49th Annual Meeting of the Division of Plasma Physics
Volume 52, Number 11
Monday–Friday, November 12–16, 2007;
Orlando, Florida
Session YI1: Ripple and Rotation Studies
9:30 AM–12:30 PM,
Friday, November 16, 2007
Rosen Centre Hotel
Room: Junior Ballroom
Chair: Steve Scott, Princeton Plasma Physics Laboratory
Abstract ID: BAPS.2007.DPP.YI1.6
Abstract: YI1.00006 : Turbulent Equipartition Theory of Toroidal Momentum Pinch*
12:00 PM–12:30 PM
Preview Abstract
Abstract
Author:
T.S. Hahm
(Plasma Physics Laboratory, Princeton University)
The turbulent convective flux (pinch) of the toroidal angular
momentum density is derived
using the nonlinear toroidal gyrokinetic equation which conserves
phase space density and energy[1], and a novel pinch mechanism
which originates from
the symmetry breaking due to
the magnetic field curvature is identified. A net parallel
momentum transfer
from the waves to the ion guiding centers is possible
when the fluctuation intensity varies on the flux surface,
resulting in imperfect
cancellation of the curvature drift contribution to the parallel
acceleration.
This pinch velocity of the angular momentum density can also be
understood as a manifestation of a tendency to
homogenize the profile of ``magnetically weighted angular
momentum density,'' $nm_{i}RU_{\parallel}/B^{2}$.
This part of the pinch flux is mode-independent (whether it's TEM
driven or ITG driven),
and radially inward for fluctuations peaked at the low-$B$-field
side, with a pinch velocity typically,
$V^{TEP}_{Ang} \sim - 2 \chi_{\phi}/R_{0}$.
We compare and contrast the pinch of toroidal angular momentum
with the now familiar ``turbulent equipartition'' (TEP)
mechanism for the particle pinch[2]
which exhibit some relevance in various L-mode plasmas in tokamaks.
In our theoretical model[3], the TEP momentum pinch is
shown to arise from the fact that,
in a low-$\beta$ tokamak equilibrium, $B^{2}{\bf u}_{E} = c{\bf B
\times \nabla} \delta \phi$ is approximately
incompressible, so that the magnetically weighted angular
momentum density ($m_{i}nU_{\parallel}/B^{3} \propto
m_{i}nU_{\parallel}R/B^{2}$) is locally advected by fluctuating
$\bf E \times B$
velocities, to the lowest order in $O(a/R)$. As a consequence
$m_{i}nU_{\parallel}R/B^{2}$ is mixed
or homogenized, so that $\frac {\partial}{\partial \psi}
m_{i}nU_{\parallel}R/B^{2} \rightarrow 0.$
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[1] T.S. Hahm, Phys. Fluids {\bf 31}, 2670 (1988)
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[2] V.V. Yankov, JETP Lett. {\bf 60}, 171 (1994); M.B. Isichenko
{\it et al.,} Phys. Rev. Lett.
{\bf 74}, 4436 (1995); X. Garbet {\it et al.,} Phys. Plasmas {\bf
12}, 082511 (2005).
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[3] T.S. Hahm, P.H. Diamond, O. Gurcan, and G. Rewoldt, Phys.
Plasmas {\bf 14}, 072302 (2007).
*In collaboration with P.H. Diamond, O. Gurcan, and G. Rewoldt. Work supported by U.S. Department of Energy.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.DPP.YI1.6