### Theory Weekly Highlights for April 2005

##### April 29, 2005

A general drift-kinetic equation has been derived without assuming the flow velocity is small or specializing its form. The drift-kinetic equation is the starting point for calculations of neoclassical transport fluxes and turbulent transport. In tokamak plasmas heated by neutral beam injection, ions and impurities flow in the toroidal direction at speeds that are comparable to the impurity thermal speed. In the new equation, the kinetic energy and magnetic moment of the particles are defined in a frame moving with the flow. As a result of rotation shear effects, these are not constant but change with time due to the fact that energy and magnetic moment are defined with their rotational components subtracted out. The variation depends on details of the flow. The guiding center drifts allow particles to carry some of the rotational kinetic energy radially, causing changes in the velocity distributions and therefore affecting the transport. We are presently attempting to simplify the drift-kinetic equation using a particular form for the flow corresponding to sheared toroidal rotation.

##### April 22, 2005

The new cluster computer for fusion applications is now operational. This new system has 116 AMD Opteron processors (64-bit, 2.4 MHz) with both gigabit ethernet and Infiniband interconnects. The network filesystem uses the gigabit backbone, while MPI is implemented over Infiniband. Per-processor, the system is four times as fast as the NERSC IBM Power3 (seaborg), twice as fast as the ORNL IBM Power4 (cheetah) and nearly twice as fast as the ORNL SGI Altix (ram). The GYRO and ORBIT-RF codes have been ported to the new cluster and are running in production mode. Porting of the NIMROD and BOUT codes is underway.

##### April 15, 2005

In collaboration with Alex James (UCSD) an option to substitute the GATO disk I/O routines with F90 dynamic allocation to memory was tested successfully. The original I/O system was developed to reduce memory requirements in the eigenvalue solver when memory was expensive. Ultimately, flexibility for trading memory and disk depending on the system load will be provided. The new version, however, presently uses either all memory or all disk and the potential savings are undergoing testing. As anticipated, there is little saving in CPU time but savings in wall clock time are expected to be significant when the system load is high. The remainder of the eigenvalue solver is also being converted to F90 syntax with dynamic allocation. In parallel, options for reducing CPU time in the Cholesky decompositions are being evaluated.

Myunghee Choi delivered an invited talk on the Simulation of Fast Wave Damping on Resonant Ions in Tokamaks at the Topical Conference on Radio Frequency Power in Park City, Utah. Carlos Estrada-Mila and Dylan Brennan respectively gave oral presentations on Gyrokinetic simulations of ion and impurity transport and on Nonlinear Evolution of Edge Localized Modes at the Sherwood Fusion Theory Conference in Stateline, Nevada.

##### April 08, 2005

The interaction between resonant plasma ion species and the fast Alfven wave was investigated by coupling fast wave electric fields from the 2D full wave code TORIC4 to the Monte-Carlo code ORBIT-RF and compared to recent measurements from Alcator C-Mod. An experimental C-Mod discharge with 5% hydrogen minority fundamental harmonic heating at 78 MHz and 1.0 MW RF power was used in the study. The wave field solutions from TORIC4 were approximated using a single dominant toroidal and poloidal wave number and input to ORBIT-RF. Results from the coupled ORBIT-RF and TORIC4 simulation agree well with the experimentally measured fast ion distribution from a CNPA diagnostic on C-Mod. Compared to the linear absorption result obtained directly from TORIC4 with an assumed tail temperature of 20 keV, ORBIT-RF produces a much broader power deposition profile. The broadening is due to radial diffusion from the fast ion finite orbits and pitch angle scattering, which are treated properly in ORBIT-RF. More detailed validation work is underway.

##### April 01, 2005

A recent GYRO simulation of non-local transport shows how local gyroBohm transport scaling is broken. The study used piecewise flat profiles to distinguish the nonlocal breaking of gyroBohm scaling from local breaking due to profile shearing. The simulations are consistent with the following picture of nonlocal transport: The transport is proportional to a locally averaged growth rate where the averaging length L is proportional to the ion gyroradius ρ*. Turbulence drains from locally unstable regions and spreads into stable (or less unstable) regions. Local gyroBohm scaling is then broken in the direction of Bohm scaling in the locally unstable draining regions and in the direction of super-gyroBohm in the less unstable spreading regions. As ρ*, and therefore L, get very small, local gyroBohm scaling in the locally unstable regions with no transport in locally stable regions is recovered. We have developed a heuristic theory of L/a that shows it to be linear in ρ* and inversely proportional to the square root of the local driving rate, in agreement with the simulations. This model of nonlocality will be built into our new GLF23 model and will allow modeling with some nonlocal transport in locally stabilized regions of ITB's and H-mode pedestals.

**Disclaimer**

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