Theory Weekly Highlights for July 2007

July 27, 2007

A detailed stability study using the ELITE code and the DIII-D pedestal database finds that the impact of the Shafranov shift on stability, together with an observed change in pedestal width, appear to explain the experimentally observed dependence of pedestal height with increasing input power. Detailed analysis of the experiments shows that the pedestal height increases strongly with input power in some configurations but not in others. The Shafranov shift generally increases with input power due to increases in the core poloidal beta. The stability study of the DIII-D pedestal database of low and high triangularity plasmas found that the observed pedestal height and the pedestal stability boundary vary only weakly with the shift for a low triangularlity configuration but that, at higher triangularity, the pedestal height increases strongly with shift in agreement with the observed trends.

EFIT has been added to the Session Leader's Checklist website. This web interface will allow users to easily update the parameters needed to run between-shot EFIT. Users will also be able to create templates of preset parameters prior to operations and apply them quickly.

July 20, 2007

Previous RMP screening results obtained from NIMROD simulations of DIII-D with applied resonant magnetic perturbations have now been compared directly with the Fitzpatrick analytic theory of error field penetration for a cylindrical geometry. The simulations performed with various rotation profiles showed greater screening of the RMP fields as the edge rotation velocity increased, as expected. The initial comparison with the Fitzpatrick theory shows that the theory reasonably predicts the stochastic boundary in two cases. The theory is closer to the NIMROD results in the deeper field penetration case, possibly because the more circular flux surfaces in the core produce better agreement with the analytic model. The energy transport model has been modified in NIMROD for the purpose of future RMP simulations, with the goal of reproducing the observed increase in pedestal temperature gradient in DIII-D RMP experiments.

An updated version of the GATO manual was released and placed on the web site at The update reflects the changes and enhancements made in the past year including the continuum restabilization, δW options, and mapping and diagnostic additions.

July 13, 2007

Analysis of the Sturmian spectrum sequence of unstable modes using GATO in three quite different physical cases shows several interesting features. It is well known analytically in 1D that a spectrum of unstable modes accumulating at the marginal point can appear under certain conditions. These satisfy the Sturmian property that the eigenvalues are ordered strictly with the number of zero crossings (see highlight for October 6 2006 at Theory Weekly Highlights for October 2006). However, the extension to 2D is not straightforward and requires numerical solutions. The three cases comprised a DIII-D sawtoothing discharge #118164 for time slices during the sawtooth cycle, a model circular cross section equilibrium and an SSPX spheromak case. In 2D, the Mercier condition is the appropriate extension of the 1D Suydam criterion and appears to be necessary for the Sturmian sequence to be present, but a superficial analysis suggests that the folding of the continuum on itself is not necessary, in contrast to the analytic theory in 1D. In addition, although the modes display multiple coupled poloidal harmonics, only one harmonic actually displays the Sturmian property. The other harmonics retain a fixed number of zero crossings, apparently not responding to the ‘Sturmian harmonic’. This has no counterpart in 1D. With no wall, the ‘non-Sturmian harmonics’ even become dominant for the higher order mode numbers. Establishing the correct necessary criterion will require further analysis of the continuum structure, which is difficult numerically. Experimental confirmation of the presence of these modes is being investigated in discharge #118164 where multiple n = 1 modes may be present in the SXR signals during the time period early in the sawtooth cycle where the Sturmian sequence is predicted.

Professor Dylan Brennan (U. Tulsa) visited GA for one week to collaborate on his work on a new method for studying coupled resistive MHD, energetic particles and turbulent field physics. He presented his plans for this work to several small groups and at the Friday Science Meeting.

July 06, 2007

Large coupled ITG/TEM-ETG GYRO simulations were run in support of Terry Rhodes's invited EPS talk highlighting recent DIII-D results using high-k diagnostics. These coupled simulations of ECH and Ohmic heated DIII-D discharges were the first to use actual experimental parameters, including an ion to electron mass ratio of 3600. Contrary to previous coupled collisionless simulations, the high collisionality, consistent with the actual physical parameters, induced significant anisotropy in the high-k turbulence spectrum. High-k diagnostics measure along the kx (radial) axis whereas the ETG transport is carried on the ky (near poloidal) axis. In the Ohmic case, the very high collisionality damped the TEM transport making the 42% electron energy transport from ETG (ky* > 1) unusually high. Even with reduced box size and resolution of these simulations, each run took 36 hours on 640 processors of the CRAY XT-4. Larger box, size higher resolution runs are needed to fully confirm these results.

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