### Theory Weekly Highlights for February 2012

##### February 24, 2012

In a collaborative effort between MIT and GA, MIT researchers and graduate students have implemented “in-between shot” initial value linear stability analysis for the first time during a tokamak experiment using GA's GYRO code. The goal of this analysis was to assess the transition between ITG and TEM driven turbulence in C-Mod. The JRT 2012 experiment “MP689: Validation of gyrokinetic transport models across the ITG/TEM boundary in L-mode and I-mode plasmas” was run at Alcator C-Mod on Feb 21st, and the linear GYRO runs were completed in-between-shots using actual experimental density and temperature profiles from Thomson scattering and ion temperature profiles from imaging X-ray crystal spectroscopy. In order to run GYRO in between C-Mod shots, 160 processors on the local MIT Plasma Science and Fusion Center cluster, LOKI, were dedicated on this day to support the experiment. This is the first time that linear GYRO has been used to inform the running of a tokamak experiment (i.e. deciding what parameters to change /for the next shot/), and the first time that dedicated experimental run time at a major facility was combined with large-scale dedicated computational resources in real-time.

##### February 17, 2012

Linear and nonlinear calculations of the response for DIII-D discharge #142603 with internal n = 3 coils have been found to yield qualitatively different results for the perturbed flux surfaces on the inboard side. Linear calculations were performed using the MARS-F code following a dynamic evolution approach and the nonlinear calculations were done using VMEC to construct a nearby perturbed equilibrium. Investigation of reasons for the discrepancy identified several possibilities. The dynamic linear response was shown to depend quantitatively on what physics is included. The linear response is also sensitive to the presence of marginal ‘near internal’ eigenmodes that can be excited by small parameter variations and these may or may not be physically excited or survive nonlinearly. Third, for finite displacements, the linearized displacements do not strictly define perturbed flux surfaces even in the ideal case. However, while these all contribute quantitatively, none appears to explain the qualitative discrepancy with the nonlinear results. The resolution appears to lie in the fact that even though the applied fields are a small fraction of the axisymmetric field, the response can be large. For finite displacements this can lead to flux surfaces crossing, invalidating the linear model. A sufficient criterion for crossing is when the initial and final points of the finite displacement differ in phase by more than π/2. For discharge #142603, a map of where this phase difference exceeds π*2 shows multiple regions occur on the inboard side.
== February 10, 2012 ==
A new paradigm for the suppression of turbulence by ExB velocity shear has been discovered by studying the radial wavenumber spectrum of electric potential fluctuations from gyro-kinetic simulations with GYRO. Including shear in the ExB velocity Doppler shift causes the peak in the non-linear spectrum to be shifted to a finite radial wavenumber at a reduced amplitude. An analytic model shows that this process has two parts. The first part is a linear destabilization due to the Doppler shear interaction with the shape of the radial wavenumber spectrum. This linear effect causes the spectrum to shift. The second part is from a non-linear mixing which re-centers the peak at a finite wavenumber. This new “spectral shift” paradigm can be modeled in the quasilinear TGLF transport model and is found to be a more accurate predictor of the reduction of the energy flux with ExB Doppler shear than is the usual quench rule. The spectral shift model in TGLF also accurately computes the toroidal Reynolds stress that is zero for the quench rule.
== February 03, 2012 ==
A significant effort was made to modify the parallel processing method used in the TGLF stiff transport solver GCNMP in the ONETWO transport code to allow an arbitrary combination of grid points and number of processors to be used. The method developed allows passing of confinement related tasks on a given grid point to be handed out to an arbitrary idle processor. The results from all processors are collected on each time step to advance the transport equations. This approach provides a more uniform work load for each processor than would be achieved if a standard division of grid points/processors were adopted. The code was ported to the DROP and other Linux clusters to take advantage of the large number of processors available on those machines. This significantly enhances the ONETWO/GCNMP capability to perform fine-grid transport simulations.
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**Disclaimer**

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