1,172 research outputs found
Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics
We report on the algorithms and numerical methods used in Viriato, a novel
fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic
Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys.
Plasmas 18, 102309 (2011)] (which reduce to the standard Reduced-MHD equations
in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations
[Schekochihin et al., Astrophys. J. Suppl. 182:310 (2009)]. Two main
applications of these equations are magnetised (Alfvenic) plasma turbulence and
magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to
separate the dynamics parallel and perpendicular to the ambient magnetic field
(assumed strong). Along the magnetic field, Viriato allows for either a
second-order accurate MacCormack method or, for higher accuracy, a
spectral-like scheme composed of the combination of a total variation
diminishing (TVD) third order Runge-Kutta method for the time derivative with a
7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is
pseudo-spectral, and the time integration is performed by means of an iterative
predictor-corrector scheme. In addition, a distinctive feature of Viriato is
its spectral representation of the parallel velocity-space dependence, achieved
by means of a Hermite representation of the perturbed distribution function. A
series of linear and nonlinear benchmarks and tests are presented, including a
detailed analysis of 2D and 3D Orszag-Tang-type decaying turbulence, both in
fluid and kinetic regimes.Comment: 42 pages, 15 figures, submitted to J. Comp. Phy
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
X-point collapse and saturation in the nonlinear tearing mode reconnection
We study the nonlinear evolution of the resistive tearing mode in slab
geometry in two dimensions. We show that, in the strongly driven regime (large
Delta'), a collapse of the X-point occurs once the island width exceeds a
certain critical value ~1/Delta'. A current sheet is formed and the
reconnection is exponential in time with a growth rate ~eta^1/2, where eta is
the resistivity. If the aspect ratio of the current sheet is sufficiently
large, the sheet can itself become tearing-mode unstable, giving rise to
secondary islands, which then coalesce with the original island. The saturated
state depends on the value of Delta'. For small Delta', the saturation
amplitude is ~Delta' and quantitatively agrees with the theoretical prediction.
If Delta' is large enough for the X-point collapse to have occured, the
saturation amplitude increases noticeably and becomes independent of Delta'.Comment: revtex4, 4 pages, 18 figure
Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests
A set of key properties for an ideal dissipation scheme in gyrokinetic
simulations is proposed, and implementation of a model collision operator
satisfying these properties is described. This operator is based on the exact
linearized test-particle collision operator, with approximations to the
field-particle terms that preserve conservation laws and an H-Theorem. It
includes energy diffusion, pitch-angle scattering, and finite Larmor radius
effects corresponding to classical (real-space) diffusion. The numerical
implementation in the continuum gyrokinetic code GS2 is fully implicit and
guarantees exact satisfaction of conservation properties. Numerical results are
presented showing that the correct physics is captured over the entire range of
collisionalities, from the collisionless to the strongly collisional regimes,
without recourse to artificial dissipation.Comment: 13 pages, 8 figures, submitted to Physics of Plasmas; typos fixe
Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory
A new analytically and numerically manageable model collision operator is
developed specifically for turbulence simulations. The like-particle collision
operator includes both pitch-angle scattering and energy diffusion and
satisfies the physical constraints required for collision operators: it
conserves particles, momentum and energy, obeys Boltzmann's H-theorem
(collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently
dissipates small-scale structure in the velocity space. The process of
transforming this collision operator into the gyroaveraged form for use in
gyrokinetic simulations is detailed. The gyroaveraged model operator is shown
to have more suitable behavior at small scales in phase space than previously
suggested models. A model operator for electron-ion collisions is also
presented.Comment: revtex, 12 page
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