### Theory Weekly Highlights for January 2001

##### January 26, 2001

The FORTRAN90 version of the resistive MHD inner layer code is now written and working well. The F90 code reproduces the results from the original MATLAB code, as well as previously published results. This code uses the same numerical algorithm for solving differential equations with singular solutions, adapted to solve a sixth order system in this case, that was developed for the TWIST-R outer layer problem. The inner and outer layer solutions can now be matched in a single code to obtain linear resistive growth rates for the standard inner layer model. Other models can be easily implemented.

##### January 19, 2001

The new numerical algorithm reported recently for solution of the axisymmetric gyrokinetic-Maxwell equations has been further adapted for solution of the general nonaxisymmetric equations. Computation of ballooning modes on sparse grids shows close agreement with the linear gyrokinetic code GKS. For finer grid resolution, however, the new method is designed to capture subtle trapped particle loop structure, which no other comparable method can. Parallelization and addition of ExB nonlinearity are next.

##### January 12, 2001

The remaining minor numerical problem in the linear resistive MHD code TWIST-R, which resulted from the singular nature of the Jacobian at the magnetic axis, was solved fully by implementing a numerical difference scheme everywhere that avoided utilizing coefficients at half integer grid points. This had previously been implemented near singular surfaces to resolve similar problems there but is now extended to include the magnetic axis. It is expected that only some minor coding changes to the way the mesh is laid down are needed to implement the 2D TWIST-R code on a fully 2D problem and extract Δ′. In parallel, work is in progress to obtain a good first benchmark by testing the PEST-III code on the 1D problem as well.

The new numerical algorithm reported recently for solution of the axisymmetric gyrokinetic-Maxwell equations has been further adapted for solution of the general nonaxisymmetric equations. Computation of ballooning modes on sparse grids shows close agreement with the linear gyrokinetic code GKS. For finer grid resolution, however, the new method is designed to capture subtle trapped particle loop structure, which no other comparable method can. Parallelization and addition of ExB nonlinearity are next.

##### January 05, 2001

The installation of ONETWO along with CORSICA in the Basis framework has been completed. Both ONETWO and CORSICA are now under a single source code management system. ONETWO as incorporated in the new code gives identical answers to the stand-alone version. ONETWO is now a fully script-capable code, and is ready for user evaluation. A tool that converts namelist files to Basis script files has also been written to facilitate the evaluation.

The remaining minor numerical problem near the magnetic axis, which resulted from the singular nature of the Jacobian at the axis, was solved fully by implementing a numerical difference scheme everywhere that avoided utilizing coefficients at half integer grid points. This had previously been implemented near singular surfaces to resolve similar problems there but is now extended to include the magnetic axis. It is expected that only some minor coding changes to the way the mesh is laid down are needed to implement the 2D code on a fully 2D problem and extract Δ′. In parallel, work is in progress to obtain a good first benchmark by testing the PEST-III code on the 1D problem as well.

**Disclaimer**

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