### Theory Weekly Highlights for October 2015

##### October 30, 2015

A new numerical dissipation scheme has been developed for treating the fast parallel streaming term in the new gyrokinetic code CGYRO. CGYRO uses (v* /v, v) velocity space coordinates to optimize accuracy of the collisional dynamics, and numerical dissipation is needed due to the discontinuity of the distribution function across the trapped/passing particle boundary. Previous use of a standard 4th-order upwinding scheme worked well electrostatically but become numerically unstable with electromagnetic effects at low k. A split-operator, implicit time stepping scheme eliminated the problem but was not ideal due to the poor parallel scalability for large (kx, ky) multi-scale nonlinear simulations. The new dissipation scheme for the explicit RK4 time-stepping scheme subtracts the v* /v contribution from the diffusion term. This ensures that the upwind diffusion does not contribute to the density moment of the kinetic equation. CGYRO has also recently been upgraded to include experimental profiles, general Fourier geometry, parallel velocity shear, and compressional electromagnetic perturbations. It is being applied to nonlinear analysis of high-collisional experimental cases.

##### October 23, 2015

The scaling with resistivity (η) of the resistive kink modes proposed as an explanation for the disruptions of diverted discharges when q95 < 2 (see Highlight from March 20 2015 at Theory Weekly Highlights for March 2015) was determined and confirmed to be a fractional power of the edge resistivity. A scatter plot for all the cases run found an anticipated η1/3 scaling with respect to either the resistivity at q = 2 (ηq=2) or at the plasma edge (ηmax), with the correlation with ηq=2 slightly better than for ηmax. Single scans with fixed profile but scaled value at q=2 verified this scaling quite precisely. This confirms the original characterization of the modes as true resistive kinks. Additionally, the resistive kink that appears in limiter discharges (see Highlight from September 4 2015 at Theory Weekly Highlights for September 2015) just prior to the ideal mode onset was found to transition from a linear η scaling at low ηq=2 to a fractional scaling at higher η and trending toward an ideal scaling. The implications of this are still being evaluated; despite the linear scaling, the growth rates prior to the ideal stage can still be substantial for large resistivity at q=2.

##### October 16, 2015

A new version of the M3D-C1 code, which utilizes improved meshing software developed by the RPI SCOREC group, has been released. This new version is able to achieve significantly higher spatial resolution. In addition, a new utility for converting M3D-C1 output into Boozer and Hamada magnetic coordinate systems was also developed. This capability will be used to allow ion-orbit integration codes and gyrokinetic codes that use Boozer coordinates to take perturbed equilibria calculated by M3D-C1 as input. The improved meshing will allow M3D-C1 to more closely model the ideal-MHD response by permitting the calculation of smooth solutions at significantly lower values of dissipative parameters (e.g., diffusivity and resistivity) relevant to DIII-D. The new coordinate mapping utility should enable comparison of fluxes using 3D equilibria from M3D-C1 against those from conventional stellarator codes.

##### October 09, 2015

The GA Theory group hosted workshops this week for the Advanced Tokamak Modeling (AToM) and Edge Simulation Laboratory (ESL) projects. Collaborators from ORNL, LLNL, UCSD and CompX were in attendance, and collaborators from LBL attended remotely. The ESL project develops and applies numerical tools for kinetic studies of the edge, pedestal, and scrape-off layer plasma. ESL is actively developing and enhancing COGENT, a continuum kinetic code for treating both the edge and SOL region in diverted geometry, as well as NEO/3D NEO, an efficient, comprehensive neoclassical code for the closed flux region, and CGYRO, a gyrokinetic code which treats the high collisionality edge region accurately. AToM is a new SciDAC project which develops tools and workflows for integrated modeling with high-performance computing components. Component coupling is accomplished through the IPS framework and workflow management, data management, and visualization are done using the graphical user interface and scripting environment OMFIT developed at GA for managing and automating integrated modeling tasks. The AToM project facilitates workflows for physics studies that require integrated modeling, and has successfully conducted self-consistent core-pedestal simulations that predict profiles across the entire closed flux region. Both the ESL and AToM projects are partnerships supported jointly by the DOE Offices of Fusion Energy Sciences (FES) and Advanced Scientific Computing Research (ASCR).

##### October 02, 2015

A new understanding of the collapse of refractory pellets has been reached. Unlike fully shielded cryogenic pellets, the ablation cloud of refractory pellets like Li and Be is thinner and only partially shields the pellet against the incident electron energy flux. As the plasma density or pellet radius is lowered, the shielding becomes progressively weaker and the sonic surface where M=1 moves inward towards the pellet surface. At some critical pellet radius, they coalescence and the subsonic region collapses. What happens beyond the threshold condition for subsonic collapse was unclear until recently when it was realized that, for “subcritical” pellets, the ablation flow becomes purely supersonic. The sonic M = 1 surface is thereafter anchored to the pellet surface as it continues to shrink and disappear. One can then analytically continue the solution into the subcritical regime; the solution smoothly transitions from transonic flow to purely supersonic flow as the pellet radius decreases. The theory is being applied to the injection of Li granules in DIII-D for ELM mitigation.

**Disclaimer**

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