### Theory Weekly Highlights for September 2011

##### September 30, 2011

Nonlinear gyrokinetic predictions for standard density QH-mode plasmas using GYRO have identified the neglect of the significant energetic fast beam ion density as the source of the over prediction in the turbulent transport previously reported at the 2010 APS-DPP meeting. The earlier results reported at the 2010 APS-DPP meeting exceeded power balance calculations by one to two orders of magnitude. By treating the fast ions as a separate gyrokinetic ion species, a factor of two reduction in transport predicted by local electrostatic simulations is found. An additional factor of two reduction is predicted when magnetic fluctuations are included, and initial results from global simulations of other H-mode discharges with comparable ρ* values suggest another factor of 2-3 reduction would be predicted by electromagnetic global simulations of these discharges which included the dynamic fast beam ions. This combination of effects brings the GYRO transport predictions down to levels consistent with the power balance calculations, and resolves the reported discrepancy. Further simulations of a high density QH-mode with corresponding low beam ion fraction also predict transport levels consistent with power balance calculations, providing additional support of this conclusion. These results will be presented at the 2011 IAEA H-mode workshop.

Tony Cooper from CRPP in Lausanne visited GA this week to participate in the Torkil Jensen Award experiment originally scheduled for Thursday September 29 and also to collaborate on a number of other issues related to 3-D effects in DIII-D. Although the experiment was rescheduled at the last minute due to unforeseen technical problems with DIII-D, the visit was productive on other fronts.

##### September 23, 2011

Eric Bass attended the IAEA Technical Meeting on Energetic Particles in Magnetically Confined Systems in Austin, TX (Sept. 7-10). There he presented a linear study of unstable Alfven eigenmodes in a shear-reversed DIII-D discharge (142111). Results were compared with simulations of the same discharge in GTC (W. Deng), TAEFL (D. Spong), and M3D-K (G. Fu).

Jon Kinsey and Phil Snyder attended the BOUT++ Workshop in Livermore CA, and Dr. Snyder presented a talk on 'Overview of Gyrofluid Equations and their Numerical Solution'. Following the workshop, Dr. Snyder attended the 13th International Workshop on Plasma Edge Theory in Fusion Devices and presented a talk on: 'Developing and Testing a Predictive Model for the Pedestal Height and Width (EPED)'.

##### September 16, 2011

Investigations into the role of radial mode structure on the suppression of gyro-kinetic turbulence by toroidal rotation have revealed a strong dependence on magnetic shear. The spectral average radial wave number induced by the equilibrium parallel velocity gradient was found to depend linearly on the local mid-plane magnetic shear. In contrast, the radial wave number induced by shear in the ExB Doppler shift has almost no magnetic shear dependence. The net impact is that toroidal rotation shear is more stabilizing for negative magnetic shear, due to the larger average radial wave number, then it is for positive magnetic shear. This work will be reported at the H-mode workshop next month.

##### September 09, 2011

An initial study of a recent DIII-D experiment to rigorously test the EPED model and kinetic ballooning mode physics has found good agreement between the EPED model and the observed pedestal structure over a wide range of pedestal height and width. The model was used to predict the pedestal height and width before the experiment was conducted. A key to enabling the test was the newly upgraded Thomson scattering system on DIII-D to provide higher spatial and temporal resolution measurements of profiles across the edge barrier. Fluctuation measurements using the Beam Emission Spectroscopy and Doppler Backscattering diagnostics find high frequency modes that rise up during the latter half of the ELM cycle in several discharges. Further analysis of this experiment and more detailed comparisons to the EPED model and direct gyro-kinetic calculations are ongoing.

##### September 02, 2011

A general expression for the partial magnetic helicity between two toroidally nested flux surfaces was obtained and evaluated for several model fields. Partial helicity conservation between low order rational surfaces is being considered as a possible constraint linking an initial unperturbed axisymmetric equilibrium with the nearby perturbed 3-D equilibrium state. For the special case where the poloidal and toroidal fluxes are spatially non-overlapping, the helicity reduces to the conventional expression for linked coils, as the product of the poloidal and toroidal fluxes and the linking number; the linking number is the number of times one coil links through the other. In a diffuse equilibrium, a particularly simple expression is obtained for a set of model safety factor profiles given as a polynomial in the poloidal flux and commonly used in analytic theories. Away from the magnetic axis, this also asymptotes to the product of the poloidal and toroidal fluxes and an effective linking number related to the shear. Using the general expression, the partial helicity can be calculated easily in both the axisymmetric 2-D configuration and the 3-D system and compared in nonlinear simulations to test ideas for its partial invariance.

**Disclaimer**

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