### Theory Weekly Highlights for February 2010

##### February 26, 2010

GYRO simulations have now demonstrated that a previous limitation of gyrokinetic simulations to about half the ideal MHD critical beta limit appears to be due to a physical nonlinear subcritical MHD beta limit. Published gyrokinetic simulations have had difficulty operating beyond about half the ideal MHD critical beta limit with stationary and low transport levels for some well known standard cases and it was unclear whether this was a numerical or physical limitation. The new GYRO simulations have now demonstrated that this limitation is not due to numerical instability. The subcritical beta limit is induced by the locally enhanced pressure gradients from the diamagnetic component of the nonlinearly driven zero frequency zonal flows. Gyrokinetic linear growth rate analysis shows that corrugated pressure gradient profiles are nonlinearly induced by these zonal flows and can act as an MHD unstable secondary equilibrium near the subcritical beta. Adding ExB shear or lowing driving gradients lowers the zonal flow pressure gradients thereby allowing low transport levels up to the normal high-n beta limit. Full physics GYRO simulations of DIIID high beta discharges appear to be in good agreement with experiment: one limited by the critical beta and another limited by the subcritical beta.

##### February 19, 2010

The effect of magnetic perturbations on linear gyrokinetic stability in high-beta plasmas has been studied using GYRO, which has recently been extended to include compressional magnetic perturbations. For these studies, we have used the new field eigenvalue solver in GYRO, which computes the eigenmodes by solving for the zeros of the Maxwell dispersion matrix. Results from analysis of high-beta plasmas based on a representative NSTX discharge find the effects of the compressional magnetic perturbations on the low k_{y} KBM and hybrid ITG/KBM growth rates to be significant. At high k_{y}, we find the formation of an interesting cascade of modes, for which the most unstable mode is an excited state along the field line. Very high spatial resolution is essential to accurately resolve these complex modes and to eliminate otherwise spurious computational modes.

##### February 12, 2010

In a study of the plasma response to external excitation coils or antennas below the Alfven frequency (B_{0}^{2}/(mu_{0}ρR_{0}) where ρ is the mass density), the frequencies of the resonant responses were found to be independent of the antenna configuration. The spectrum of the plasma response was studied using the MARS-F code with different antenna configurations. The resonant responses were identified when the responses had large kinetic energy relative to the external input energy. Although the frequency did not depend on the antenna configuration, the amplitudes of the excitation do depend quite significantly on the configuration.

##### February 05, 2010

A completed benchmark of ideal linear stability calculations with M3D-C1, a resistive two-fluid code, found good agreement with both ELITE, and GATO for ideal peeling/ballooning mode growth rates for a variety of equilibria, including a diverted equilibrium. Using M3D-C1, the effects on edge stability of equilibrium rotation, Spitzer resistivity, proximate conducting walls, and isotropic thermal conductivity have been explored. The sensitivity of equilibria to artificial cutoffs employed by some ideal codes (including ELITE) in diverted equilibria has also been quantified. Ongoing and future work with M3D-C1 will explore the role of other non-ideal effects on edge stability, including that of two-fluid terms, gyroviscosity, and anisotropic viscosity and heat fluxes.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification