Speaker
Prof.
Paul Terry
(University of Wisconsin-Madison)
Description
An analytic saturation theory for toroidal ion temperature gradient turbulence is derived
from a well-known fluid model, providing the saturated levels of the unstable fluctuation, a
nearly conjugate stable mode, and the zonal flow, along with their dependencies on the
model parameters. The theory utilizes the eigenmode decomposition of the dynamical
equations, applies statistical closure, and introduces an ordering expansion to isolate and
analyze zonal-flow-catalyzed energy transfer. This is the dominant energy transfer channel,
carrying energy from the instability, through a zonal flow to the dissipated stable mode via
nearly resonant wavenumber triads. Solution of closed energy balance equations for the
critical sources and sinks yields a turbulence level that is proportional to the ratio of the
zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow
catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio
of the growth rate and the inverse correlation time. The analytic solutions for saturation
level and scalings are applied to the ion heat flux, showing that it has a factor given by the
standard prediction of quasilinear theory, and correction factors that include the inverse of
the triplet correlation time a reduction due to the stable mode. This form, which holds for
both zero and finite plasma beta, is used to model the beta scan of modified cyclone-base-case
gyrokinetic ITG turbulence in simulations with GENE. Standard quasilinear theory does not
fall off sufficiently fast with beta to match the nonlinear flux. Inclusion of the correlation time
factor, which increases strongly with beta at low perpendicular wavenumber, produces a modified quasilinear prediction
that agrees well with the nonlinear flux.
| Country or International Organization | United States of America |
|---|---|
| Paper Number | TH/P6-19 |
Primary author
Prof.
Paul Terry
(University of Wisconsin-Madison)
Co-authors
Mr
Benjamin Faber
(University of Wisconsin-Madison)
Chris Hegna
(University of WIsconsin-Madison)
Mr
Garth Whelan
(University of Wisconsin-Madison)
Dr
M.J. Pueschel
(University of Texas at Austin)
Mr
Ping-Yu Li
(University of Wisconsin-Madison)
Dr
Vladimir Mirnov
(University of Wisconsin - Madison)
