### Theory Weekly Highlights for April 2007

##### April 27, 2007

The δf gyrokinetic code EGK has been used to extend studies of neoclassical transport to include effects from the poloidal variation of the potential and kinetic electron dynamics. Using the expansion Φ(r,θ) = -r E_{r0} + δΦ(θ) for the electrostatic potential Φ, this is solved as a radially local problem with k_{x} = 0. E_{r0} is the equilibrium-scale radial electric field. A semi-implicit algorithm was required to numerically solve the kinetic plus Poisson equations since the k_{x} = 0 Poisson equation involves no explicit Φ dependence. In general, the poloidal correction to E_{r0} is weak, as expected. The sinusoidal variation in θ of δΦ, and its dependence on the collisionality were found to be in agreement with analytical neoclassical theory. Overall, while the poloidal correction to the potential does not significantly affect the ion dynamics, it does produce an enhanced electron heat flux, in qualitative agreement with analytical theory. Finite k_{x} corrections will be explored in future work.

##### April 20, 2007

Simulations of DIII-D plasmas with resonant magnetic perturbations using NIMROD for a range of toroidal rotation profiles show increased screening of the RMP fields as rotation increases, as intuitively expected. Sufficiently high rotation at the separatrix partially suppresses the n=3 mode that is associated with enhanced particle transport, but fully suppresses the transport itself. Sensitivity of the penetration and particle transport results to the initial condition was tested by turning off the rotation in a very well screened, high rotation simulation. Subsequent RMP penetration and particle transport was very similar to the no-rotation case beginning with fully penetrated vacuum fields.

##### April 13, 2007

A new tool for profile input was added to the GYRO toolset. Now, in addition to direct inclusion of experimental data from TRANSP (via the TRGYRO tool) and ONETWO (via the ITERDB2GYRO tool), flexible data input is possible via the PRO2GYRO tools. This should simplify inclusion of experimental data from arbitrary sources, as well as adding the facility to modify the data, for example, to map an elongated plasma to a circular cross section.

Jeff Candy presented a talk entitled “Status of Gyrokinetic Transport Modeling for ITER” at the 3rd IAEA Technical Meeting on the Theory of Plasma Instabilities in York, U.K. (26-28 March 2007). He also visited Chalmers University of Technology where he collaborated with researchers on the topic of impurity transport in ITER.

##### April 06, 2007

GATO ideal kink calculations through a complete sawtooth cycle for three quite different discharges show some important modifications to the usual sawtooth picture. The calculations for the neutral beam (NB) and fast wave heated (FW) discharge #96043 with giant sawteeth, and the bean and oval shape comparison discharges #118162 and #118164, both with low fast ion contributions, use reconstructed discharge equilibria through a single sawtooth cycle. Contrary to expectations of a degrading of stability through the cycle, the ideal stability in the ellipse case remains fairly constant and, in the other two cases, actually improves through much of the sawtooth cycle, despite q0 starting near one and continually dropping in all three. For the bean shape, q0 decreases from 0.95 to below 0.85 by the end of the cycle and the discharge actually becomes ideally stable for some time in the middle of the sawtooth period. In all cases, the q0 returns to values near 1.0 after the crash. The result from GATO is also considerably different from the formula for the ideal contribution used in the usual Porcelli model, which comprises the analytic Bussac formula with a correction for elongation (http://w3.pppl.gov/rib/repositories/NTCC/catalog/Asset/porcelli.html). For the FW heated discharge, GATO predicts the equilibria to be much more unstable and the ellipse to be slightly more unstable than the model. On the other hand, the GATO calculation is considerably more stable for the bean. This is understandable since the modified Bussac formula partly accounts for elongation but not for other shaping factors and these are strongly stabilizing for the bean.

**Disclaimer**

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