145 research outputs found
An alternative approach to field-aligned coordinates for plasma turbulence simulations
Turbulence simulation codes can exploit the flute-like nature of plasma
turbulence to reduce the effective number of degrees of freedom necessary to
represent fluctuations. This can be achieved by employing magnetic coordinates
of which one is aligned along the magnetic field. This work presents an
approach in which the position along the field lines is identified by the
toroidal angle, rather than the most commonly used poloidal angle. It will be
shown that this approach has several advantages. Among these, periodicity in
both angles is retained. This property allows moving to an equivalent
representation in Fourier space with a reduced number of toroidal components.
It will be shown how this duality can be exploited to transform conventional
codes that use a spectral representation on the magnetic surface into codes
with a field-aligned coordinate. It is also shown that the new approach can be
generalised to get rid of magnetic coordinates in the poloidal plane
altogether, for a large class of models. Tests are carried out by comparing the
new approach with the conventional approach employing a uniform grid, for a
basic ion temperature gradient (ITG) turbulence model implemented by the two
corresponding versions of the ETAI3D code. These tests uncover an unexpected
property of the model, that localized large parallel gradients can
intermittently appear in the turbulent regime. This leaves open the question
whether this is a general property of plasma turbulence, which may lead one to
reconsider some of the usual assumptions on micro-turbulence dynamics.Comment: 19 pages (once in pdf format). 1 LaTeX file and 10 eps figures in the
zip folde
Gyrokinetic Equations for Strong-Gradient Regions
A gyrokinetic theory is developed under a set of orderings applicable to the
edge region of tokamaks and other magnetic confinement devices, as well as to
internal transport barriers. The result is a practical set equations that is
valid for large perturbation amplitudes [q{\delta}{\psi}/T = O(1), where
{\delta}{\psi} = {\delta}{\phi} - v_par {\delta}A_par/c], which is
straightforward to implement numerically, and which has straightforward
expressions for its conservation properties. Here, q is the particle charge,
{\delta}{\phi} and {\delta}A_par are the perturbed electrostatic and parallel
magnetic potentials, v_par is the parallel velocity, c is the speed of light,
and T is the temperature. The derivation is based on the quantity
{\epsilon}:=({\rho}/{\lambda})q{\delta}{\psi}/T << 1 as the small expansion
parameter, where {\rho} is the gyroradius and {\lambda} is the perpendicular
wavelength. Physically, this ordering requires that the E\times B velocity and
the component of the parallel velocity perpendicular to the equilibrium
magnetic field are small compared to the thermal velocity. For nonlinear
fluctuations saturated at "mixing-length" levels (i.e., at a level such that
driving gradients in profile quantities are locally flattened), {\epsilon} is
of order {\rho}/L, where L is the equilibrium profile scale length, for all
scales {\lambda} ranging from {\rho} to L. This is true even though
q{\delta}{\psi}/T = O(1) for {\lambda} ~ L. Significant additional
simplifications result from ordering L/R =O({\epsilon}), where R is the spatial
scale of variation of the magnetic field. We argue that these orderings are
well satisfied in strong-gradient regions, such as edge and screapeoff layer
regions and internal transport barriers in tokamaks, and anticipate that our
equations will be useful as a basis for simulation models for these regions.Comment: Accepted for publication in the Physics of Plasmas, 12/30/201
An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field
This paper is concerned with the numerical approximation of the isothermal
Euler equations for charged particles subject to the Lorentz force. When the
magnetic field is large, the so-called drift-fluid approximation is obtained.
In this limit, the parallel motion relative to the magnetic field direction
splits from perpendicular motion and is given implicitly by the constraint of
zero total force along the magnetic field lines. In this paper, we provide a
well-posed elliptic equation for the parallel velocity which in turn allows us
to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system.
This scheme gives rise to both a consistent approximation of the Euler-Lorentz
model when epsilon is finite and a consistent approximation of the drift limit
when epsilon tends to 0. Above all, it does not require any constraint on the
space and time steps related to the small value of epsilon. Numerical results
are presented, which confirm the AP character of the scheme and its Asymptotic
Stability
Recommended from our members
Erratum: Time-step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas [B.I. Cohen, A. M. Dimits, A. Friedman, and R. E. Caflisch, IEEE Trans. Plasma Sci. 38, 2394 (2010)]
Recommended from our members
Particle Simulation of Coulomb Collisions: Comparing the Methods of Takizuka & Abe and Nanbu
The interactions of charged particles in a plasma are in a plasma is governed by the long-range Coulomb collision. We compare two widely used Monte Carlo models for Coulomb collisions. One was developed by Takizuka and Abe in 1977, the other was developed by Nanbu in 1997. We perform deterministic and stochastic error analysis with respect to particle number and time step. The two models produce similar stochastic errors, but Nanbu's model gives smaller time step errors. Error comparisons between these two methods are presented
Suppression of turbulence and subcritical fluctuations in differentially rotating gyrokinetic plasmas
Differential rotation is known to suppress linear instabilities in fusion
plasmas. However, even in the absence of growing eigenmodes, subcritical
fluctuations that grow transiently can lead to sustained turbulence. Here
transient growth of electrostatic fluctuations driven by the parallel velocity
gradient (PVG) and the ion temperature gradient (ITG) in the presence of a
perpendicular ExB velocity shear is considered. The maximally simplified case
of zero magnetic shear is treated in the framework of a local shearing box.
There are no linearly growing eigenmodes, so all excitations are transient. The
maximal amplification factor of initial perturbations and the corresponding
wavenumbers are calculated as functions of q/\epsilon (=safety factor/aspect
ratio), temperature gradient and velocity shear. Analytical results are
corroborated and supplemented by linear gyrokinetic numerical tests. For
sufficiently low values of q/\epsilon (<7 in our model), regimes with fully
suppressed ion-scale turbulence are possible. For cases when turbulence is not
suppressed, an elementary heuristic theory of subcritical PVG turbulence
leading to a scaling of the associated ion heat flux with q, \epsilon, velocity
shear and temperature gradient is proposed; it is argued that the transport is
much less stiff than in the ITG regime.Comment: 36 pages in IOP latex style; 12 figures; submitted to PPC
- …