### Theory Weekly Highlights for July 2005

##### July 29, 2005

Joint GA PPPL Highlight:

In joint work with PPPL, further improvements to the 2D Green's function calculation for the vacuum energy in &delta-W stability codes were made to avoid the Riemann-Lebesgue like cancellation due to the oscillatory behavior of the integrand for large toroidal mode number n. This was accomplished by deforming the integration contour into the complex plane so that the integrand now decays exponentially. An accurate evaluation is then obtained by using Gaussian quadratures over a finite range. An analytic result obtained by expanding the integrand in a power series to fifth order agrees well with the new algorithm. The recursion and direct quadrature methods described previously (see Highlight for June 10 2005 at Theory Weekly Highlights for June 2005) works well for small values of the normalized distance between source and observer points, ρ, but the cancellation destroys the precision for moderately large values ρ ~ 1. There is considerable overlap in the applicability of all these techniques so that the Green's function can now be accurately calculated for any practical values of n and ρ.

##### July 22, 2005

A plausible theoretical scenario for explaining a key feature of the hybrid scenario discharges in DIII-D has been developed. In these discharges the central plasma evolves to a quasi-steady state without sawteeth. The central safety factor, q0, is pegged close to 1 and this correlates with the development of a rotating 3/2 magnetic island. Equilibria modeling these discharges with different central q were analyzed using the PEST-III stability code. The linearly unstable 3/2 island develops a 2/2 side-band with increasing amplitude as q0 approaches 1. This near-resonant Alfven wave propagates with enhanced phase speed relative to the background plasma. With sufficient phase speed, the 2/2 sideband could drive currents which impede the decrease in q, causing q0 to remain just above 1 as observed.

##### July 15, 2005

The conference room in building 15 is now equipped with a QuickTime broadcaster and a streaming server. Currently, the presenter video and meeting audio are configured for broadcasting in real time to participants from remotely located fusion sites. The plan is to improve remote participation capability of fusion meetings held at General Atomics by adding the web browser-based broadcasting interface. This capability will be ready and used during the 2004-2005 DIII-D Year-End Review.

##### July 08, 2005

An incompressible fluid model for pellet breakup has shown that high velocity pellets are incompatible with the curved waveguides currently envisaged for ITER pellet fuelling. It is anticipated that in ITER, guide tubes will carry pellets of frozen DT accelerated by gas guns to a velocity of V ~ 1 km/s to a launch position along the high field side of the separatrix. These tubes have one or more 90^{o}. bends. The new analysis predicts that the centrifugal force in the waveguide bends fractures pellets when V > 500m/s. This is in agreement with recent ORNL experiments. For V > 1 km/s, successive fractures turn the pellet into a DT dust cloud. The fluid model finds that the cloud diameter decreases to preserve volume so that the dust cloud will extend a length L = 2(Δφ (R_{d})^{1/2} along the guide tube, where Δφ denotes the angle the waveguide bends through, R ≈ 1m denotes the curvature radius, and d ≈ 0.005m is the pellet diameter. Interestingly, the pellet elongation is independent of pellet velocity. The pellet velocity limitations are avoided by pellet launch from the transformer core.

Justin Burruss gave an invited talk entitled “Grid Performance and Fusion Science” at the Grid Performance Workshop in Edinburgh, Scotland.

##### July 01, 2005

A detailed justification has been obtained for the approach of calculating the neoclassical angular momentum flux in the banana and Pfirsch-Schluter regimes using the drift-kinetic-equation theory. The justification is restricted to the case of up-down symmetric flux surfaces and small values for the ratio of poloidal to toroidal fields. The use of the drift-kinetic-equation approach in general geometry has been questioned because second order terms in gyro-radius over the plasma scale length are not included. It turns out that the drift-kinetic approach does incorporate the leading part of the second-order terms in a subsidiary expansion in the ratio of poloidal to toroidal fields. Revisiting the Pfirsch-Schluter regime calculation has revealed substantial errors, which are now being corrected using the adjoint equation approach that was successfully used recently for the banana regime. (See February 11 2005 highlight at Theory Weekly Highlights for February 2005).

**Disclaimer**

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