Gyrofluid simulations of turbulence suppression in reversed-shear
experiments on TFTR.

Michael A. Beer
In collaboration with G. W. Hammett, G. Rewoldt, E. J. Synakowski, and
M. C. Zarnstorff, PPPL, and W.~Dorland, IFS.


We investigate the improved confinement in Enhanced Reversed Shear
(ERS) modes[1] and supershots, using nonlinear gyrofluid
simulations[2] extended to higher accuracy and including a
bounce-averaged trapped electron fluid model.[3] This nonlinear
electron fluid model includes the kinetic effects of the
trapped-electron precession resonance and retains the full pitch angle
dependence of the electron response, and should be useful in a wide
range of plasmas where mirror-trapped particles play an important
role, such as tokamaks and planetary magnetospheres.  Retaining the
pitch angle dependence is essential to describe the suppression of
Trapped Electron Modes (TEM) in ERS discharges where the dominant
stabilizing effect is the reversal of the toroidal precession drifts
of barely trapped electrons.  This model has been validated by
detailed linear comparisons with the most comprehensive kinetic
calculations,[4] and has extended the validity of our simulations to
include the ERS and supershot core in TFTR, where the dominant
instability is the TEM.  In the core of RS modes (before the
transition to ERS) and supershots, our simulations predict fluxes in
rough agreement with TRANSP, and the ion heat transport is convection
dominated.  After the transition to ERS, the TEM is strongly
suppressed by the combination of negative magnetic shear and the
Shafranov shift.  In ERS, the Shafranov shift is more important, since
the core of these plasmas is well into the ballooning second stable
regime.  After the transition, a shorter wavelength TEM is still
weakly unstable, but nonlinear simulations find that the transport is
reduced by a factor of 40, in rough agreement with experiment,
although the electron heat transport is underestimated.  In contrast
to magnetic shear, the Shafranov shift stabilization is a positive
feedback mechanism and is a possible trigger for the transition to
ERS, since steeper pressure gradients lead to larger shifts, more
drift reversal, less transport, and in turn, to even steeper pressure
gradients.  Another potentially important mechanism is stabilization
via radially sheared electric fields.[5] We find that in the ERS
mode, the amount of electric field shear is usually near the level
required to completely stabilize the TEM.  Detailed comparisons are
needed to elucidate the relative importance of these two mechanisms.

[1]F. M. Levinton, et al., Phys. Rev. Lett. 75, 4417 (1995).

[2]W. Dorland and G. W. Hammett, Phys. Fluids B 5, 812 (1993); R. Waltz,
R. Dominguez, and G. Hammett, Phys. Fluids B 4, 3138 (1992).

[3]M. A. Beer, Ph. D. Thesis, Princeton University (1995).

[4]G. Rewoldt, W. M. Tang, and R. J. Hastie, Phys. Fluids 30, 807 (1987);
M. Kotschenreuther, G. Rewoldt, W. M. Tang, Comput. Phys. Commun. 88, 128
(1995).

[5]P. H. Diamond, et al. submitted to Phys. Rev. Lett.; T. S. Hahm and
K. H. Burrell, Phys. Plasmas 2, 1648 (1995); M. Artun, W. M. Tang, and
G. Rewoldt, Phys. Plasmas 2, 3384 (1995); R. E. Waltz, G. D. Kerbel, and
J. Milovich, Phys. Plasmas 1, 2229 (1994).