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Register a new userAstrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond
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We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. Turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it, and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (2015). At scales at and below the ion Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalisation of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a general free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy can cause large variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects the turbulent fluctuation spectra, the differential heating of particle species, and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.
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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) for pressure-anisotropic plasmas, allowing for species drifts---a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas (e.g. intracluster medium). Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g., the Alfven 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. The main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvenic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvenic cascade is fluid, satisfying RMHD equations (with the Alfven speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping. Secondly, the organising principle of this turbulence is elucidated in the form of a generalised kinetic free-energy invariant. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses; 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.
A two-dimensional particle-in-cell simulation is performed to investigate weakly magnetized perpendicular shocks with a magnetization parameter of 6 x 10^-5, which is equivalent to a high Alfven Mach number M_A of ~130. It is shown that current filaments form in the foot region of the shock due to the ion-beam--Weibel instability (or the ion filamentation instability) and that they generate a strong magnetic field there. In the downstream region, these current filaments also generate a tangled magnetic field that is typically 15 times stronger than the upstream magnetic field. The thermal energies of electrons and ions in the downstream region are not in equipartition and their temperature ratio is T_e / T_i ~ 0.3 - 0.4. Efficient electron acceleration was not observed in our simulation, although a fraction of the ions are accelerated slightly on reflection at the shock. The simulation results agree very well with the Rankine-Hugoniot relations. It is also shown that electrons and ions are heated in the foot region by the Buneman instability (for electrons) and the ion-acoustic instability (for both electrons and ions). However, the growth rate of the Buneman instability is significantly reduced due to the relatively high temperature of the reflected ions. For the same reason, ion-ion streaming instability does not grow in the foot region.
The constraint imposed by magnetic helicity conservation on the alpha effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the alpha effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha ( H$alpha$) effect. Direct numerical simulations of the H$alpha$ effect are prese nted for two examples---the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.
In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $vB_0$, exists if the ratio of parallel to perpendicular (with respect to $vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor--Karman-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, DC field strength, and cross-helicity, on the nature of similarity decay is discussed.
textit{Parker Solar Probe} has shown the ubiquitous presence of strong magnetic field deflections, namely switchbacks, during its first perihelion where it was embedded in a highly Alfvenic slow stream. Here, we study the turbulent magnetic fluctuations around ion scales in three intervals characterized by a different switchback activity, identified by the behaviour of the magnetic field radial component, $B_r$. textit{Quiet} ($B_r$ does not show significant fluctuations), textit{weak} ($B_r$ has strong fluctuations but no reversals) and textit{strong} ($B_r$ has full reversals) periods show a different behaviour also for ion quantities and Alfvenicity. However, the spectral analysis shows that each stream is characterized by the typical Kolmogorov/Kraichnan power law in the inertial range, followed by a break around the characteristic ion scales. This frequency range is characterized by strong intermittent activity, with the presence of non-compressive coherent structures, such as current sheets and vortex-like structures, and wave packets, identified as ion cyclotron modes. Although, all these intermittent events have been detected in the three periods, they have a different influence in each of them. Current sheets are dominant in the textit{strong} period, wave packets are the most common in the textit{quiet} interval; while, in the textit{weak} period, a mixture of vortices and wave packets is observed. This work provides an insight into the heating problem in collisionless plasmas, fitting in the context of the new solar missions, and, especially for textit{Solar Orbiter}, which will allow an accurate magnetic connectivity analysis, to link the presence of different intermittent events to the source region.
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