### Theory Weekly Highlights for February 2003

##### February 28 2003

A new formulation of the gyrokinetic equation has been derived that includes the effects of toroidal rotation shear. The equilibrium distribution function was chosen to be a Maxwellian in a rotating frame with the density chosen to be consistent with parallel momentum balance and the gyrokinetic equation was transformed to use an energy variable defined as the kinetic energy in the rotating frame plus the centrifugal potential energy. Then a new energy derivative term appears in the equation, but is small in the gyrokinetic parameter and can be neglected. The main differences between this and the previous form are that a toroidal angular velocity derivative term appears in the diamagnetic velocity and that the guiding center velocity is consistent with conservation of canonical angular momentum as defined in the lab frame. The new formulation will allow future simulations to include the effect of toroidal rotation shear on ITG turbulence, which is believed to be crucial during the L-H transition.

##### February 14 2003

An up-down asymmetric version of the inverse equilibrium code, TOQ, has been successfully developed. A new coordinate gridding algorithm, which is both fast and robust, was implemented to complete the developments throughout the code required for up-down asymmetry. This algorithm required construction of a new equal arclength poloidal distribution using a fast linear correction iterative method to resolve points on contours not encircling the origin, while solving for points on contours encircling the origin in a manner similar to the previous up-down symmetric version. Well converged, up-down asymmetric, ITER-like equilibria have been successfully generated in test cases. A public version of the new code will be released after testing and benchmarking is completed.

##### February 07 2003

The efficient and accurate solution of stiff confinement models in tokamak transport (exemplified by the GLF23 model) presents a serious challenge for predictive calculations. We have developed a method of lines solution and a globally convergent trust region approach, which, although much more computationally intensive than standard methods, can achieve converged solutions in cases where the standard methods fail. We have successfully applied these techniques to time evolved and steady state DIII-D advanced tokamak scenarios, as well as BPX reactor configurations. A parallel version of these algorithms will be developed in the future.

**Disclaimer**

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