### Theory Weekly Highlights for December 2008

##### December 19, 2008

Numerical experiments quantifying the role of both 'residual' Rosenbluth-Hinton zonal flows and geodesic acoustic modes (GAMs) in saturating drift-wave turbulence have revealed several key findings. The GAMs can represent an important source of shear stabilization, as they can be excited to sufficiently strong levels to counter-act the reduced 'per-unit' shearing efficiency due to their finite frequency. Also, the ExB component of the zonal flow shear is stabilizing for finite-n drift-waves, while the diamagnetic component appears to destabilize the finite-n modes, and that the entropy generation peaks at wavelengths corresponding to peak transport production, but entropy dissipation is spread broadly over many wave numbers (including the n=0 zonal modes). These results appear to hold for ITG, TEM and mixed ITG/TEM turbulence. The results have been published in the December 2008 issue of Physics of Plasmas.

C. Holland gave a seminar on validation and high performance computing in fusion plasmas at the Fermilab weekly colloquium on Wednesday, Dec. 17. A video of the seminar will be made available on the Fermilab website.

##### December 12, 2008

The capability to treat general flux-surface shape has been added to the GYRO suite (TGYRO/GYRO/NEO). To generate the relevant data required in GYRO, use has been made of the ELITE geometry backend (ELITEEQ), together with a new toolset that provides a unified framework to compute either model shape parameters (kappa, delta, squareness) or Fourier coefficients for an arbitrary shape. The method has the benefit that precise, direct comparisons between parameterized and general shape are made by changing only a single input parameter. Moreover, in the case where the parameterized shape coincides with the general shape, the two methods give identical answers.

Christian Konz, is visiting GA for four weeks from IPP Garching to work on edge stability with GA and DIII-D colleagues.

##### December 05, 2008

A study of Onsager symmetries of the flux-gradient relations for gyro-Landau fluid (GLF) models, showed that there are non-trivial constraints on the form of the closure of the GLF equations for both the slab and toroidal limits that must be satisfied in order to preserve the Onsager symmetries. Including electromagnetic fluctuations generates additional constraints. Symmetries between various terms in flux-gradient relations are known to ensure the positivity of entropy production. These Onsager symmetries in collisional transport theory result from terms having the same energy moments of the distribution function and the theory of gyrokinetic turbulence driven fluxes yields similar symmetries. The analysis shows that if these symmetries are not respected in the closure of the GLF equations then the ratio of ion to electron energy flux or of energy flux to particle flux will be inaccurate even if the linear growth rates are accurate.

**Disclaimer**

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