### Theory Weekly Highlights for March 2004

##### March 26 2004

A new variation of the model for mass shedding due to magnetic shear induced differential drift of a pellet cloud has been implemented in the Pressure Relaxation Lagrangian (PRL) code. This code calculates the fast inward MHD drift and fuel deposition profile of pellet ablation material following HFS pellet injection. The code has also been coupled with the PELLET code to initialize the cloud parameters along the ablation track. Penetration calculations were done with temperature profiles having a tanh function pedestal, where the pedestal height is defined as the inflection point. The resulting deposition profiles for a 6mm pellet injected into an ITER-like Te profile (To=20 kev, Tped = 4 kev and pedestal width = 8.5 cm), are significantly different for pellets with velocities of 300 and 1000 m/s, but there is little difference between pellets with velocities of 1000 and 1500 m/s. The conventional, curved guide tube, ITER injection scheme limits pellet speeds to 300 m/s, but the PELLET code predicts that these pellets will burn out in the pedestal region, and this degrades subsequent MHD penetration of the ablated and ionized material. Parameter scans and sensitivity tests for the temperature and q profile are underway to confirm if this holds universally.

##### March 19 2004

GYRO simulations motivated by SciDAC benchmarking efforts have revealed several encouraging general results. Global GYRO simulations yield transport coefficients that agree in the limit of small gyroradius to system size, with local (flux-tube) turbulence simulations from the GS2 and PG3EQ codes. This firmly establishes the “local hypothesis” which forms the basis of the GLF23 transport modeling code. However, the GTC results, which originally popularized this case, do not satisfy the local hypothesis. In addition, very-long-time GYRO flux-tube simulations (10x the usual simulation time, or about 10ms of a DIII-D discharge) have verified that the turbulence achieves a true statistical steady state; this validates the use of a time-dependent turbulence simulation to determine time-independent transport coefficients.

##### March 12 2004

The algorithm to extract the coefficients of the large and small Frobenius solutions in the TWIST-R linear resistive stability code was successfully adapted from the original 1D version to the 2D toroidal case. The ratio of the leading small and large Frobenius components for the odd and even parity solutions yields the tearing and interchange stability indices Δ' and Γ'. The 2D case has the additional complication that the solution contains a regular component in addition to the two Frobenius components that must be carefully extracted to reveal the subdominant small solution accurately. In a sample test case, mocking a solution for a 2D Solovev equilibrium, the coefficients of the small solution were extracted to sufficient accuracy on a moderate radial grid. For the more difficult situations that TWIST-R is designed to handle with the Mercier index μ > 1, the small solution is buried below two terms of the large and regular solutions each. However, the same accuracy should be recovered by simply doubling the mesh size.

##### March 5 2004

The ONETWO suite of codes was installed at ORNL on the RANIER computer. This provides additional, badly needed, computing power to analyze Advanced Tokamak current drive scenarios using the computationally demanding GLF23 transport model. Results from these calculations were recently presented at the DIII-D PAC meeting. Of particular value is the ability to model steady state current drive situations using the nonlinear solution methods recently introduced into ONETWO; these increase the efficiency an order of magnitude by solving directly for the steady state solution without having to evolve through intermediate time steps. The RANIER system is presently being used for steady state ITER-FEAT modeling and the combination of the additional computing resources and nonlinear methods reduces meaningful current drive studies using the GLF23 model from the order of days to a more feasible several hours.

**Disclaimer**

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