A kinetic model of plasma turbulence

Abstract

A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T⊥/T∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T⊥/T∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas

Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory

“…We observe here in spacecraft data the same kind of fine scale velocity structure reported frequently in Vlasov simulations [9,16]. This motivates a further analysis of the velocity space structure in terms of a Hermite spectral analysis, which has the physically interesting heuristic interpretation as a moment heirarchy.…”

“…Previous works [6,8] show that kinetic processes such as heating are connected to sharp gradients of magnetic, velocity and density fields. In simulations, such coherent structures are correlated with strong distortions of the proton VDFs [2,3,9]. To select structures, here we compute a multiple-data stream variation of the Partial Variance of Increments method, defining PVI max (t) = MAX {PVI n (t), PVI u (t), PVI b (t)}, where, for each field g (density n, velocity u, magnetic field b), the value of PVI is computed in the standard way as PVI g (t) = |∆g|/ |∆g| 2 .…”

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

“…This is an important problem that can impact PIC applications in areas such as plasma turbulence (see, e.g. [6,80]), suggesting that denoising techniques are mandatory for PIC there.…”

Energy transfer, pressure tensor, and heating of kinetic plasma

“…These effects are associated typically with coherent structures such as magnetic structures. Indeed, intense kinetic activity is often found in the general proximity to strong gradients, including not only magnetic, but also strong density and velocity gradients [16,[55][56][57][58][59][60]. In particular, Refs.…”