Theory Weekly Highlights for February 2015

February 27, 2015

NIMROD MGI simulations have shown that an injected impurity plume rapidly expands parallel to field lines before the onset of the thermal quench (TQ) [see 29 Aug 2014 highlight at Theory Weekly Highlights for August 2014. Further analysis reveals that the parallel expansion of the injected plume is radially localized and appears to be centered near the q = 2 surface. The parallel expansion has been explained by a nozzle equation, but the driving pressure gradient depends on parallel temperature equilibration. Differences in the heat transport on a rational surface, in which parallel heat transport is localized to a single flux tube, as opposed to an irrational surface, in which the entire flux surface must equilibrate, may play a role in the more rapid parallel expansion of the plume at the q = 2 rational surface. The effect of q-profile on TQ onset time (due to importance of cooling the q=2 surface) has been understood for many years and experimentally confirmed, but the parallel spreading of impurities prior to the TQ is less well understood in general, and what if any role the q-profile may play has not been investigated in experiments. This will be considered in future work.

February 20, 2015

Using the well known kinematic relation between the initial pitch-angle and energy of secondary or knock-on electrons, an exact analytical expression for the fraction of secondary electrons born on trapped particle orbits as a function of birth radius, r/a, and energy was derived in the large aspect ratio circular flux surface limit. A secondary electron is produced when a high-energy primary electron collides with a thermal background electron. The threshold energy for knockons to runaway if they are on untrapped orbits is ~ 20-60 keV. Since the primary electrons are passing particles, uniformly distributed over a flux surface, one should expect that the secondary electron source is also uniformly distributed over a flux surface. As an example, for 51 keV knock-on electrons born inside r/a =1/3, the trapped fraction is found to be 78.5%.

February 13, 2015

A local critical-gradient model of Alfvén eigenmode (AE) beam ion transport is being applied to DIII-D discharge (146102) with strong AE activity. The model predicts an approximately 50% drop in the central beam ion density and a 50% loss of confinement inside the half minor radius. The core loss is nearly all regained by re-deposition in the outer half radius. The predictive model combines a quasilinear approximation for micro-turbulent transport with an assumption of stiff critical gradient transport by AEs . The AE critical gradient is set at the point where the local AE growth rate matches the local ITG growth rate at the same toroidal mode number, not at the AE linear stability threshold. This higher threshold choice was motivated by nonlinear GYRO simulations that showed an ITG-enhanced upshift of the critical AE density gradient. The threshold is mapped by local GYRO simulations, which now include the beam-like velocity-space anisotropic slowing down NBI distribution. Beam anisotropy somewhat reduces the AE critical onset threshold, but does not qualitatively change the transport result. Crucially, AE diffusive enhancement does not propagate to the edge or to the center in the simulation. Depletion from the center peak is caused by micro-turbulent transport filling in a mid-core region depleted by AEs. A detailed comparison of the predicted FIDA signal to experimental FIDA measurement is still underway.

February 06, 2015

The preliminary framework for the CGYRO code has been completed, including kinetic electrons, multi-ion species, general geometry, transverse electromagnetic fluctuations, nonlinearities, and ExB shear. CGYRO is a new gyrokinetic code that uses the NEO pitch-angle/energy velocity space coordinates to optimize the accuracy of the collision dynamics, which are expected to be significant in the edge. Unlike the treatment of collisions in GYRO, which includes only Lorentz pitch angle scattering, CGYRO implements the full, multi-species linearized Fokker-Planck-based model of Sugama, including finite k⊥ corrections. A de-aliased 2D pseudo-spectral method was developed for CGYRO using FFTW3. For adiabatic electrons, CGYRO reproduces the nonlinear GYRO result with nearly a factor-of-two speedup. Parallel communication libraries were completely rewritten from the ground up to be more suitable for very large multi-scale, multi-ion cases. The code has been extensively benchmarked with GYRO for linear ITG/TEM/KBM modes and the zonal flow damping. Full physics nonlinear benchmarks for a DIII-D core case have also successfully recovered the ion and electron fluxes. Methods to improve the behavior near the trapped/passing boundary, where the distribution function becomes discontinuous, are still being explored. The code is being applied to high collisionality pedestal cases, where previous GYRO simulations had difficulty due to the high condition number of the collision matrix.

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