### Theory Weekly Highlights for June 2006

##### June 30, 2006

Construction of the new TGLF transport model (the successor to the GLF23 model) is in its final stage and nearing completion. A preliminary model for the saturated turbulence amplitude has been fit to the database compiled from non-linear GYRO runs. The model is in the form of a generalized mixing length rule that depends only on the linear growth rate, frequency and wavenumber of the most unstable mode. The fluxes of particles and energy are computed by multiplying the saturation rule model by the quasilinear weights found with the new TGLF eigenmode solver. A set of 63 GYRO runs in shifted circle geometry over a range of plasma parameters was used for the fitting of the model. The model achieves an 18% fractional deviation for ion and electron energy fluxes and 32% for the particle flux. The higher fractional deviation for the particle flux is due to the large number of cases near zero particle flux in the database. The model works very well for large particle outflow or pinch.

##### June 23, 2006

Stability calculations in support of studies of the fast-ion stabilization of DIII-D discharges with the Porcelli model showed that there are some significant differences from the predictions of the analytic, large aspect ratio, circular cross section Bussac model for the ideal internal kink. For reconstructed equilibria in discharges with large sawteeth, the eigenfunction has approximately the “Top-Hat” structure of the Bussac model where the Porcelli model is applicable. For a discharge with much smaller sawteeth, however, the eigenfunction shape is significantly different. GATO calculations show that the difference in structure of the eigenfunctions is due to the change in the position of the q = 1 surface, r(q=1), rather than to a change in the safety factor q on axis. As r(q = 1) increases the computed eigenmode becomes closer to “Top Hat” model. In addition, both the growth rate and marginal point can be sensitive to removing the wall with little visible change in the mode structure. This, the so-called 'toroidal kink' mode, has been noted in previous studies of model equilibria. For real discharges, the Porcelli model incorporating the Bussac internal kink will need to be extended to account for these deviations.

##### June 16, 2006

The linear stability properties of a reconstructed DIII-D discharge equilibrium, unstable to an edge-localized mode, has been studied with the NIMROD code. The poloidal drift frequency ω* for this case is peaked in the edge region where the electron pressure gradient is strongest. The stability analysis consequently included both the Hall and gyroviscous effects.; this was the first time these effects have been included in a calculation for ELMs in a real reconstructed DIII-D discharge. The Lundquist number S was approximately 2×107 and the Prandtl number was 0.1. The linear, single fluid growth rate spectrum with respect to toroidal mode number is peaked around n=10 and drops to marginality near n=20. In contrast, with the Hall and gyroviscous terms included, the peak growth rate is reduced and mode numbers above n=16 are completely stabilized but the low n stability is weakly affected. This is in agreement with the conventional wisdom and with previous calculations for model equilibria. Future studies will include the Hall and gyroviscous effects in the nonlinear calculations as well.

Carlos Estrada-Mila successfully defended his doctoral thesis at UCSD on June 5. The thesis “Gyrokinetic Studies of Particle Transport in Tokamaks” covered the work detailed in several previous highlights (see the highlights for January 21 2005 at Theory Weekly Highlights for January 2005). and January 6 2006 at Theory Weekly Highlights for January 2006). Carlos is returning to Colombia where he will be pursuing new adventures.

##### June 09, 2006

A new 2D magnetohydrodynamic simulation of pellet ablation in the electrostatic approximation was developed in collaboration with R. Samulyak and T. Lu of BNL. The major conclusion of the study is that in purely hydrodynamic simulations (without the JxB force), changing the heat flux from spherically symmetric 1D to axisymmetric 2D deposition leads to a minor reduction in the ablation rate, contrary to the prevailing expectation of a “factor of 2” reduction. However, in the magnetohydrodynamic simulations with the JxB force included, the magnetic field channels the flow into an extended plasma shield and significantly reduces the ablation rate by a factor of 2 to 3, depending on the time it takes for the heat flux to ramp up as seen by a moving pellet. Fast pellets crossing pedestal regions in ITER would lead to shorter warm-up times, which in turn lead to narrower ablation channels, stronger shielding, and reduced ablation rates.

##### June 02, 2006

Numerical 3D turbulence studies show a strong impact of magnetic geometry on the oscillating zonal flows known as geodesic acoustic modes (GAMs), a ubiquitous phenomenon detected five years ago that is prevalent near the tokamak edge. On one hand, changing the Shafranov shift, ellipticity, safety factor, or magnetic shear, individually alter the drive efficiency from Reynolds Stress, Stringer-Winsor force, and finite-Larmor-radius heat flux. On the other hand, geometric effects also couple the GAMs to various parallel sound waves, giving rise to complex interactions. A deep understanding of the experimental GAM amplitudes would open up a novel way to improve tokamak performance, since - at least in the simulations - dramatic reductions in transport are possible by choosing a GAM-optimized configuration.

An EFIT version that incorporates the new DIII-D vacuum vessel and limiter geometry, new magnetic diagnostics in the new lower divertor shelf, and a new more complete magnetic uncertainty matrix has been released to support DIII-D plasma operations. The new magnetic uncertainty algorithms are currently being tested and will be available for general public use in the summer after this testing is completed.

**Disclaimer**

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