### Theory Weekly Highlights for October 2004

##### October 29, 2004

A new analysis has clarified the effects of electron-ion collisions on the linear zonal flow polarization. Previously, GYRO simulations found little or no effect of electron-ion collisions on zonal flows. Though this agreed with the Rosenbluth-Hinton collisionless residual obtained including only the m = 0 potential, it was a puzzle because the electron-ion collision frequency is much larger than the ion-ion collision frequency so the effect was expected to be much larger than the effect of ion-ion collisions. By including the m = 0, +1, -1 potentials in the gyrokinetic equation for ions and the drift kinetic equation for electrons, a new damped root appears in the “dispersion relation” for the zonal flows at approximately the electron-ion collision frequency. However, when the system of equations is solved to determine all three potentials, the additional m = +1, -1 potentials are found to be smaller than the m = 0 potential by two orders in the ion Larmor radius, because the coupling between the m = +1, -1 potentials and the m=0 potential is small in the Larmor radius. The residual in the m = 0 potential is therefore only weakly affected by the electron damping from the m = +1, -1 potentials.

##### October 22, 2004

A Singular Value Decomposition (SVD) method was developed to calculate surface perturbations from measurements of the magnetic field at the DIII-D vessel wall. Normally, the VACUUM code calculates the magnetic field at or near the surface of the vacuum vessel as a response matrix to the normal component of the perturbed magnetic field at the plasma surface. In inverting this relation, the SVD provides an effective way to deal with the different dimensionalities of the variables as well as the possible singular behavior of the response matrix. For model cases with 256 data points describing the plasma surface, as few as 64 observation points (Mirnov loops), are sufficient to accurately reproduce the plasma surface perturbation in DIII-D. Both the poloidal and toroidal components of the Mirnov loop measurements are now calibrated with respect to the plasma magnetic perturbation.

##### October 15, 2004

Simple ITG-adiabatic electron simulations have been to quantify the nonlocal transport mechanism for breaking gyroBohm scaling. The simulations are described by a heuristic formula that has been developed for a nonlocal growth rate corresponding to a localized radial average of local growth rates. The nonlocal growth rate can be used in place of the local growth rate in local gyroBohm transport models like GLF23. This will quantify how turbulence from locally unstable regions drains into locally stable region as ρ* increases and growth rates decrease. GyroBohm transport scaling will be broken toward Bohm in the unstable regions and toward super-gyroBohm scaling in the stable regions.

##### October 08, 2004

Modeling of feedback stabilization using the MARS-F stability code has yielded an improved understanding of RWM active stabilization experiments using the internal I-coils in DIII-D. The optimum phasing angle of the upper and the lower I-coils with respect to the sensor signal has been obtained and agrees with the experimentally measured angle. Moderate deviations from this phasing angle lead to a reduced feedback effectiveness. Large deviation of more than 90 degrees leads to a failure of the feedback, as expected from general theoretical expectations. This also correlates with the observation of disruptions in the experiments.

##### October 01, 2004

During a visit to GA by Alan Glasser, significant progress was made in understanding the source of the major difficulty in the linear resistive asymptotic matching code TWIST-R, namely that the calculated Δ' values are clearly unphysical despite solutions that look reasonable. This problem also occurred in the DCON-R resistive code; the source of the difficulty turned out to be that the usual equilibrium accuracy for input to ideal codes is insufficient for a linear resistive asymptotic matching code. This is also the likely source of the problems in TWIST-R and is suggested by the observation that the results are sensitive to numerically implementing different analytically equivalent expressions for j and ∇×B. A new method is being developed by Glasser to obtain 'refined equilibria' from input equilibrium codes. Several alternative options were discussed but equilibrium refinement may be solution in both approaches.

**Disclaimer**

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