Coronal Heating and Reduced MHD

Oughton, Sean; Dmitruk, P.; Matthaeus, W. H.

doi:10.1007/3-540-36238-x_2

Cited by 12 publications

(3 citation statements)

References 87 publications

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“…Reduced magnetohydrodynamics (RMHD) is a nonlinear system of fluid equations used to describe anisotropic fluctuations in magnetised plasmas at length scales much larger than the ion gyroradius and at frequencies much smaller than the ion gyrofrequency . It was initially used to model elongated structures in tokamaks (Kadomtsev & Pogutse 1974; Strauss 1976, 1977) but has since become a standard paradigm for astrophysical contexts such as solar-wind turbulence (Zank & Matthaeus 1992 a , b ; Bhattacharjee, Ng & Spangler 1998) and the solar corona (Oughton, Dmitruk & Matthaeus 2003; Perez & Chandran 2013).…”

Section: Introductionmentioning

confidence: 99%

Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

et al. 2015

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A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al. 2009) to the case where the mean distribution function of the plasma is pressure-anisotropic and different ion species are allowed to drift with respect to each other-a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas such as the intracluster medium. Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g., the Alfvén ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. Beyond these order-unity corrections, the main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvénic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvénic cascade is fluid, satisfying RMHD equations (with the Alfvén speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping (and for a bi-Maxwellian plasma splits into three independent collisionless cascades). Secondly, the organising principle of this turbulence is elucidated in the form of a conservation law for the appropriately generalised kinetic free energy. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses, and that these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics.

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Section: Introductionmentioning

confidence: 99%

Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

et al. 2015

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“…The presence of a magnetic field makes MHD turbulence anisotropic (Montgomery & Turner 1981;Matthaeus et al 1983;Shebalin et al 1983;Higdon 1984;Goldreich & Sridhar 1995; see Oughton et al 2003 for a review). The relative importance of hydrodynamic and magnetic forces changes with scale, so the anisotropy of MHD turbulence does too.…”

Section: Magnetohydrodynamic Turbulencementioning

confidence: 99%

Fast Magnetic Reconnection and Spontaneous Stochasticity

Eyink

Lazarían²,

Vishniac

2011

ApJ

183

260

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Magnetic field lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic-flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfvén flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic," so that infinitely many magnetic field lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive at the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity," but of the field lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian & Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth δ i is much smaller than the turbulent integral length or injection-scale L i .

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“…Departures from pure Alfvén waves may arise from active turbulence which appear to exist among the observed fluctuations. MHD simulations and analysis have shown that outgoing and ingoing Alfvén waves can interact and bring about anisotropic turbulence [e.g., Shebalin et al, 1983;Oughton et al, 1994;Matthaeus et al, 1996;Ng and Bhattacharjee, 1996;Goldreich and Sridhar, 1997;Bhattacharjee et al, 1998Bhattacharjee et al, , 1999Ghosh et al, 1998aGhosh et al, , 1998bCho and Vishniac, 2000;Galtier et al, 2000Galtier et al, , 2002Bhattacharjee and Ng, 2001;Dmitruk et al, 2002;Cho et al, 2002;Lithwick and Goldreich, 2003;Ng et al, 2003;Oughton et al, 2003].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Alfvén waves: 1. Interactions between outgoing and ingoing waves according to an amplitude expansion

Vasquez

Hollweg

2004

J. Geophys. Res.

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[1] We expand the compressible magnetohydrodynamic (MHD) equations in terms of the amplitude of first-order Alfvén waves. Incompressible MHD equations are treated as a special case. We examine the evolution of mildly oblique Alfvén waves consisting of forward and backward propagating waves so that these would correspond to the interactions of outgoing and ingoing Alfvén waves in the solar wind. We obtain the solutions of these equations through second order. We find and distinguish three types of second-order modes which have zero frequency and are generated in association with nonsecular interactions of mildly oblique first-order Alfvén waves. Two of these modes have wave vectors which are perpendicular to the background magnetic field. Both are associated with magnetic energy but they do not have kinetic energy.

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Coronal Heating and Reduced MHD

Cited by 12 publications

References 87 publications

Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

Fast Magnetic Reconnection and Spontaneous Stochasticity

Nonlinear Alfvén waves: 1. Interactions between outgoing and ingoing waves according to an amplitude expansion

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