51st Annual Meeting of the APS Division of Plasma Physics
Volume 54, Number 15
Monday–Friday, November 2–6, 2009;
Atlanta, Georgia
Session BP8: Poster Session I: Plasma Sources and Boundaries; Gyrokinetics and Turbulence; Complex, Non-neutral and Other Novel Plasmas
Monday, November 2, 2009
Room: Grand Hall East
Abstract ID: BAPS.2009.DPP.BP8.19
Abstract: BP8.00019 : Properties of Multiscale Finite-Beta Gyrokinetic Plasmas
Preview Abstract
Abstract
Authors:
W.W. Lee
E.A. Startsev
R.A. Kolesnikov
(Princeton Plasma Physics Laboratory)
The numerical issues arise from the finite-$\beta$ gyrokinetic
Maxwell equation of the form,
$
[\nabla_\perp^2 - \beta m_i / m_e -\beta] (\partial \psi
\ \partial t)
= - \beta (\hat{\bf b}_0 \cdot \nabla) \int v_\parallel^3 (\delta g_i
- \delta g_e) dv_\parallel + (\hat{\bf b}_0 \cdot \nabla) \int
v_\parallel (\delta g_i - \delta g_e)dv_\parallel
+ \beta \nabla \psi \times \hat{\bf b}_0 \cdot [(m_i /
m_e) ({\kappa}_n + {\kappa}_{Te}) - ({\kappa}_n
+ {\kappa}_{Ti})/\tau)]
$
will be discussed. The equation is the result of a new
simulation scheme which
separates out the fast particle response due to quasi-static bending
of magnetic field lines by letting
$\delta g=\label = F-(1 + \psi) F_0 - \int dx_{||} {\kappa} \cdot
\delta{\bf B} $,
so that a new full density and/or temperature gradient,
which is set up by the fast particles, is transverse to the
direction of
the full field, background plus perturbation,
where $\hat {\bf b}=\hat {\bf b}_0+\delta
{\bf B}/B_0$,
$\delta {\bf B} = \nabla A_\parallel \times \hat{\bf b}_0$,
$\psi = \phi + \int (\partial A_\parallel / \partial t)
d x_\parallel/c$, $\phi$ and $A_\parallel$ are the perturbed
potentials, and
$\kappa$
represents the zeroth-order inhomogeneities.
For $\beta m_i/m_e (\equiv \rho_s^2 / \delta_e^2) \gg 1$, it is
found that, we need to use a computational grid based on the
electron skin depth
$\delta_e$, which can be an order smaller than $\rho_s$, the
length of interest, in agreement with the analytical perturbative
methods in solving this type of singular equations. The adequacy
of the above equation for the perturbations of the
order of $k \sim \kappa$,$^1$ where $k$ is the perturbed
wavenumber, will also be presented along with their conservation
properties. The issue of transition from $\delta f$ to {\it
total-F} in finite-$\beta$ PIC simulations in general geometry,
based on the particle weights, will also be discussed.
$^1$W. W. Lee and R. Kolesnikov, Phys. Plasmas {\bf 16}, 04506
(2009).
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.DPP.BP8.19