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ess in developing new hybrid fluid/drift-kinetic
closure models, which are being implemented in
codes that are used to describe nonlinear macroscopic
behavior in tokamaks. The focus to date
has been on the electron dynamics, with ion behavior
to be considered next. The hybrid fluid/
drift-kinetic description being developed and
implemented in the nonlinear MHD stability code
“NIMROD” will be used to model longer wavelength
features associated with macroscopic behavior
in tokamak plasmas. The motivation here
is to develop a well-grounded theoretical model
to analyze slowly growing macroscopic instabilities
in high-temperature, magnetically confined
tokamak plasmas. We were able to derive analytic
dispersion relations, valid over a wide range of
plasma parameters that could be used to verify
large extended MHD codes, such as NIMROD.
Other work in this area has included improved
analytic solutions to the MHD equilibrium equations,
and the derivation of various stability comparison
theorems.
We have also performed extensive investigations
of turbulence in tokamaks, where density fluctuation
levels are normally regulated by plasma
flow shear referred to as zonal flow. In trapped
electron mode (TEM) turbulence, an apparent
contradiction had emerged. On the one hand,
we had previously discovered that zonal flows
produced a large nonlinear upshift of the critical
density gradient for the onset of TEM turbulence.
PSFC Associate Director Jeffrey Freidberg with Librarian Jason Thomas.
On the other hand, a separate study of TEM turbulence
claimed zonal flows were unimportant.
In collaboration with researchers from the SciDAC
Center for the Study of Plasma Microturbulence,
we reconciled the two results by showing that
TEM zonal flows vary strongly with the ratio of
density to temperature gradient scale lengths.
This study took the important step of comparing
gyrokinetic particle and continuum microturbulence
simulations with full electron dynamics. In
complementary work, we continued to improve
gyrokinetic collision operators for use in realistic
plasma microturbulence simulations. Collisions
play an important role in plasma turbulence near
the threshold for excitation of the modes, where
most experiments operate.
Existing nonlinear gyrokinetic and extended MHD
codes are unable to predict the evolution of tokamak
plasma on transport time scales since that
requires a simultaneous knowledge of the global
axisymmetric radial electric field and its associated
flow. To predict long-time-scale plasma evolution
along with the superimposed zonal flow
established on shorter time scales and at shorter
radial scale lengths, hybrid fluid/gyrokinetic descriptions
are required. The theory group developed
the first such description (valid for arbitrary
collisionality) by using conservation and other
moment equations along with solutions to the
gyrokinetic equation. This hybrid description is
presently being implemented in the GS2/Trinity
codes. In a separate study, an analytical evaluation
of the residual zonal flow level was performed in
the high-confinement pedestal region just inside
the separatrix. Beyond the separatrix the magnetic
field lines connect to the vacuum chamber
wall. Inside the pedestal the plasma gradients are
strong, and the resulting strong radial electric
field and its shear were shown to modify zonal
flow behavior. In addition, the effect of this strong
electric field and its shear on ion and impurity
flow, ion heat transport, and parallel current was
evaluated. These results explained pedestal flow
measurements on Alcator C-Mod.
In a new program that complements our extensive
tokamak research program, the theory group
has begun an effort focused on equilibrium and
transport in stellarators. Unlike tokamaks, stellarators
are inherently steady state, but with magnetic
16 PSFC Progress Report 09–11