Numerical and Theoretical Studies of Turbulence and Transport with E x B Shear Flows Page: 3 of 10
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numerical MHD equilibria. This global code takes into account equilibrium profile varia-
tion effects has low particle noise. Using a non-spectral Poisson solver [6], the equilibrium
quantities such as gyroradius and sound speed are allowed to be spatially dependent. In the
simulations reported here, these equilibrium parameters are assumed to be uniform based
on a two-scale expansion. Furthermore, a single code can simulate both a full poloidal cross
section and an annular box to provide a connection between global and local simulations.
The GTC code was implemented as a platform-independent program and achieved nearly
perfect scalability on various massively parallel processing (MPP) systems (e.g., about 350
speedup on a 512-node Cray-T3E computers).
Rosenbluth and Hinton [7] emphasized the importance of an accurate prediction of the
undamped component of turbulence-generated poloidal flows in determining the transport
level in nonlinear turbulence simulations and provide an analytical test for predicting the
residual flow level in response to an initial flow perturbation. We reproduced this test
in gyrokinetic particle simulations by solving the collisionless toroidal gyrokinetic equation
with an initial source that is constant on a flux surface and introduced a perturbation of
the poloidal flow. This flow was relaxed through the transit time magnetic pumping effect,
followed by a slower damped oscillation with a characteristic frequency corresponding to
that of the geodesic acoustic mode (GAM). The residual level of this flow measured from
the simulation agrees well with the theoretical prediction. In the nonlinear simulations of
toroidal ITG instabilities, the E x B flows can be generated nonlinearly by the Reynolds
stress [8]. Our global simulations clearly demonstrate the existence and the importance of
such self-generated flows, in qualitative agreement with flux-tube simulations [9,10]. These
simulations used representative parameters [2] of DIII-D H-mode core plasmas. The size
of the plasma column was a = 160pi. The simplified physics model includes the electron
response of 8ne/no = e(4 - (4))/Te, where (- - -) represents the flux surface average. In a
typical nonlinear simulation, we calculated 5000 time steps of the trajectories of 100 million
guiding centers interacting with the self-consistent turbulent field, which was discretized
by 25 million (128x768x256) grid points in a 3-dimensional configuration. The instabilities3
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Krommes, J. A.; Chance, M. S.; Hahm, T. S. & Lin, Z. Numerical and Theoretical Studies of Turbulence and Transport with E x B Shear Flows, report, October 1, 1999; Princeton, New Jersey. (https://digital.library.unt.edu/ark:/67531/metadc621168/m1/3/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.