Non-thermal particle acceleration from maximum entropy in collisionless plasmas

Zhdankin, Vladimir

doi:10.1017/s0022377822000551

Cited by 9 publications

(9 citation statements)

References 63 publications

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“…2020; Vega et al. 2022 b ; Uzdensky 2022, and references therein) or as maximisers of a judiciously chosen entropy (e.g., Zhdankin 2022 b ; Ewart et al. 2022).…”

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confidence: 99%

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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“…2020; Vega et al. 2022 b ; Uzdensky 2022, and references therein) or as maximisers of a judiciously chosen entropy (e.g., Zhdankin 2022 b ; Ewart et al. 2022).…”

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confidence: 99%

MHD turbulence: a biased review

Schekochihin

2022

J. Plasma Phys.

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“…As an example, consider the case of entropy in a collisionless (or weakly collisional) plasma, as measured in-situ by spacecraft (in the solar wind or Earth's magnetosphere) or in particle-in-cell simulations [58][59][60][61][62]. Our previous work introduced dimensional entropies for the (relativistic) Vlasov-Maxwell system of equations used to described a collisionless plasma [6,26]. In this case, P = R 6 for a population of N particles with three-dimensional coordinates in both space and momentum, such that X = (x, p).…”

Section: Applicationsmentioning

confidence: 99%

“…1), yielding a quantity that has the same physical dimensions as the phase-space volume. The dimensional entropies are well suited as a diagnostic for irreversibility, and may be applied to elucidate the role of generalized entropy in a range of physical systems, such as collisionless plasmas [e.g., 6,26,27], strongly coupled plasmas [28], gravitationally interacting systems [e.g., [29][30][31][32][33], collisionless systems with long-range interactions [34,35], classical turbulence [36][37][38], quantum processes [39][40][41][42], chemical reactions [43], and biophysics [44].…”

Section: Introductionmentioning

confidence: 99%

Dimensional measures of generalized entropy

Zhdankin

2023

J. Phys. A: Math. Theor.

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Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond the additive definition pioneered by Boltzmann, Gibbs, and Shannon (applicable to thermodynamic equilibria). For generalized entropies to be applied rigorously to nonequilibrium statistical mechanics, we suggest that there is a need for a physically interpretable (dimensional) framework that can be connected to dynamical processes operating in phase space. In this work, we introduce dimensional measures of entropy that admit arbitrary invertible weight functions (subject to curvature and convergence requirements). These ``dimensional entropies'' have physical dimensions of phase-space volume and represent the extent of level sets of the distribution function. Dimensional entropies with power-law weight functions (related to Renyi and Tsallis entropies) are particularly robust, as they do not require any internal dimensional parameters due to their scale invariance. We also point out the existence of composite entropy measures that can be constructed from functionals of dimensional entropies. We calculate the response of the dimensional entropies to perturbations, showing that for a structured distribution, perturbations have the largest impact on entropies weighted at a similar phase-space scale. This elucidates the link between dynamics (perturbations) and statistics (entropies). Finally, we derive corresponding generalized maximum-entropy distributions. Dimensional entropies may be useful as a diagnostic (for irreversibility) and for theoretical modeling (if the underlying irreversible processes in phase space are understood) in chaotic and complex systems, such as collisionless systems of particles with long-range interactions.

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“…2019), magnetic reconnection (Sironi & Spitkovsky 2014; Werner & Uzdensky 2021; Uzdensky 2022), and various types of plasma turbulence (Kunz, Stone & Quataert 2016; Zhdankin et al. 2017, 2019; Comisso & Sironi 2018, 2022; Zhdankin 2021, 2022 b ).…”

Section: Introductionmentioning

confidence: 99%

“…Livadiotis & McComas (2009), Pierrard & Lazar (2010), and references therein). While this model produces good fits to observed distributions, it has a free parameter that is needed to quantify the degree of the non-extensivity and cannot be determined without fitting data, or additional input of physics currently lacking (note some recent progress suggesting that this additional physics might be deducible from free-energy considerations: Zhdankin 2022 a , b ).…”

Section: Introductionmentioning

confidence: 99%

Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria

Ewart,

Nastac,

Schekochihin

2023

J. Plasma Phys.

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Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a ‘hard’ power-law tail $\propto \varepsilon ^{-2}$ , where $\varepsilon$ is the particle energy. The shape of the ‘core’ of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or ‘halo’) that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas.

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Non-thermal particle acceleration from maximum entropy in collisionless plasmas

Cited by 9 publications

References 63 publications

MHD turbulence: a biased review

MHD turbulence: a biased review

Dimensional measures of generalized entropy

Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria

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