### Theory Weekly Highlights for July 2017

##### July 28, 2017

Paul Parks presented an invited talk at the “Theory and Simulation of Disruptions Workshop” held at PPPL on July 17-19, entitled “A Theoretical Model for the Penetration of a Shattered-Pellet Debris Plume”.

Gary Staebler presented plans for establishing the physics basis for validated predictive whole device modeling at the Burning Plasma Physics Plenary Session on Wednesday, July 26 as part of the US Magnetic Fusion Research Strategic Directions Workshop held at the University of Wisconsin, Madison this past week.

##### July 21, 2017

Extensive nonlinear GYRO simulations have verified a critical-gradient model of Alfvén eigenmode (AE)-driven energetic particle (EP) transport, including for the first time an extension of the critical-gradient model to include the effect of ExB flow shear. Initial results had suggested an upward shift of the AE critical gradient analogous to the tokamak microturbulence quench condition: growth rates must exceed the ExB shearing rate. However, an extensive search of parameter space in nonlinear simulations with rotation has now shown that the more appropriate quench condition has the ExB shearing rate divided by the dimensionless magnetic shear. The new slab-like scaling is understood to be a consequence of the very weak ballooning behavior of AEs due to relatively weak coupling of poloidal harmonics. The result has recently been submitted to Physics of Plasmas.

##### July 14, 2017

A new paper “Onset of helical cores in tokamaks” by A. Wingen et al., determines the threshold for spontaneous symmetry breaking, resulting in the growth of m/n = 1/1 helical cores in tokamaks. The study used the VMEC 3D equilibrium code to construct the 3D equilibria, based on a DIII-D hybrid discharge with a helical core. This is also the first full 3-D equilibrium reconstruction in a tokamak. The model predicts that ITER (15MA scenario) will operate well into the helical core formation regime. The helical core onset threshold is proportional to (dp/dpsi)/Bt2 around q = 1 (see (Helical_Core_Onset.pdf)). Below the threshold, applied 3-D fields can drive a helical core to finite size, as in DIII-D. Above it, the axisymmetric equilibrium is unstable and a random 3-D kick causes a bifurcation from axisymmetry and generating a spontaneous helical core. A comparison of the helical core onset threshold for discharges from DIII-D, C-Mod and ITER confirms that while DIII-D is marginally stable, C-Mod and especially ITER are highly susceptible to helical core formation.

##### July 07, 2017

Simulations with the new CGYRO gyrokinetic code have led to progress on the well-known L-mode edge transport shortfall problem. Local flux tube GYRO simulations of the DIII-D L-mode discharge 128913 reported a 10-fold shortfall at the far edge (r/a=0.9) in 2012 [R.E. Waltz, BAPS 57,105 (2012), DPP.DI3.2]. However, new CGYRO and GENE simulations were in good agreement with no shortfall from experiment evident at the far edge in this case. Both CGYRO and GENE are spectral (k-space grid) in both the toroidal and radial directions whereas GYRO is only spectral in the toroidal direction with a radial (x-space) grid. The k-space grid enables more accurate radial gyro-averaging. Recent very high radial grid resolution GYRO simulations with more accurate radial gyro-averages and radial derivatives also find the 10-fold shortfall largely vanishes. This particular far edge case is a good test case for code comparison because finite-beta and ExB shear stabilization effects can be neglected.

**Disclaimer**

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