### Theory Weekly Highlights for April 2002

##### April 26 2002

Feedback stabilization of the RWM using poloidal and radial field sensors was studied in DIII-D geometry using the normal mode formulation. Poloidal field sensing is found to be much more effective than radial field sensing. The study found that, with poloidal field sensing, a single central band of external feedback coils is sufficient for stabilization of RWMs with growth rates up to 30 times as fast as the rate of flux diffusion through the resistive wall.

Two invited talks were given at the 2002 International Sherwood Theory Meeting in Rochester, NY by Theory Group staff. The talk by Jeff Candy “GYRO Modeling of Anomalous Transport in Tokamaks”, described the recent progress with the GYRO code. Jon Kinsey presented the recent work on “Renormalization of the GLF23 Transport Model and Burning Plasma Projections on a Universal Curve of Q versus Tped”. In addition, Andrea Garofalo gave an invited talk on theory/experiment comparisons entitled “MHD Stability in a Tokamak Above the Free Boundary Pressure Limit”, which described the recent DIII-D wall stabilization results.

##### April 19 2002

One of the most computationally intensive problems in transport analysis is the generation of fully evolved equilibrium states because of the long simulation times required to relax the toroidal electric field to a steady state. A new solution method that allows us to determine the steady state directly has now been added to the ONETWO transport code. Previously, with stiff confinement models (such as GLF23), the standard approach of evolving the system until a steady state is achieved was extremely time consuming since the time steps need to be sufficiently small to avoid artificial bifurcations in the profiles. The new approach uses globally convergent variations of the Newton method to solve the nonlinear finite difference form of the time independent transport equations directly. In favorable circumstances, the required computation time is reduced from about 30 hours to about 15 min. This allows the mapping out of steady state AT modeling scenarios for DIII-D and ITER-FEAT using stiff confinement models to be achieved much more reasonably.

##### April 12 2002

The mapping of the last closed flux surface in GATO was rewritten to eliminate the most common failure mode. The new mapping routine now detects for multiple branches of the flux value being contoured exiting from each grid cell and attempts to choose the correct branch of the flux surface to continue to trace. If the mapping fails to find a branch that leads to a closed surface, the code now automatically repeats the mapping of the boundary, continually increasing the decrement in flux inside the input last closed flux value, until it successfully maps a closed flux surface. The new mapping will be released publicly after complete testing with the standard suite of benchmarks and is expected to greatly enhance the robustness of the GATO code.

##### April 05 2002

Using NIMROD simulations of DIII-D discharge #86166 with accurate kinetic equilibrium fits between sawteeth as initial conditions, 1/1 modes were found to nonlinearly drive an unstable 3/2 mode, in agreement with experimental observations. For this sawtoothing discharge, the axis pressure increases over several neutral beam slowing down times. The NIMROD simulations are also in agreement with PEST-III Δ' calculations for the same equilibrium sequence, where Δ' at the 3/2 surface was found to increase during the sequence, and also with experimental observations of a decrease in the decay rates of the earlier 3/2 modes seeded by each sawtooth; according to the modified Rutherford model, the increase in Δ' reduces the neoclassical threshold for the sawtooth-generated seed islands and decreases the island decay rates below that threshold size. Issues still being addressed are, does the nonlinear saturated island size correlate with the computed linear Δ' and, is a reduced neoclassical threshold and a reduced decay rate for the 3/2 mode from the larger Δ', observed computationally. To answer these, differences in the evolution of the 3/2 mode from an early time between sawteeth, which did not trigger a 3/2 NTM in the experiment, and a later time with slightly higher core pressure and Δ', which does trigger a 3/2 NTM, are being analyzed.

**Disclaimer**

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