Kinetic effects in a Hall thruster discharge

Abstract

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.

Plasma-sheath instability in Hall thrusters due to periodic modulation of the energy of secondary electrons in cyclotron motion

“…However, if the velocity distribution of emitted electrons is a monotonically decreasing function, the two-stream instability does not develop, 11 the emitted electrons do not lose energy and freely propagate between the walls of a thruster channel, forming counter-streaming secondary electron beams. 12 These beams produce the major part of the electron flux penetrating through the sheath, which results in interesting effects described below.…”

Instability, collapse, and oscillation of sheaths caused by secondary electron emission

“…In applications where collisionality is low, some new kinetic SEE effects arise, including the possibility of secondaries propagating to other surfaces 24,29,48 . The source EEDF f(w // ,w  ) in front of each surface is much different from the Maxwellian case of Sec.…”

“…al 27 . The applicability of the model for HT's is justified elsewhere 28,29,25 . The main control parameters are the uniform applied fields E z and B x , neutral gas density n a , plasma density n 0 , plasma width H and turbulent collision frequency ν turb .…”

General Cause of Sheath Instability Identified for Low Collisionality Plasma in Devices with Secondary Electron Emission

“…But in low collisionality plasmas, kinetic effects arise. For instance, simulations modeling the PPPL HT [15] show the bulk plasma is anisotropic with a strongly depleted loss cone, while SEE from each wall forms a beam that propagates across the plasma, impacting the other wall. These features create an irregular EVDF, making dJ/dΦ difficult to evaluate directly.…”

“…The bulk EVDF in this HT model can be approximated as bi-Maxwellian with temperatures T // = T z and T x , where T z scales as E z 2 ν turb [15]. As γ WC depends on the parallel energies of electrons at the bulk edge, see (4), instability occurs if T z exceeds a critical value.…”