### Theory Weekly Highlights for March 2011

##### March 25, 2011

An assessment of stiffness in GYRO simulations of turbulent transport in L-mode discharges with varying elongation has found that a wide range of values is possible. Stiffness is normally defined relative to the most important driving gradient for a particular instability, but can also be calculated for a range of dimensionless parameters, providing insight on their role in turbulent transport. The stiffness of an energy flux Q with respect to a given dimensionless parameter z is then defined as S = d ln Q / d ln z. Thus, a 10% increase in z yields a 10% increase in Q when S =1, but a 100% increase when S = 10, or a 20% decrease when S = -2. Stiffness of the ion and electron heat fluxes Q_{i} and Q_{e} were assessed at two different radii (r/a = 0.55 and 0.75) in two discharges for a suite of parameters, z = {a/L_{Ti}, a/L_{Te}, a/L_{ne}, γ_{ExB}}, covering the ion and electron temperature scale lengths, the electron density scale length, and the equilibrium ExB shearing rate, respectively. Depending upon the location and dominant turbulence mode, the stiffness of Q_{i} with respect to a/L_{Ti} was found to vary from S =11.6 in ITG-dominated turbulence at r/a = 0.55 to S =-2.6 in TEM-dominated turbulence at r/a = 0.75. A somewhat smaller, but still large range was found for Q_{e} (S = 7.5 to S = -2.5) with respect to a/L_{Ti}. The fluxes were found to be most sensitive to a/L_{Ti} and a/L_{Te}, moderately sensitive to changes in γ_{ExB}, and weakly sensitive (S ⇐ 1) to changes in a/L__{ne}. These results show that significant care must be taken in assessing model prediction uncertainties.

Valerie Izzo attended a “NIMROD coding camp” from 3/21 to 3/23 held at Tech-X in Boulder, CO. The purpose was to complete code revisions needed to allow two major branches of the code to be merged.

##### March 18, 2011

The quasi-linear (QL) heating operator in ORBIT-RF was improved by implementing an expression for the change in parallel velocity due to fast Alfven wave (FW) absorption by particles. The previous QL operator was based on the assumption that particles receive increments only in perpendicular energy when particles pass through cyclotron resonance surfaces. This assumption has been conventionally adopted in FW heating simulations in present tokamaks. However, although the effect is expected to be small, it is not strictly rigorous since FWs have finite k_{//}. The additional parallel velocity kick operator is implemented in a random walk model with the mean change and dispersion terms derived using the Chandrasekhar theory for Brownian motion of individual particles. Comparisons with previous simulations for DIII-D and NSTX HHFW heating experiments indicate that the inclusion of the kick in parallel velocity has no significant effect on the FW absorption by particles, validating the assumption that particles receive increments mostly in perpendicular energy in those simulations. Future efforts will focus on checking the effect in ITER, where k_{//} is much higher, and of consistently including finite E_{//}.

##### March 11, 2011

A new, modern, parallel version of the NFREYA neutral beam deposition code has been developed for use at DIII-D for between shot analyses. Instead of following the fast ions from birth to thermalization like the more comprehensive NUBEAM package, NFREYA follows the fast ion through only one poloidal orbit and smears the deposition across the spatial zones encountered. This and careful design of the parallel communications scheme has shown that the new parallel version, P_NFREYA, scales well to beyond 20 processors, making simulations with 8 beam lines possible in less than 10 seconds. Each beam-line can have more than 100,000 injected pseudo-neutrals giving a comprehensive sampling of initial conditions in phase space. The code is part of the IMFIT suite of integrated modeling codes and is driven by the state file interface.

##### March 04, 2011

The first simulations of multi-species transport of particle, energy and momentum transport with TGLF with the XPTOR code found that kinetic impurity ions are required for momentum transport. When there is no external torque, TGLF predicts a toroidal rotation similar in magnitude to the neoclassical poloidal ion flows. The predicted spontaneous rotation profile depends on a number of competing small corrections to the standard gyro-kinetic ordering making it sensitive to input data errors. Since the measurement of the flows is also near the limit of detection, a direct comparison is presently inconclusive.

**Disclaimer**

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