Theory and simulations of electron vortices generated by magnetic pushing

Abstract

Vortex formation and propagation are observed in kinetic particle-in-cell (PIC) simulations of magnetic pushing in the plasma opening switch. These vortices are studied here within the electron-magnetohydrodynamic (EMHD) approximation using detailed analytical modeling. PIC simulations of these vortices have also been performed. Strong v×B forces in the vortices give rise to significant charge separation, which necessitates the use of the EMHD approximation in which ions are fixed and the electrons are treated as a fluid. A semi-analytic model of the vortex structure is derived, and then used as an initial condition for PIC simulations. Density-gradient-dependent vortex propagation is then examined using a series of PIC simulations. It is found that the vortex propagation speed is proportional to the Hall speed vHall≡cB0/4πneeLn. When ions are allowed to move, PIC simulations show that the electric field in the vortex can accelerate plasma ions, which leads to dissipation of the vortex. This electric field contributes to the separation of ion species that has been observed to occur in pulsed-power experiments with a plasma-opening switch.

Proton acceleration in a laser-induced relativistic electron vortex

“…Due to the approximate anti-symmetry of , shown in figure 2, the drifts in direction must average to zero and the EV moves in a direction consistent with , as found in weakly inhomogeneous plasmas (Richardson et al. 2013; Angus et al. 2014).…”

“…Since the laser-induced electrons propagate with the EV (see figure 3(a) and supplementary movie, available at https://doi.org/10.1017/S0022377819000485), their average drift velocity must equal the EV propagation speed. Due to the approximate anti-symmetry of E x , shown in figure 2, the drifts in y direction must average to zero and the EV moves in a direction consistent with B × ∇n, as found in weakly inhomogeneous plasmas (Richardson et al 2013;Angus et al 2014).…”

“…Here the EVs are micro-scale, long lived, coherent magnetic flux ropes with a unipolar magnetic structure in two dimensions, and share similarities with a particular class of stable solutions to the electron magnetohydrodynamic equations (Nycander & Pavlenko 1991; Gordeev & Levchenko 1998; Yadav, Das & Kaw 2008; Richardson et al. 2013; Angus et al. 2014).…”

“…The EVs are not susceptible to the instabilities arising at the laser-plasma interface, as they form after the laser depletion. Here the EVs are micro-scale, long lived, coherent magnetic flux ropes with a unipolar magnetic structure in two dimensions, and share similarities with a particular class of stable solutions to the electron magnetohydrodynamic equations (Nycander & Pavlenko 1991;Gordeev & Levchenko 1998;Yadav, Das & Kaw 2008;Richardson et al 2013;Angus et al 2014). Unlike the classic TNSA scheme, the acceleration mechanism described here is able to produce a quasi-monoenergetic proton beam, and the drift velocity of the EV -and thus the beam energy -can be Proton acceleration in a laser-induced relativistic electron vortex 3 tuned more easily compared to the collisionless shock acceleration (Silva et al 2004;Fiuza et al 2012;Haberberger et al 2012;Pak et al 2018).…”

Fast magnetic field penetration into low resistivity plasma

“…1996; Fruchtman, Ivanov & Kingsep 1998; Chuvatin, Ivanov & Rudakov 2004; Richardson et al. 2013, 2016) explained the measurements by showing that the Hall electric field can induce a fast magnetic field penetration if the plasma is non-uniform, even if the resistivity is small (but not zero). The velocity of the penetration was shown by the theory to be larger than the hydrodynamic velocity of the plasma pushed by magnetic field pressure, when the scale length of the plasma non-uniformity was smaller than the ion skin depth.…”