567 research outputs found
A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
A class of simple kinetic systems is considered, described by the 1D
Vlasov-Landau equation with Poisson or Boltzmann electrostatic response and an
energy source. Assuming a stochastic electric field, a solvable model is
constructed for the phase-space turbulence of the particle distribution. The
model is a kinetic analog of the Kraichnan-Batchelor model of chaotic
advection. The solution of the model is found in Fourier-Hermite space and
shows that the free-energy flux from low to high Hermite moments is suppressed,
with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma
echo). This implies that Landau damping is an ineffective route to dissipation
(i.e., to thermalisation of electric energy via velocity space). The full
Fourier-Hermite spectrum is derived. Its asymptotics are at low wave
numbers and high Hermite moments () and at low Hermite
moments and high wave numbers (). These conclusions hold at wave numbers
below a certain cut off (analog of Kolmogorov scale), which increases with the
amplitude of the stochastic electric field and scales as inverse square of the
collision rate. The energy distribution and flows in phase space are a simple
and, therefore, useful example of competition between phase mixing and
nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but
more complicated multi-dimensional systems that have not so far been amenable
to complete analytical solution.Comment: 35 pages, minor edits, final version accepted by JP
On geometric properties of passive random advection
We study geometric properties of a random Gaussian short-time correlated
velocity field by considering statistics of a passively advected metric tensor.
That describes universal properties of fluctuations of tensor objects frozen
into the fluid and passively advected by it. The problem of one-point
statistics of co- and contravariant tensors is solved exactly, provided the
advected fields do not reach dissipative scales, which would break the symmetry
of the problem. Asymptotic in time duality of the problem is established, which
in the three-dimensional case relates the probabilities of the volume
deformations into "tubes" and into "sheets".Comment: latex, 8 page
Constraints on dynamo action in plasmas
Upper bounds are derived on the amount of magnetic energy that can be
generated by dynamo action in collisional and collisionless plasmas with and
without external forcing. A hierarchy of mathematical descriptions is
considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the
double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and
other kinetic models. It is found that dynamo action is greatly constrained in
models where the magnetic moment of any particle species is conserved. In the
absence of external forcing, the magnetic energy then remains small at all
times if it is small in the initial state. In other words, a small "seed"
magnetic field cannot be amplified significantly, regardless of the nature of
flow, as long as the collision frequency and gyroradius are small enough to be
negligible. A similar conclusion also holds if the system is subject to
external forcing as long as this forcing conserves the magnetic moment of at
least one plasma species and does not greatly increase the total energy of the
plasma (i.e., in practice, is subsonic). Dynamo action therefore always
requires collisions or some small-scale kinetic mechanism for breaking the
adiabatic invariance of the magnetic moment
Self-inhibiting thermal conduction in high-beta, whistler-unstable plasma
A heat flux in a high- plasma with low collisionality triggers the
whistler instability. Quasilinear theory predicts saturation of the instability
in a marginal state characterized by a heat flux that is fully controlled by
electron scattering off magnetic perturbations. This marginal heat flux does
not depend on the temperature gradient and scales as . We confirm this
theoretical prediction by performing numerical particle-in-cell simulations of
the instability. We further calculate the saturation level of magnetic
perturbations and the electron scattering rate as functions of and the
temperature gradient to identify the saturation mechanism as quasilinear.
Suppression of the heat flux is caused by oblique whistlers with
magnetic-energy density distributed over a wide range of propagation angles.
This result can be applied to high- astrophysical plasmas, such as the
intracluster medium, where thermal conduction at sharp temperature gradients
along magnetic-field lines can be significantly suppressed. We provide a
convenient expression for the amount of suppression of the heat flux relative
to the classical Spitzer value as a function of the temperature gradient and
. For a turbulent plasma, the additional independent suppression by the
mirror instability is capable of producing large total suppression factors
(several tens in galaxy clusters) in regions with strong temperature gradients.Comment: accepted to JP
Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is
developed in the framework of Reduced MHD. A local analysis is performed taking
into account the dependence of a generic equilibrium profile on the outflow
coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14},
100703 (2007)] is recovered, i.e., current sheets are unstable to the formation
of a large-wave-number chain of plasmoids (k_{\rm max}\Lsheet \sim S^{3/8},
where is the wave-number of fastest growing mode, S=\Lsheet
V_A/\eta is the Lundquist number, \Lsheet is the length of the sheet,
is the Alfv\'en speed and is the plasma resistivity), which grows
super-Alfv\'enically fast (\gmax\tau_A\sim S^{1/4}, where \gmax is the
maximum growth rate, and \tau_A=\Lsheet/V_A). For typical background
profiles, the growth rate and the wave-number are found to {\it increase} in
the outflow direction. This is due to the presence of another mode, the
Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the
layer, where the outflow velocity exceeds the Alfv\'en speed associated with
the upstream magnetic field. The KH instability grows even faster than the
plasmoid instability, \gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}. The
effect of viscosity () on the plasmoid instability is also addressed. In
the limit of large magnetic Prandtl numbers, , it is found that
\gmax\sim S^{1/4}Pm^{-5/8} and k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16},
leading to the prediction that the critical Lundquist number for plasmoid
instability in the regime is \Scrit\sim 10^4Pm^{1/2}. These results
are verified via direct numerical simulation of the linearized equations, using
a new, analytical 2D SP equilibrium solution.Comment: 21 pages, 9 figures, submitted to Phys. Rev.
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