39 research outputs found
Dissipation-Scale Turbulence in the Solar Wind
We present a cascade model for turbulence in weakly collisional plasmas that
follows the nonlinear cascade of energy from the large scales of driving in the
MHD regime to the small scales of the kinetic Alfven wave regime where the
turbulence is dissipated by kinetic processes. Steady-state solutions of the
model for the slow solar wind yield three conclusions: (1) beyond the observed
break in the magnetic energy spectrum, one expects an exponential cut-off; (2)
the widely held interpretation that this dissipation range obeys power-law
behavior is an artifact of instrumental sensitivity limitations; and, (3) over
the range of parameters relevant to the solar wind, the observed variation of
dissipation range spectral indices from -2 to -4 is naturally explained by the
varying effectiveness of Landau damping, from an undamped prediction of -7/3 to
a strongly damped index around -4.Comment: 6 pages, 2 figures, accepted for publication in AIP Conference
Proceedings on "Turbulence and Nonlinear Processes in Astrophysical Plasmas
Transition from collisionless to collisional MRI
Recent calculations by Quataert et al. (2002) found that the growth rates of
the magnetorotational instability (MRI) in a collisionless plasma can differ
significantly from those calculated using MHD. This can be important in hot
accretion flows around compact objects. In this paper we study the transition
from the collisionless kinetic regime to the collisional MHD regime, mapping
out the dependence of the MRI growth rate on collisionality. A kinetic closure
scheme for a magnetized plasma is used that includes the effect of collisions
via a BGK operator. The transition to MHD occurs as the mean free path becomes
short compared to the parallel wavelength 2\pi/k_{\Par}. In the weak magnetic
field regime where the Alfv\'en and MRI frequencies are small compared
to the sound wave frequency k_{\Par} c_0, the dynamics are still effectively
collisionless even if , so long as the collision frequency \nu
\ll k_{\Par} c_{0}; for an accretion flow this requires \nu \lsim \Omega
\sqrt{\beta}. The low collisionality regime not only modifies the MRI growth
rate, but also introduces collisionless Landau or Barnes damping of long
wavelength modes, which may be important for the nonlinear saturation of the
MRI.Comment: 20 pages, 4 figures, submitted to ApJ with a clearer derivation of
anisotropic pressure closure from drift kinetic equatio
Shearing Box Simulations of the MRI in a Collisionless Plasma
We describe local shearing box simulations of turbulence driven by the
magnetorotational instability (MRI) in a collisionless plasma. Collisionless
effects may be important in radiatively inefficient accretion flows, such as
near the black hole in the Galactic Center. The MHD version of ZEUS is modified
to evolve an anisotropic pressure tensor. A fluid closure approximation is used
to calculate heat conduction along magnetic field lines. The anisotropic
pressure tensor provides a qualitatively new mechanism for transporting angular
momentum in accretion flows (in addition to the Maxwell and Reynolds stresses).
We estimate limits on the pressure anisotropy due to pitch angle scattering by
kinetic instabilities. Such instabilities provide an effective ``collision''
rate in a collisionless plasma and lead to more MHD-like dynamics. We find that
the MRI leads to efficient growth of the magnetic field in a collisionless
plasma, with saturation amplitudes comparable to those in MHD. In the saturated
state, the anisotropic stress is comparable to the Maxwell stress, implying
that the rate of angular momentum transport may be moderately enhanced in a
collisionless plasma.Comment: 20 pages, 9 figures, submitted to Ap
The Magnetorotational Instability in a Collisionless Plasma
We consider the linear axisymmetric stability of a differentially rotating
collisionless plasma in the presence of a weak magnetic field; we restrict our
analysis to wavelengths much larger than the proton Larmor radius. This is the
kinetic version of the magnetorotational instability explored extensively as
mechanism for magnetic field amplification and angular momentum transport in
accretion disks. The kinetic calculation is appropriate for hot accretion flows
onto compact objects and for the growth of very weak magnetic fields, where the
collisional mean free path is larger than the wavelength of the unstable modes.
We show that the kinetic instability criterion is the same as in MHD, namely
that the angular velocity decrease outwards. However, nearly every mode has a
linear kinetic growth rate that differs from its MHD counterpart. The kinetic
growth rates also depend explicitly on beta, i.e., on the ratio of the gas
pressure to the pressure of the seed magnetic field. For beta ~ 1 the kinetic
growth rates are similar to the MHD growth rates while for beta >> 1 they
differ significantly. For beta >> 1, the fastest growing mode has a growth rate
of sqrt{3} Omega for a Keplerian disk, larger than its MHD counterpart; there
are also many modes whose growth rates are negligible, < beta^{-1/2} Omega <<
Omega. We provide a detailed physical interpretation of these results and show
that gas pressure forces, rather than just magnetic forces, are central to the
behavior of the magnetorotational instability in a collisionless plasma. We
also discuss the astrophysical implications of our analysis.Comment: Accepted by ApJ; 24 pages (4 figures
Astrophysical Gyrokinetics: Basic Equations and Linear Theory
Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of
astrophysical plasmas, including accretion disks, the solar wind, and the
interstellar and intracluster medium. On small scales, this turbulence is often
expected to consist of highly anisotropic fluctuations with frequencies small
compared to the ion cyclotron frequency. For a number of applications, the
small scales are also collisionless, so a kinetic treatment of the turbulence
is necessary. We show that this anisotropic turbulence is well described by a
low frequency expansion of the kinetic theory called gyrokinetics. This paper
is the first in a series to examine turbulent astrophysical plasmas in the
gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations
and explore the linear properties of gyrokinetics as a prelude to nonlinear
simulations. The linear dispersion relation for gyrokinetics is obtained and
its solutions are compared to those of hot-plasma kinetic theory. These results
are used to validate the performance of the gyrokinetic simulation code {\tt
GS2} in the parameter regimes relevant for astrophysical plasmas. New results
on global energy conservation in gyrokinetics are also derived. We briefly
outline several of the problems to be addressed by future nonlinear
simulations, including particle heating by turbulence in hot accretion flows
and in the solar wind, the magnetic and electric field power spectra in the
solar wind, and the origin of small-scale density fluctuations in the
interstellar medium.Comment: emulateapj, 24 pages, 10 figures, revised submission to ApJ:
references added, typos corrected, reorganized and streamline