### Theory Weekly Highlights for November 2012

##### November 30, 2012

Several discrepancies between a new semi-analytic model for pellet ablation in spherically symmetric 1-D geometry, and previously published numerical simulations were resolved. In the new model, pellet ablation is treated within a unified framework embracing icy and refractory pellets of arbitrary atomic number Z, with a kinetic treatment to properly include the Z- dependent pitch angle scattering effect on the attenuation of the Maxwellian incident plasma electrons. For the “standard” benchmarking case: Z =1 deuterium, with pellet radius 2mm, electron temperature 2 keV, and density1020 m-3, the ablation rate was found to be G = 119.1 g/s. In contrast, numerical simulations using the CAP [R. Ishizaki, et al., Phys. Plasmas, 11 (2004), 4064] and FronTier [R. Samulyak, et al., Nucl Fusion, 47 (2007), 103] pellet ablation codes found G = 113 g/s, and G = 112 g/s, respectively. Other larger discrepancies in the ablation flow quantities were also worrisome. The discrepancies were found to be due to a number of relatively small inaccuracies in the CAP and FronTier codes. These were corrected and much closer agreement is now established, with G = 120 g/s, and G =120.7 g/s for the CAP and FronTier codes, respectively, both very close to the model value of 119.1 g/s.

##### November 23, 2012

The new “spectral-shift” model for EXB shear was brought to a final form after extensive verification with GYRO results. A new numerical technique was found that greatly helps the convergence of the Newton implicit time advance method in the XPTOR transport code when momentum transport is evolved. A relaxation is applied to the update of the shear in the ExB Doppler shift but not the parallel velocity shear. The Doppler shear variation is also not included in computing the Newton direction. Together these two changes keep the Newton iterations from getting stuck at fixed points.

##### November 16, 2012

Nonlinear calculations of the plasma response to applied 3D fields have been carried out with M3D-C1 for a DIII-D discharge, #126006, from a resonant magnetic field perturbation experiment. Notably, these nonlinear calculations were run using the Spitzer resistivity and the experimental electron temperature profiles, although the viscosity and thermal conductivity were larger than experimental values by roughly a factor of 50. After an initial transient response, the calculations find the plasma settling into a quasi-steady state. The displacements of magnetic surfaces in this quasi-steady state are found to be qualitatively very similar to those found using a time-independent linear code. These calculations will help address cases in which the plasma response is found to be large enough to violate the assumptions of linearity. Higher resolution calculations, which are necessary to address the edge response accurately, are underway.

##### November 09, 2012

Analysis using the ELITE code for DIII-D discharges suggests that pellet-triggered edge localized modes (ELMs) are driven by local physics associated with the pellet deposition. The ELITE code was used to study the edge stability of a series of DIII-D discharges in which pellets are used to trigger small frequent ELMs. Without pellets, the pedestal evolves towards a peeling-ballooning unstable state, at which point large ELMs are triggered. However, with the pellets triggering rapid, small ELMs, ELITE finds that the pedestal remains in the stable region, implying that the pellet-triggered ELMs are driven by local physics associated with the pellet deposition. Notably, in the pellet driven case, the pedestal remains narrow, while without pellets, the pedestal broadens until the ELM occurs. This suggests that the pellets interrupt the natural ELM cycle at a time when the pedestal is too narrow for the natural ELM to occur.

##### November 02, 2012

To investigate the effects of non-axisymmetric magnetic perturbations on beam ion loss during neutral beam injection, the 5-D Monte-Carlo Hamiltonian guiding center code ORBIT-RF has been interfaced with M3D-C1, which calculates perturbation fields including plasma response using a linear two-fluid model. The first simulation results for a DIII-D discharge with a rotating n=2 perturbation indicates that the effects of the perturbed fields on beam ion loss are small in both co-beam and counter-beam cases. This may be due to the use of a simplified criterion used to evaluate fast ion loss in the present simulations, where the fast ions are assumed to be lost when they hit the last closed poloidal flux surface based on the unperturbed 2-D axisymmetric equilibrium. The detailed changes of the equilibrium profiles due to magnetic perturbations are also ignored, which may lead to an underestimate of the loss. Nevertheless, at the maximum allowable I-coil current (7 kA), it was found that the perturbed fields can significantly modify the beam ion loss spatial distribution, especially in the co-beam case where the prompt loss of fast ions is not significant. In future work, the coupled code will be applied to ITER scenarios as well as additional DIII-D cases.

**Disclaimer**

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