70 research outputs found
Thermal disequilibration of ions and electrons by collisionless plasma turbulence
Does overall thermal equilibrium exist between ions and electrons in a weakly
collisional, magnetised, turbulent plasma---and, if not, how is thermal energy
partitioned between ions and electrons? This is a fundamental question in
plasma physics, the answer to which is also crucial for predicting the
properties of far-distant astronomical objects such as accretion discs around
black holes. In the context of discs, this question was posed nearly two
decades ago and has since generated a sizeable literature. Here we provide the
answer for the case in which energy is injected into the plasma via Alfv\'enic
turbulence: collisionless turbulent heating typically acts to disequilibrate
the ion and electron temperatures. Numerical simulations using a hybrid
fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an
increasing function of the thermal-to-magnetic energy ratio,
: it ranges from at to at
least for . This energy partition is
approximately insensitive to the ion-to-electron temperature ratio
. Thus, in the absence of other equilibrating
mechanisms, a collisionless plasma system heated via Alfv\'enic turbulence will
tend towards a nonequilibrium state in which one of the species is
significantly hotter than the other, viz., hotter ions at high
, hotter electrons at low . Spectra of
electromagnetic fields and the ion distribution function in 5D phase space
exhibit an interesting new magnetically dominated regime at high and
a tendency for the ion heating to be mediated by nonlinear phase mixing
("entropy cascade") when and by linear phase mixing
(Landau damping) when $\beta_\mathrm{i}\gg1
MHD Turbulence: A Biased Review
This review puts the developments of the last few years in the context of the
canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to
Boldyrev). It is argued that Beresnyak's objection that Boldyrev's alignment
theory violates the RMHD rescaling symmetry can be reconciled with alignment if
the latter is understood as an intermittency effect. Boldyrev's scalings,
recovered in this interpretation, are thus an example of a physical theory of
intermittency in a turbulent system. Emergence of aligned structures brings in
reconnection physics, so the theory of MHD turbulence intertwines with the
physics of tearing and current-sheet disruption. Recent work on this by
Loureiro, Mallet et al. is reviewed and it is argued that we finally have a
reasonably complete picture of MHD cascade all the way to the dissipation
scale. This picture appears to reconcile Beresnyak's Kolmogorov scaling of the
dissipation cutoff with Boldyrev's aligned cascade. These ideas also enable
some progress in understanding saturated MHD dynamo, argued to be controlled by
reconnection and to contain, at small scales, a tearing-mediated cascade
similar to its strong-mean-field counterpart. On the margins of this core
narrative, standard weak-MHD-turbulence theory is argued to require adjustment
- and a scheme for it is proposed - to take account of the part that a
spontaneously emergent 2D condensate plays in mediating the Alfven-wave
cascade. This completes the picture of the MHD cascade at large scales. A
number of outstanding issues are surveyed, concerning imbalanced MHD turbulence
(for which a new theory is proposed), residual energy, subviscous and decaying
regimes of MHD turbulence (where reconnection again features prominently).
Finally, it is argued that the natural direction of research is now away from
MHD and into kinetic territory.Comment: 188 pages, 49 figures; (re)submitted to JPP; this version is
substantially modified from v1, especially secs 7.3, 8.2, 11, 12.4, 13.4 and
appendices B.3, C.5, C.
Fluidization of collisionless plasma turbulence
In a collisionless, magnetized plasma, particles may stream freely along
magnetic-field lines, leading to phase "mixing" of their distribution function
and consequently to smoothing out of any "compressive" fluctuations (of
density, pressure, etc.,). This rapid mixing underlies Landau damping of these
fluctuations in a quiescent plasma-one of the most fundamental physical
phenomena that make plasma different from a conventional fluid. Nevertheless,
broad power-law spectra of compressive fluctuations are observed in turbulent
astrophysical plasmas (most vividly, in the solar wind) under conditions
conducive to strong Landau damping. Elsewhere in nature, such spectra are
normally associated with fluid turbulence, where energy cannot be dissipated in
the inertial scale range and is therefore cascaded from large scales to small.
By direct numerical simulations and theoretical arguments, it is shown here
that turbulence of compressive fluctuations in collisionless plasmas strongly
resembles one in a collisional fluid and does have broad power-law spectra.
