1,670 research outputs found
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
A scaling theory of long-wavelength electrostatic turbulence in a magnetised,
weakly collisional plasma (e.g., ITG turbulence) is proposed, with account
taken both of the nonlinear advection of the perturbed particle distribution by
fluctuating ExB flows and of its phase mixing, which is caused by the streaming
of the particles along the mean magnetic field and, in a linear problem, would
lead to Landau damping. It is found that it is possible to construct a
consistent theory in which very little free energy leaks into high velocity
moments of the distribution function, rendering the turbulent cascade in the
energetically relevant part of the wave-number space essentially fluid-like.
The velocity-space spectra of free energy expressed in terms of Hermite-moment
orders are steep power laws and so the free-energy content of the phase space
does not diverge at infinitesimal collisionality (while it does for a linear
problem); collisional heating due to long-wavelength perturbations vanishes in
this limit (also in contrast with the linear problem, in which it occurs at the
finite rate equal to the Landau-damping rate). The ability of the free energy
to stay in the low velocity moments of the distribution function is facilitated
by the "anti-phase-mixing" effect, whose presence in the nonlinear system is
due to the stochastic version of the plasma echo (the advecting velocity
couples the phase-mixing and anti-phase-mixing perturbations). The partitioning
of the wave-number space between the (energetically dominant) region where this
is the case and the region where linear phase mixing wins its competition with
nonlinear advection is governed by the "critical balance" between linear and
nonlinear timescales (which for high Hermite moments splits into two
thresholds, one demarcating the wave-number region where phase mixing
predominates, the other where plasma echo does).Comment: 45 pages (single-column), 3 figures, replaced with version published
in JP
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
Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas
This letter presents the first ab initio, fully electromagnetic, kinetic
simulations of magnetized turbulence in a homogeneous, weakly collisional
plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic and
electric-field energy spectra show a break at the ion gyroscale; the spectral
slopes are consistent with scaling predictions for critically balanced
turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of
kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for
magnetic and -1/3 for electric fluctuations). This behavior is also
qualitatively consistent with in situ measurements of turbulence in the solar
wind. Our findings support the hypothesis that the frequencies of turbulent
fluctuations in the solar wind remain well below the ion cyclotron frequency
both above and below the ion gyroscale.Comment: 4 pages, 3 figures, submitted to Physical Review Letter
Transition to subcritical turbulence in a tokamak plasma
Tokamak turbulence, driven by the ion-temperature gradient and occurring in
the presence of flow shear, is investigated by means of local, ion-scale,
electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of
the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A
parameter scan in the local values of the ion-temperature gradient and flow
shear is performed. It is demonstrated that the experimentally observed state
is near the stability threshold and that this stability threshold is nonlinear:
sheared turbulence is subcritical, i.e. the system is formally stable to small
perturbations, but, given a large enough initial perturbation, it transitions
to a turbulent state. A scenario for such a transition is proposed and
supported by numerical results: close to threshold, the nonlinear saturated
state and the associated anomalous heat transport are dominated by long-lived
coherent structures, which drift across the domain, have finite amplitudes, but
are not volume filling; as the system is taken away from the threshold into the
more unstable regime, the number of these structures increases until they
overlap and a more conventional chaotic state emerges. Whereas this appears to
represent a new scenario for transition to turbulence in tokamak plasmas, it is
reminiscent of the behaviour of other subcritically turbulent systems, e.g.
pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic
Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows
This paper presents a complete theoretical framework for plasma turbulence
and transport in tokamak plasmas. The fundamental scale separations present in
plasma turbulence are codified as an asymptotic expansion in the ratio of the
gyroradius to the equilibrium scale length. Proceeding order-by-order in this
expansion, a framework for plasma turbulence is developed. It comprises an
instantaneous equilibrium, the fluctuations driven by gradients in the
equilibrium quantities, and the transport-timescale evolution of mean profiles
of these quantities driven by the fluctuations. The equilibrium distribution
functions are local Maxwellians with each flux surface rotating toroidally as a
rigid body. The magnetic equillibrium is obtained from the Grad-Shafranov
equation for a rotating plasma and the slow (resistive) evolution of the
magnetic field is given by an evolution equation for the safety factor q.
Large-scale deviations of the distribution function from a Maxwellian are given
by neoclassical theory. The fluctuations are determined by the high-flow
gyrokinetic equation, from which we derive the governing principle for
gyrokinetic turbulence in tokamaks: the conservation and local cascade of free
energy. Transport equations for the evolution of the mean density, temperature
and flow velocity profiles are derived. These transport equations show how the
neoclassical corrections and the fluctuations act back upon the mean profiles
through fluxes and heating. The energy and entropy conservation laws for the
mean profiles are derived. Total energy is conserved and there is no net
turbulent heating. Entropy is produced by the action of fluxes flattening
gradients, Ohmic heating, and the equilibration of mean temperatures. Finally,
this framework is condensed, in the low-Mach-number limit, to a concise set of
equations suitable for numerical implementation.Comment: 113 pages, 3 figure
Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence
Electrostatic turbulence in weakly collisional, magnetized plasma can be
interpreted as a cascade of entropy in phase space, which is proposed as a
universal mechanism for dissipation of energy in magnetized plasma turbulence.
When the nonlinear decorrelation time at the scale of the thermal Larmor radius
is shorter than the collision time, a broad spectrum of fluctuations at
sub-Larmor scales is numerically found in velocity and position space, with
theoretically predicted scalings. The results are important because they
identify what is probably a universal Kolmogorov-like regime for kinetic
turbulence; and because any physical process that produces fluctuations of the
gyrophase-independent part of the distribution function may, via the entropy
cascade, result in turbulent heating at a rate that increases with the
fluctuation amplitude, but is independent of the collision frequency.Comment: Revtex, 4 pages, 3 figures; replaced to match published versio
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