Velocity-space cascade in magnetized plasmas: Numerical simulations

Abstract

Plasma turbulence is studied via direct numerical simulations in a two-dimensional spatial geometry. Using a hybrid Vlasov-Maxwell model, we investigate the possibility of a velocity-space cascade. A novel theory of space plasma turbulence has been recently proposed by Servidio et al. [PRL, 119, 205101 (2017)], supported by a three-dimensional Hermite decomposition applied to spacecraft measurements, showing that velocity space fluctuations of the ion velocity distribution follow a broad-band, power-law Hermite spectrum P (m), where m is the Hermite index. We numerically explore these mechanisms in a more magnetized regime. We find that (1) the plasma reveals spectral anisotropy in velocity space, due to the presence of an external magnetic field (analogous to spatial anisotropy of fluid and plasma turbulence); (2) the distribution of energy follows the prediction P (m) ∼ m −2 , proposed in the above theoretical-observational work; and (3) the velocity-space activity is intermittent in space, being enhanced close to coherent structures such as the reconnecting current sheets produced by turbulence. These results may be relevant to the nonlinear dynamics weakly-collisional plasma in a wide variety of circumstances.

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

“…The electric and magnetic spectra obtained in the two runs perfectly match, and reveal the typical features observed in solar-wind plasma. Indeed, similarly to previous numerical experiments Valentini et al 2016;Pezzi et al 2018a), an inertial-like range is observed, where the magnetic PSD recalls the Kolmogorov prediction (orange dashed-line) (Kolmogorov 1941), although a proper power-law scaling is not observed due to the limited size of the simulation domain. Around kd p ∼ 1, the usual spectral steepening is recovered (Leamon et al 1998).…”

“…These features are commonly observed in the solar wind and in the terrestrial magnetosheath, manifesting as strong temperature anisotropy enhancements, beams of accelerated particles, rings, and velocity-space vortices (Marsch 2006;Servidio et al 2015;Wilder et al 2016;Lapenta et al 2017). Because of these observational evidences, a turbulent velocity-space enstrophy cascade has been conjectured Servidio et al 2017) and it has been recently observed in the Earth's magnetosheath and in Eulerian hybrid Vlasov simulations Cerri, Kunz & Califano 2018;Pezzi et al 2018a).…”

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

“…One of the more fascinating developments prompted by the interest in energy partition in plasma turbulence has been the realization that, in a kinetic system, we are dealing with a free-energy cascade through the entire phase space, with energy travelling from large to small scales in both position and velocity space (6, 33, 44, 45, 48–54). This is inevitable because the plasma collision operator is a diffusion operator in phase space and so the only way for a kinetic system to have a finite rate of dissipation at very low collisionality is to generate small phase-space scales—just like a hydrodynamic system with low viscosity achieves finite viscous dissipation by generating large flow-velocity gradients.…”

“…This is inevitable because the plasma collision operator is a diffusion operator in phase space and so the only way for a kinetic system to have a finite rate of dissipation at very low collisionality is to generate small phase-space scales—just like a hydrodynamic system with low viscosity achieves finite viscous dissipation by generating large flow-velocity gradients. The study of velocity-space cascades in kinetic systems is still in its infancy—but advances in instrumentation and computing mean that the amount of available information on such cascades in both real (space) physical plasmas (52) and their numerical counterparts (33, 46, 54) is rapidly increasing. Let us then investigate the nature of the phase-space cascade in our ion-heating simulations.…”

Finite-Larmor-radius equilibrium and currents of the Earth’s flank magnetopause

“…We have explicitly shown that first-order FLR corrections exhibit what we have called † Clearly, here we are not taking into account additional deviations from isotropy (and from pure gyrotropy) due to local current and vorticity sheets forming in a turbulent plasma (see, e.g., Servidio et al 2012;Valentini et al 2014Valentini et al , 2016Franci et al 2016;Cerri et al 2018;Pezzi et al 2018) and/or during reconnection events (see, e.g., Scudder & Daughton 2008;Aunai et al 2013) "ωb asymmetry", i.e., an asymmetry that depends on the relative orientation of the fluid vorticity, ω, and of the magnetic-field direction, b, through the scalar product ω · b. Moreover, depending again on the parameter ω · b, it has been demonstrated that the free energy available in the shear flow is able to develop and sustain a non-negligible level of agyrotropy, i.e., a pressure (and temperature) anisotropy that is not limited to the directions parallel and perpendicular to the magnetic field (the so-called gyrotropy), but that manifests also within the plane perpendicular to b as p = p ⊥,1 = p ⊥,2 .…”