plasma (ne ∼ 109−1010 cm−3and Te ∼ 10−50 eV). The authors find that the floating point method gives a value around 2Te/e below the inflection point method, which is shown to be a more accurate emissive probe technique than other techniques used in this work for measurements of the plasma potential.

The problem of long wavelength instabilities in Hall thruster plasmas is revisited. A fluid model of the instabilities driven by the E0×B drift in plasmas with gradients of density, electron temperature, and magnetic field is proposed. It is shown that full account of compressibility of the electron flow in inhomogeneous magnetic field leads to quantitative modifications of earlier obtained instability criteria and characteristics of unstable modes. Modification of the stability criteria due to finite temperature fluctuations is investigated.