### Theory Weekly Highlights for October 2008

##### October 31, 2008

A TGYRO interface to the Weiland transport model (more recently called the QFM model) has been developed in collaboration with Hans Nordman from Chalmers University. Running different transport models (TGLF, QFM, etc) through TGYRO ensures the consistency required to compare these models against one another, or against direct gyrokinetic calculations. Users of the QFM model now have the option to manage and parallelize their modeling tasks with the convenient TGYRO infrastructure. QFM will also be used as an additional test for robustness of the TGYRO iteration scheme, which is still under development.

##### October 24, 2008

The discretization of the collision operator in GYRO (http://fusion.gat.com/theory/gyro) has been completely rewritten to compute the collisional advance more simply and accurately. Collisions in GYRO are numerically challenging because an implicit scheme must be formulated on an irregular mesh. The new method, based on a mesh-free cubic/quintic radial basis function (RBF – see http://en.wikipedia.org/wiki/Radial_basis_function) approach is significantly more elegant and accurate than the previous finite-difference approach. The new approach will also greatly simplify the coding of a more advanced collision operator that includes inter-species momentum exchange, FLR effects, etc.

##### October 17, 2008

As part of the SciDAC GSEP project recent, small flux tube GYRO gyrokinetic studies of energetic particle modes have identified the TAE mode gap, with the most unstable modes found in the center of the gap. The TAE mode frequencies track the gap around omega ~ v_{A}/2Rq to higher values with decreasing q as expected (v_{A} is the Alfven frequency, R the major radius and q the safety factor at the TAE mode location). Also, at fixed fast particle gradient, the growth rates decrease with increasing fraction of fast particles as expected. Evidence for significantly unstable “energetic particle driven” modes at higher densities and distinct from TAE modes, inside or outside the gap have not yet been identified. This may require the new GYRO facility to identify subdominant modes; this facility is now working for the usual ITG/TEM modes. Adding background plasma gradients appears to reduce the TAE growth rates. Large cyclic and non-cyclic (zero boundary condition) flux tube results track the small tube results. Global eigenmode runs with real shaped geometry and actual DIIID profiles are not inconsistent with the circular geometry flux tube runs. The new results will be presented by Eric Bass at the APS08 meeting.

##### October 10, 2008

An extensive benchmark of the 5-D Monte-Carlo particle ORBIT-RF and 2-D linear full wave AORSA codes was carried out to test their predictions for standard linear heating theory. In a modeling study of the ICRF wave-plasma interaction in tokamaks, the local power absorption, calculated from ORBIT-RF without updating resonant ion characteristics, was compared with that from AORSA. The two codes use quite different numerical approaches but yield excellent agreement in prediction of fundamental heating of a minority hydrogen Maxwellian plasma in Alcator C-Mod. However a factor of two difference was found in modeling of high harmonic ICRF heating of energetic beam ions in DIII-D. The difference is currently understood as due to missing physics implemented in each code. Loss of energetic particles to the wall due to their finite orbits, which is not implemented in AORSA, produces significant differences in the outer region of the plasma. ORBIT-RF requires phase information between the electric field amplitudes E+ and E-, and a perpendicular wave spectrum from hot plasma, which are not readily available from the wave codes. These could also produce non-negligible differences. More accurate modeling is being considered under the RF SciDac project.

##### October 03, 2008

A more in depth investigation of the equilibrium and stability analysis of the bean and oval sawtooth experiments revealed some additional surprises. The growth rate does not fully follow the sawtooth cycle and is quite different in the two cases but new analysis shows that the local shear at q=1 tracks the ideal growth rates in both cases. None of the other key variables q0, qmin, r(q0) and r(qmin), is strongly correlated. Also, there is a small event about a third of the way into the sawtooth ramp in both cases, which causes a small drop in Te. The analysis revealed that for the bean case, the ideal unstable mode is a quasi-interchange until this event, after which the plasma becomes ideally stable for a sizeable fraction of the sawtooth period until, as reported earlier (see Theory Weekly Highlights for April 2007 and Theory Weekly Highlights for September 2007), the internal kink becomes unstable somewhat before the final sawtooth crash. For the oval, the growth rate drops after the event but the plasma is not fully stabilized and the mode remains a quasi-interchange throughout. The implications for interpreting the experimental observations are being worked through.

**Disclaimer**

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