Effects of finite electron temperature on gradient drift instabilities in partially magnetized plasmas

Abstract

The gradient-drift instabilities of partially magnetized plasmas in plasma devices with crossed electric and magnetic fields are investigated in the framework of the two-fluid model with finite electron temperature in an inhomogeneous magnetic field. The finite electron Larmor radius (FLR) effects are also included via the gyroviscosity tensor taking into account the magnetic field gradient. This model correctly describes the electron dynamics for k ? q e > 1 in the sense of Pad e approximants (here, k ? and q e are the wavenumber perpendicular to the magnetic field and the electron Larmor radius, respectively). The local dispersion relation for electrostatic plasma perturbations with the frequency in the range between the ion and electron cyclotron frequencies and propagating strictly perpendicular to the magnetic field is derived. The dispersion relation includes the effects of the equilibrium E Â B electron current, finite ion velocity, electron inertia, electron FLR, magnetic field gradients, and Debye length effects. The necessary and sufficient condition of stability is derived, and the stability boundary is found. It is shown that, in general, the electron inertia and FLR effects stabilize the short-wavelength perturbations. In some cases, such effects completely suppress the high-frequency short-wavelength modes so that only the long-wavelength low-frequency (with respect to the lower-hybrid frequency) modes remain unstable.

Micro instabilities and rotating spokes in the near-anode region of partially magnetized plasmas

“…A very complete overview of the theory of instabilities in partially magnetized plasmas of E B discharges that includes the effects of density gradients, magnetic field gradients, electron gyroviscosity and collisions has been recently given by A. Smolyakov and his colleagues 9,10,20,24,48 .…”

“…(19) of Ref. 10 ) to properly describe the ion acoustic wave, and the wavelength of the instability at the maximum growth rate should depend on the Debye length for lower values of the plasma density.…”

“…The results presented here give a useful estimate of the average magnetic field (more precisely root mean square magnetic field) in the near-anode region below which electron transport can be considered as classical and above which azimuthal instabilities leading to anomalous transport are likely to develop. The effect of the magnetic field gradient present in the near-anode region of Hall thrusters will be explored in a future work and the results from PIC simulations will be compared with the predictions from the theory 9,10,20,48 .…”

“…The design of Hall thrusters or magnetrons is such that the E B and P B electron drift currents are in the azimuthal direction of a cylindrical geometry (these plasma devices are sometimes called "closed drift" devices 6 ). Since ions are essentially not magnetized, the azimuthal velocity of electrons is much larger than that of ions, and this difference in velocity can generate charge separation and trigger numerous types of instabilities [7][8][9][10] .…”

“…In this first approach we consider the simplifying assumption of a constant magnetic field in the near-anode region. Magnetic field gradients can modify the development of these instabilities 10,20,[46][47][48][49] and we leave the study of their effect for future work.…”