This "fluidization" of collisionless plasmas occurs because phase mixing is
strongly suppressed on average by "stochastic echoes", arising due to nonlinear
advection of the particle distribution by turbulent motions. Besides resolving
the long-standing puzzle of observed compressive fluctuations in the solar
wind, our results suggest a conceptual shift for understanding kinetic plasma
turbulence generally: rather than being a system where Landau damping plays the
role of dissipation, a collisionless plasma is effectively dissipationless
except at very small scales. The universality of "fluid" turbulence physics is
thus reaffirmed even for a kinetic, collisionless system
Firehose and Mirror Instabilities in a Collisionless Shearing Plasma
Hybrid-kinetic numerical simulations of firehose and mirror instabilities in
a collisionless plasma are performed in which pressure anisotropy is driven as
the magnetic field is changed by a persistent linear shear . For a
decreasing field, it is found that mostly oblique firehose fluctuations grow at
ion Larmor scales and saturate with energies ; the pressure
anisotropy is pinned at the stability threshold by particle scattering off
microscale fluctuations. In contrast, nonlinear mirror fluctuations are large
compared to the ion Larmor scale and grow secularly in time; marginality is
maintained by an increasing population of resonant particles trapped in
magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors
are formed and particles scatter off their sharp edges. Both instabilities
drive sub-ion-Larmor--scale fluctuations, which appear to be
kinetic-Alfv\'{e}n-wave turbulence. Our results impact theories of momentum and
heat transport in astrophysical and space plasmas, in which the stretching of a
magnetic field by shear is a generic process.Comment: 5 pages, 8 figures, accepted for publication in Physical Review
Letter
Magneto-immutable turbulence in weakly collisional plasmas
We propose that pressure anisotropy causes weakly collisional turbulent
plasmas to self-organize so as to resist changes in magnetic-field strength. We
term this effect "magneto-immutability" by analogy with incompressibility
(resistance to changes in pressure). The effect is important when the pressure
anisotropy becomes comparable to the magnetic pressure, suggesting that in
collisionless, weakly magnetized (high-) plasmas its dynamical relevance
is similar to that of incompressibility. Simulations of magnetized turbulence
using the weakly collisional Braginskii model show that magneto-immutable
turbulence is surprisingly similar, in most statistical measures, to critically
balanced MHD turbulence. However, in order to minimize magnetic-field
variation, the flow direction becomes more constrained than in MHD, and the
turbulence is more strongly dominated by magnetic energy (a nonzero "residual
energy"). These effects represent key differences between pressure-anisotropic
and fluid turbulence, and should be observable in the turbulent
solar wind.Comment: Accepted for publication in J. Plasma Phy
Weak Alfvén-wave turbulence revisited
Weak Alfvénic turbulence in a periodic domain is considered as a mixed state of Alfvén waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed, and, indeed, none is found. If the 2D modes are not directly forced, k−2 and k−1 spectra are found for the Alfvén waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar, and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagating Alfvén waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved
Astrophysical gyrokinetics: Turbulence in pressure-anisotropic plasmas at ion scales and beyond
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.Comment: 59 pages, 6 figures, accepted for publication in Journal of Plasma
Physics (original 28 Nov 2017); abstract abridge
Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
The existence of a weak galactic magnetic field has been repeatedly confirmed
by observational data. The origin of this field has not as yet been explained
in a fully satisfactory way and represents one of the main challenges of the
astrophysical dynamo theory. In both the galactic dynamo theory and the
primordial-origin theory, a major influence is exerted by the small-scale
magnetic fluctuations. This article is devoted to constructing a systematic
second-order statistical theory of such small-scale fields. The statistics of
these fields are studied in the kinematic approximation and for the case of
large Prandtl numbers, which is relevant for the galactic and protogalactic
plasma. The advecting velocity field is assumed to be Gaussian and short-time
correlated. Theoretical understanding of this kinematic dynamo model is a
necessary prerequisite for any prospective nonlinear dynamo theory. The theory
is developed for an arbitrary degree of compressibility and formally in d
dimensions, which generalizes the previously known results, elicits the
structure of the solutions, and uncovers a number of new effects. The magnetic
energy spectra are studied as they grow and spread over scales during the
initial stage of the field amplification. Exact Green's-function solutions are
obtained. The spectral theory is supplemented by the study of magnetic-field
correlation functions in the configuration space, where the dynamo problem can
be mapped onto a particular one-dimensional quantum-mechanical problem. The
latter approach is most suitable for the description of the kinematic dynamo in
the long-time limit, i.e. when the magnetic excitation has spread over all
scales present in the system. A simple way of calculating the growth rates of
the magnetic fields in this long-time limit is proposed.Comment: aastex, 52 pages, 10 figures; final version of the paper as published
in Ap
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