### Theory Weekly Highlights for August 2010

##### August 27, 2010

By using an extended energy principle, the response of a tokamak to external magnetic perturbations has been shown to be well approximated by the vacuum response for a force free tokamak when there are no pitch resonances present. The effect of the plasma response introduces a paramagnetic effect that amplifies the vacuum response slightly. The amplification factor is inversely proportional to the aspect ratio and the safety factor. For the resonant components, paramagnetic amplification to relatively large amplitudes is possible inside of the resonant surfaces. However, the ideal MHD constraint of ‘frozen in flux’ at the resonant surfaces imposes a diamagnetic response. The vacuum response is then a poor approximation. The effect of plasma resistivity reduces the effectiveness of the ideal MHD constraint and moves the response towards being less diamagnetic. Similar behavior is expected for a tokamak with finite beta.

##### August 20, 2010

The new version of the GATO mapping which writes input for the NOVA code (see October 9 2009 highlight at Theory Weekly Highlights for October 2009) was simplified to produce only the two 1977-era direct access binary files, bypassing the earlier NetCDF option, since the NOVA code option to read the NetCDF files is not yet publicly available. In addition the changes were merged with the other changes to read inverse equilibria in an arbitrary angle format (see May 14 2010 highlight at Theory Weekly Highlights for May 2010), as well as the traditional equal-arclength formats. The new code, along with compatible changes in the remainder of the GATO code, is now ready to be released publicly. With the new mapping in particular, the NOVA code can now utilize equilibria from all the same sources as the GATO code, including direct equilibria from EFIT and inverse equilibria from a variety of formats, such as that produced by TOQ, CORSICA and CHEASE and JSOLVER, and the PPPL QSOLVER code that is currently embedded in the NOVA code scripts. For use with NOVA, the standard scripts need to be rewritten to bypass the QSOLVER equilibrium iterations and mapping and replaced by running the GATO mapping to produce the required direct access binary files from a selected input equilibrium.

##### August 13, 2010

A more complete analytic calculation of the effects of orbit squeezing on the ion neoclassical transport than the usual heuristic approach has been derived via solution of the hierarchy of drift-kinetic equations ordered in the ion gyroradius relative to the system size ρ*_{i} = ρ_{i}/a. For the simple case of a single ion species with uniform temperature and assuming s-alpha geometry, an analytic solution was derived for the first-order (standard local neoclassical) and second-order distribution functions in both the banana and Pfirsch-Schluter collisional regimes and for the third-order distribution function in the latter regime. The third-order solution is necessary to study the non-local transport corrections due to finite-orbit-width effects since the transport coefficients from the second-order solution are zero for up-down symmetric plasmas. The radial dependence of the non-local transport is found to have a coupled dependence on higher-order derivatives of the geometry parameters, the ion density gradient dn_{i}/dr, and the radial electric field E = -∇Φ. This dependence is significantly more complicated than the usual orbit-squeezing factor, S ~ (d^{2} Φ/ dr^{2})(1/n_{i})(dn_{i}/dr), would imply.

##### August 06, 2010

A new set of IDL-based workflow tools has been developed to quantify statistical uncertainties in turbulent transport calculations and validation studies. These tools use as their starting point ensembles of Monte Carlo trial profile fits generated by the GAPROFILES tools for quantifying profile uncertainties. These profile ensembles are then given as inputs to generate ensembles of power balance calculations using the ONETWO code, and turbulent flux predictions with the TGLF quasilinear transport model. Initial results from application to a typical DIII-D L-mode discharge show that the dominant statistical uncertainty in all transport channels is due to the uncertainty in the ion temperature profile, and that the relative uncertainty generally decreases with radius. These tools were developed and tested in collaboration with P. Namasondhi, who is a summer NUF student, and the results will be presented in a poster at the fall APS meeting.

**Disclaimer**

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