### Theory Weekly Highlights for June 2005

##### June 24, 2005

A gyrokinetic entropy diagnostic has been derived and added to GYRO. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key new confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor flux is changed by a four-fold increase (from 64 to 256 grid points per cell) in velocity-space resolution. Third, the measured flux is invariant to an eight-fold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure.

##### June 17, 2005

In a more detailed analysis of the simulations using ORBIT-RF with TORIC4 for DIII-D it was found that the ORBIT-RF simulation predicts a much weaker absorption at 8Ω_{D} than expected from the linear theory result. Linear theory predicts non-negligible absorption at 8Ω_{D} due to a large k_{⊥} ρ_{i} at the resonance location. The ORBIT-RF simulations use experimentally reconstructed equilibria and profiles of the wave fields and wave numbers from the 2-D full wave code TORIC4 with Monte-Carlo collision operators for pitch angle scattering and fast particle slowing down. Steady state is modeled by re-injecting thermalized ions. Stochastic RF resonant kicks are then modeled using a quasilinear diffusion operator. By analyzing the finite orbit and pitch angle scattering effects, the weak absorption in the simulations is explained by Coulomb scattering of finite orbit resonant ions, which curtails the resonant interaction.

##### June 10, 2005

Joint PPPL-GA Theory Highlight:

The Green's function calculation for the magnetic scalar potential used for the vacuum in most delta-W stability codes currently employs a recursion relation to generate modified elliptic functions at finite toroidal mode number, n. The recursion is initiated from the complete elliptic integrals of the first and second kind, E(ρ) and K(ρ) of the normalized source-observer distance 0 < ρ < 1. At each recursion there is a loss of precision due to subtraction of increasingly large terms scaling like n*^{1)} is lost for n ~ 9. In joint work between PPPL and GA, a new method to calculate the Green's function was developed by directly integrating the relevant integral representation. A judicious treatment of the singular behavior of the function, together with a transformation of the independent variable, and an accurate quadrature scheme enable a precision that is much greater than before, even approaching machine accuracy at high n. This should eliminate the limit to calculating stability at high n and low aspect ratios.

GA Theory Highlight:

A videoconference using the Access Grid was held with Korean Basic Science Institute (KBSI) physicists to discuss the GA-KBSI KSTAR Modeling and Analysis Collaboration Plan. The agreed plan consists of 4 collaboration topics: EFIT equilibrium reconstruction, ONETWO transport, GATO ideal stability, and KSTAR scenario development. KBSI physicists will become familiar with ONETWO and GATO through participation in the development of those codes for the Fusion Grid. Dr. K.I. You of KBSI is visiting GA 6/6 - 6/17 under this plan to collaborate on the application of EFIT and GATO to KSTAR, and the installation of EFITTools at KBSI.

##### June 03, 2005

In collaboration with Dr. Christian Konz from IPP Garching, a successful three-way benchmark of the ELITE, GATO and MISHKA MHD stability codes was performed for intermediate n peeling-ballooning modes in simple geometry using an equilibrium from the HELENA code. HELENA is a commonly used equilibrium code and is tightly interfaced with the European stability code MISHKA. All three stability codes agree to within 2% accuracy on this benchmark case. In order to perform this study, we have set up both ELITE and GATO to work with HELENA. This will enhance our ability to routinely collaborate on studies of edge stability on JET, ASDEX-U and MAST. Dr. Konz will continue working with the GA theory group this summer, studying the effect of rotation on edge stability.

**Disclaimer**

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

1+ρ)/(1-ρ)n times E(ρ) and K(ρ). For an NSTX or MAST case ρmax ~ a/R ~ 0.7 and approximately 108 precision (the precision of the standard expansions for E(ρ) and K(ρ

^{1)}

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