Collisionless relaxation of a Lynden-Bell plasma

Ewart, R. J.; Brown, Andrew; Adkins, T.; Schekochihin, A. A.

doi:10.48550/arxiv.2201.03376

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“…And if so, what is the correct definition of entropy for a collisionless plasma (cf. Fowler 1968;Eyink 2018;Matthaeus et al 2020;Zhdankin 2022a;Chavanis 2021;Ewart et al 2022)?…”

Section: J C Maxwell Molecular Evolutionmentioning

confidence: 99%

“…What is the relaxation rate (i.e., the 'effective collision rate')? It is at this step that the structure of phase-space turbulence, which was flagged as interesting in its own right in § 14.3, comes in as an essential ingredient: in the same way as the 'fluid' theory of turbulent transport in, e.g., a gyrokinetic plasma, requires knowledge of the statistical properties of turbulence, which determine turbulent fluxes of conserved 'fluid' quantities (e.g., Abel et al 2013), the kinetic theory of collisionless relaxation requires one to know the phase-space correlation function of the perturbed distribution function, which determines the turbulent flux of phase density (Kadomtsev & Pogutse 1970;Chavanis 2021;Ewart et al 2022).…”

Section: J C Maxwell Molecular Evolutionmentioning

confidence: 99%

“…The firehose corresponds to the Alfvén speed (14.1) turning imaginary, i.e., it is an instability caused by negative tension; the mirror is not quite as simple to 91 Of course, collisionless equilibrium distributions do not have to be 'thermal', i.e., they can have extended tails at high energies -such tails are indeed observed by astronomers and so non-thermal particle acceleration by turbulence is an object of intense interest to astrophysicists: see references in footnote 90. Mathematically, distribution functions with non-thermal, power-law tails can be derived as solutions of kinetic equations containing phase-space advection and diffusion with velocity-dependent coefficients (see, e.g., Wong et al 2020;Vega et al 2022b;Uzdensky 2022, and references therein) or as maximisers of a judiciously chosen entropy (e.g., Zhdankin 2022b; Ewart et al 2022). In a complete theory, they should appear as fixed points of the 'collisionless collision integrals'.…”

Section: Macro-and Microphysical Consequences Of Pressure Anisotropymentioning

confidence: 99%

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MHD turbulence: a biased review

Schekochihin

2022

J. Plasma Phys.

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This review of scaling theories of magnetohydrodynamic (MHD) turbulence aims to put the developments of the last few years in the context of the canonical time line (from Kolmogorov to Iroshnikov–Kraichnan to Goldreich–Sridhar to Boldyrev). It is argued that Beresnyak's (valid) objection that Boldyrev's alignment theory, at least in its original form, violates the Reduced-MHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, a version of which is recovered in this interpretation, and the concept of dynamic alignment (equivalently, local 3D anisotropy) are thus an example of a physical theory of intermittency in a turbulent system. The emergence of aligned structures naturally brings into play reconnection physics and thus the theory of MHD turbulence becomes intertwined with the physics of tearing, current-sheet disruption and plasmoid formation. Recent work on these subjects by Loureiro, Mallet et al. is reviewed and it is argued that we may, as a result, finally have a reasonably complete picture of the MHD turbulent cascade (forced, balanced, and in the presence of a strong mean field) all the way to the dissipation scale. This picture appears to reconcile Beresnyak's advocacy of the Kolmogorov scaling of the dissipation cutoff (as $\mathrm {Re}^{3/4}$ ) with Boldyrev's aligned cascade. It turns out also that these ideas open the door to some progress in understanding MHD turbulence without a mean field – MHD dynamo – whose saturated state is argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart (this is a new result). On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require some adjustment – and a new scheme for such an adjustment is proposed – to take account of the determining part that a spontaneously emergent 2D condensate plays in mediating the Alfvén-wave cascade from a weakly interacting state to a strongly turbulent (critically balanced) one. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed: imbalanced turbulence (for which a new, tentative theory is proposed), residual energy, MHD turbulence at subviscous scales, and decaying MHD turbulence (where there has been dramatic progress recently, and reconnection again turned out to feature prominently). Finally, it is argued that the natural direction of research is now away from the fluid MHD theory and into kinetic territory – and then, possibly, back again. The review lays no claim to objectivity or completeness, focusing on topics and views that the author finds most appealing at the present moment.

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“…And if so, what is the correct definition of entropy for a collisionless plasma (cf. Fowler 1968;Eyink 2018;Matthaeus et al 2020;Zhdankin 2022a;Chavanis 2021;Ewart et al 2022)?…”

Section: J C Maxwell Molecular Evolutionmentioning

confidence: 99%