The effect of electron inertia in Hall-driven magnetic field penetration in electron-magnetohydrodynamics

Abstract

Magnetic field penetration in electron-magnetohydrodynamics (EMHD) can be driven by density gradients through the Hall term [Kingsep et al., Sov. J. Plasma Phys. 10, 495 (1984)]. Particle-in-cell simulations have shown that a magnetic front can go unstable and break into vortices in the Hall-driven EMHD regime. In order to understand these results, a new fluid model had been derived from the Ly/Ln≪1 limit of EMHD, where Ly is the length scale along the front and Ln is the density gradient length scale. This model is periodic in the direction along the magnetic front, which allows the dynamics of the front to be studied independently of electrode boundary effects that could otherwise dominate the dynamics. Numerical solutions of this fluid model are presented that show for the first time the relation between Hall-driven EMHD, electron inertia, the Kelvin-Helmholtz (KH) instability, and the formation of magnetic vortices. These solutions show that a propagating magnetic front is unstable to the same KH mode predicted for a uniform plasma. This instability causes the electron flow to break up into vortices that are then driven into the plasma with a speed that is proportional to the Hall speed. This demonstrates that, in two-dimensional geometry with sufficiently low collisionality [collision rate ν ≲ vHall/(4δe)], Hall-driven magnetic penetration occurs not as a uniform shock front but rather as vortex-dominated penetration. Once the vortices form, the penetration speed is found to be nearly a factor of two larger than the redicted speed (vHall/2) obtained from Burgers' equation in the one-dimensional limit.

Electron density evolution during a fast, non-diffusive propagation of a magnetic field in a multi-ion-species plasma

“…The apparent absence of a low-velocity value is likely a result of a combination of the rapid acceleration and the limited temporal-response of the spectroscopic system. However, the appearance of a lower velocity at a later time, a phenomenon observed in a large percent of the discharges, may arise from a 2D or 3D effect and could indicate a fluctuation in the magnetic-field (as suggested, for example, in a recent simulation 28 ).…”

“…22,23 More recent simulations show that when electron inertia is considered turbulence effects may develop 24 and the current layer is expected to break into vortices [25][26][27][28] that may affect the velocity and nature of magnetic field penetration. 28 Laboratory observations in such systems of low-resistivity, multi-ion-species plasmas (mostly protons and carbon ions) revealed a phenomenon of simultaneous field penetration and plasma pushing.…”

“…22,23 More recent simulations show that when electron inertia is considered turbulence effects may develop 24 and the current layer is expected to break into vortices [25][26][27][28] that may affect the velocity and nature of magnetic field penetration. 28 Laboratory observations in such systems of low-resistivity, multi-ion-species plasmas (mostly protons and carbon ions) revealed a phenomenon of simultaneous field penetration and plasma pushing. 29 In these experiments, the heavier-ion plasma component (carbon) is penetrated by the magnetic field at a rate much faster than that expected from diffusion, 30 whereas the light-ion plasma (protons) is reflected off the field front, acquiring velocities that are about twice the magnetic-field front propagation velocity.…”

Propagation speed, linear stability, and ion acceleration in radially imploding Hall-driven electron-magnetohydrodynamic shocks

“…One further simplification is to drop the terms in these equations that arise from the electron inertia, as was done in Ref. 5. In this case, Eq.…”

“…For more details about this linear analysis, see Ref. 5, where the calculation is described in detail for the slab model.…”