Theory Weekly Highlights for September 2005

September 30, 2005

A globally convergent Newton method based module, GCNM, for solution of stiff transport equations typically encountered in the analysis and modeling of DIII-D and other tokamaks was developed. This module will be part of the NTCC “Predictive Transp” project and is also included in the SWIM project. The module demonstrates the setup of some of the transport equations required to use the solver, analytic and numerical test cases and use of GLF23. It was created to allow easy addition of MPI and OpenMP parallel methods in the near future. The methods developed are suitable for “small scale” problems where direct (as opposed to iterative) solvers are suitable. However, extension to large sparse systems can be done if, for example, it is found that a more direct coupling between core and edge models is appropriate.

September 23, 2005

In a collaboration to calculate kinetic corrections to the resistive wall mode (RWM) stability, three DIII-D wall stabilized cases were provided to Bo Hu and Riccardo Betti of the University of Rochester for analysis. This is intended to evaluate the importance of kinetic effects in the stabilization of RWM. All three cases were predicted from GATO convergence studies to be wall stabilized. As part of the exchange, the GATO results are being benchmarked against PEST and DCON in detail to further confirm the ideal stability predictions. One case is the near current hole discharge reported previously (see September 9 2005 highlight) and the benchmarking will provide a stringent test of the convergence properties of all the ideal codes in the new interesting strongly reversed central shear regime.

September 16, 2005

Dr. Christian Konz from Max-Planck Institute of Plasma Physics in Garching has concluded a three month visit collaborating on studies of tokamak edge stability and edge localized modes. During his visit, Dr. Konz has become familiar with the ELITE stability code, and also employed the MISHKA and CASTOR codes for extensive successful benchmarks. In collaboration with Dr. Philip Snyder of GA, Dr Konz has employed the recently added toroidal rotation capabilities of ELITE, and developed a formulation for efficiently including toroidal rotation in MISHKA and CASTOR. ELITE has now been employed in extensive studies of flow shear effects on modes with intermediate to high toroidal mode number n, finding strong stabilization at high n which weakens at intermediate n. Ballooning modes are generally found to be more strongly stabilized than kink modes.

September 09, 2005

The mesh packing algorithm in the ideal MHD stability code GATO was significantly improved to be more flexible for equilibria with strongly inverted q profiles where a large number of rational surfaces pile up in the core and now works extremely well even for equilibria approaching a current hole. Additional packing can be directed separately to either the innermost or outermost specified q surface if q is inverted and to negative, low, and positive shear, or to the edge or core regions, as desired. The modifications allowed consistent converged results to be obtained for recent high performance (normalized β = 4.1) strongly inverted DIII-D discharges with minimum q > 2. Variation of the packing confirmed that the unstable mode for these discharges with no wall is global, with a large m=2 and m = 3 component across the low shear region but that the mode is wall stabilized. There is little activity in the inner negative shear region where up to 30 rational surfaces were resolved (q on axis ~ 33). Near the marginal wall position (1.05 times the DIII-D wall), the m = 2 is strongly narrowed but the m = 3 component remains broadly extended.

A new GATO manual describing the overall structure and the use of the most important input options can be found on the web at:

September 02, 2005

Thomas Johnson from JET visited GA between July 5 and July 29, 2005 to initiate a collaboration between GA and JET on ICRH modeling. During his visit, he became familiar with the ORBIT-RF code. In addition, modifications were made to improve the efficiency and performance of ORBIT-RF simulations. Equilibrium mapping codes that were previously run on different computers (SEABORG at NERSC and STELLA at GA) were ported to the new cluster DROP at GA and a script file was written to run all codes sequentially on the same platform. To improve the performance of the RF operator, the changes in perpendicular magnetic moment due to wave-particle interactions are now calculated over several steps. ORBIT-RF and the related codes were also ported to and successfully tested on the JEC computer at JET. Comparison scenarios for DIII-D and JET experiments between ORBIT-RF and SELFO at JET were discussed and planned.

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