### Theory Weekly Highlights for June 2013

##### June 28, 2013

The new 3D local equilibrium solver LE3 has been extended to enable local equilibrium calculations for arbitrary deviations from axisymmetry, rather than small 3D perturbations. The solver is analogous to a 3D extension of the Miller local equilibrium method for shaped axisymmetric plasmas. The approach enforces zero radial current (similar to work by C. Hegna (UWM)), from the grad psi projection of Ampere’s law, consistent with MHD force balance. However, the method is novel in that a nonlinear differential equation is solved for the mapping from straight to twisted field lines. We have improved on a previous simple fixed-point iteration scheme by now using minpack to solve for the nonlinear root of the discretized PDE. The improved solver is being used to study the onset of stochasticity and will be coupled with NEO for 3D neoclassical transport studies of magnetic field ripple and resonant magnetic perturbations.

##### June 21, 2013

Runaway electron confinement in NIMROD simulations of massive gas injection in DIII-D has been compared for cases with toroidally peaked and toroidally symmetric gas sources, as well as for low field side (LFS) versus high-field side (HFS) injection. In the simulations, in which runaway electron losses were determined by test-particle orbits, toroidally localized sources were found to de-confine runaways earlier in time, consistent with an earlier growth of the n=1 mode. For both HFS and LFS injection, increasing the toroidal peaking of the source produced slightly earlier runaway losses than a somewhat broader n=1 gas distribution. Most notably, HFS injection was found to be especially effective at de-confining runaways. Unlike any other simulations, the two HFS injection cases showed significant losses of runaways prior to the growth and saturation of the n=1 mode, indicating that the applied perturbation of the HFS gas jet itself can produce runaway losses across much of the plasma cross-section. The reasons for this will be investigated in more detail by examining individual particle orbits.

##### June 14, 2013

In the linearized response calculations reported earlier (see Highlight for April 26 2013 at Theory Weekly Highlights for April 2013), a surprising result is that the perturbed 8/3 surface has a predominantly m = 9 structure instead of the expected resonant m = 8. This was found in all three linear codes, MARS-F, IPEC, and M3D-C1. The result, however, appears to be sensitive to other factors and the cause of the sensitivity is not well understood at this stage. In general, from counting zero crossings, the perturbations near rational surfaces exhibit predominantly either an m = n*q or m = n*q + 1 oscillation. Rotation by itself does not seem to provide the crucial physics since the results from IPEC at zero rotation also show the m = 9 structure near the 8/3 surface, whereas calculations assuming a linear two-fluid physics model in M3D-C1 show a predominantly resonant m = 8 harmonic. The structure is also only weakly dependent on finite resistivity. The results have clear implications for our understanding of the resonant singular currents generated by 3D perturbations.

##### June 07, 2013

Preliminary studies show that a multi-layer feed-forward back-propagation neural network, trained over a large database of DIII-D data is able to predict to a large degree the heat transport profiles observed in the DIII-D experiments, from the core to the near edge of the plasma at ρ = 0.95. For applications such as plasma control, between-shot analyses, or parametric studies, it is necessary to use a solution method that can provide quick throughput as required by such applications. At present, high fidelity numerical models such as GYRO and TGLF require a large amount of computational resources and are thus not suitable for such applications. An alternative approach that uses neural networks to efficiently compute electron and ion heat fluxes is currently being explored. Once the neural network is built, the numerical cost of evaluating the transport coefficients is minimal and the evolution of the temperature profiles can be done efficiently. The predictions of the neural network model are not limited to the availability of experimental training data. For example, for future devices and previously unexplored regimes, a database of TGLF or GYRO simulations could be used. The OMFIT modeling framework provides the infrastructure for building and training the neural networks on the experimental DIII-D data and is used to compare neural network predictions with those from theory-based models as well as against the experiments.

**Disclaimer**

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