### Theory Weekly Highlights for April 2014

##### April 25, 2014

In collaboration with Y. Liu (Culham) and Z. Wang (PPPL), the public version of the MARS-F code at GA was updated to include some important bug fixes in the kinetic stabilization terms. MARS-F is a linear stability code that includes a number of non-ideal effects, specifically resistive and kinetic effects and plasma rotation. The code has also been modified and is used routinely to study the plasma response from externally applied fields. The correction applied only to stabilization from fast ions and tests so far indicate that the differences are relatively minor. Additionally, the most recent version, MARS-Q, which includes several entirely new features, such as quasilinear effects on the rotation via various rotation damping mechanisms, has been ported to GA and is currently undergoing testing. MARS-Q is expected to be publicly available within the next few weeks.

Phil Snyder, Gary Staebler, Orso Meneghini, Chris Holland, and Eric Bass attended the TTF meeting in San Antonio this week.

##### April 18, 2014

Global GYRO simulations have tentatively identified the alpha-driven Alfvén eigenmode (AE) linear stability threshold for the hybrid and steady-state with reversed shear ITER scenarios. For toroidal mode number n=16, identified as the most unstable from the 2014 energetic particle milestone code comparisons, GYRO places the AE threshold at a peak alpha particle beta of approximately 2.4% for the hybrid case and 0.7% for the steady-state case. The AE threshold predictions are in good agreement with GEM results for the same cases; GYRO solves the gyrokinetc equations on a continuum grid for all species (ions, electrons, and alpha particles), whereas GEM (in its present implementation) uses a particle-in-cell method treating ions and alpha particles gyrokinetically and treating electrons with an adapted fluid model. For each scenario, the classical peak alpha particle beta is predicted at about 1%, implying unstable AEs should occur only in the steady-state case.

##### April 11, 2014

Vertical displacement events (VDEs) in DIII-D have been modeled using the new resistive wall capability in M3D-C1. The calculations were initialized using a reconstruction of a DIII-D discharge immediately after a thermal quench initiated by massive gas injection. In both the experiment and in the simulation, the plasma was observed to become vertically unstable and drift into the wall. These nonlinear M3D-C1 calculations are notable because they include the resistive wall within the computational domain, and are therefore able to resolve eddy currents and Halo currents in the wall. These results were presented in a poster at the Sherwood Fusion Theory conference in March. Axisymmetry was assumed in these simulations; similar calculations will be repeated in three dimensions in order to observe the onset of n=1 instabilities as the outer layers of the plasma are scraped off by the wall. Ultimately this capability will be used to predict and understand the plasma evolution during disruptions, including electromagnetic forces in the wall and the transport of runaway electrons.

##### April 04, 2014

A detailed critical gradient analysis of DIII-D H-mode discharges was performed by a collaboration of researchers from SWIP, UCSD, and GA as part of the ongoing analysis of a dedicated 2011 transport stiffness experiment. Using the GYRO eigenvalue solver capability, the stability of ion temperature gradient (ITG) modes as a function of grad Ti was calculated at multiple radii and wave numbers and used to identify the critical gradient at which the mode becomes unstable. The calculations found that at ρ = 0.25, ITG modes were essentially stable in all conditions considered at all wavenumbers. (rho is the square root of normalized toroidal magnetic flux.) At ρ = 0.5 and 0.75, it was found that the ITG critical gradients were generally between 40% and 80% lower than the observed experimental gradients. Consistent with theoretical expectations, this difference increased with increased injected neutral beam heating and/or torque. However, no clear correlation was found between the difference and local ExB shear rates, magnetic safety factor, or shear. Future work will focus on examining possible correlations with local density gradient scale lengths and Ti/Te/ ratios, extending this work to additional simulations, and comparing the linear thresholds with predictions from nonlinear simulations.

**Disclaimer**

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