Theory of gradient drift instabilities in low-temperature, partially magnetised plasmas

Abstract

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the $\boldsymbol {E} \times \boldsymbol {B}$ and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the $\boldsymbol {E} \times \boldsymbol {B}$ and $-\boldsymbol {E} \times \boldsymbol {B}$ directions.

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

“…other typical E × B plasmas, such as Hall thrusters [9][10][11][12][13] and Penning discharges [14][15][16][17]. The spoke significantly affects the dynamics of electrons and ions and its fundamental understanding is hereby of importance in the operation and control of these E × B plasma based applications [15,[18][19][20][21][22][23][24][25][26][27]. In magnetrons, the spoke refers to a locally enhanced ionization zone rotating in the azimuthal (E × B) direction above the erosion area (i.e.…”

“…Previous theoretical works (in particular, those related to Hall thrusters [15,33,34]) suggested that a spoke is originated from the drift instability driven by gradients of potential and density. Various theoretical modifications of the gradient drift instability (GDI) were developed, taking into account a variety of effects, such as the magnetic field gradient, inertia, collisions, ion beam and ionization [23,[25][26][27]35]. In recent years, the evidence of GDI being the origin of the spoke was identified by PIC/MCC simulations in planar magnetrons [19], cylindrical magnetrons [18,22,36] and Penning-type discharges [37].…”

Full fluid moment modeling of rotating spokes in Penning-type configuration

“…Recent theoretical work [39] tied to the current study revisited these conditions, re-deriving the fluid dispersion relation for this regime. Assuming the equilibrium electric field and plasma density gradient are in the radial (x) direction, with no variation in the azimuthal (y) direction, with an axial (z) constant, uniform magnetic field, the fluid dispersion relation for a partially magnetized plasma is given by [17]:…”