Some results / ideas on the effect of flows D. Strintzi, C. Angioni, A. Bottino, A.G. Peeters

Parallel velocity shear The effect of a toroidal rotation can be thought of as the combination of the perpendicular ExB shearing and a parallel velocity shear The parallel velocity shear is found to be destabilizing for the ITG. At high values of the parallel velocity shear one obtains the parallel velocity shear instability At lower values it drives the ITG more unstable A.G. Peeters et al., Phys. Plasmas 12, (2005) Growth rate of the mode from gyro-kinetic calculations (adiabatic electrons) as a function of the parallel velocity shear for various values of the ion temperature gradient length

Experimental values The parallel velocity shear is generally found to be smaller than 2 (normalized units), well below the threshold for the parallel velocity shear instability (5.4) Data from ASDEX Upgrade, various scenarios (H-mode (o), improved H-mode (*), and internal barriers(+)) There appears to be a positive correlation between toroidal rotation shear and inverse ion temperature gradient length A.G. Peeters et al., PPCF 48 (2006) B413 The parallel velocity shear as a function of the ion temperature gradient length for various plasma scenarios: H-mode (o), Improved H- mode (*), and internal barriers (+)

In the experimental parameter region ExB shear should dominate For a purely toroidally rotating plasma the parallel velocity shear and the ExB shear are directly related. Estimating the effect of the ExB shear using the Waltz formula (subtracting the shearing rate from the growth rate of the mode) the two effects can be combined In the experimental range (u’ < 2) the ExB shearing dominates over the effect of the parallel velocity drive In first approximation one can then use the ExB shearing only A.G. Peeters et al., PPCF 48 (2006) B413 Growth rates corrected for the ExB shearing as a function of the parallel velocity shear (assuming a purely toroidally rotating plasma)

Growth rate calculations using GYRO JET like parameter case of the ions stiffness / ion temperature modulation experiments (q and shear slightly different than used in the GS2 simulations) Global runs (needed for the ExB shear to be taken into acount) Linear one mode (k = 0.3) Various values of the shearing rate Simple Waltz rule with alpha = 1 appears to apply Quoted shearing rates of the experiments have a somewhat small effect D. Strintzi, unpublished Growth rates from GYRO as a function of the ion temperature gradient length: Blue no ExB shear, Red with 1.1e4 s-1 shearing, green Waltz formula with alpha = 0.5, Balck with alpha =1

Preliminary Nonlinear Gyro-runs Preliminary, many things need to be checked still Same parameters as for the linear runs 16 toroidal modes (150 radial points) k<0.8 Ion heat flux decreases due to ExB shear Effect for the quoted shearing is somewhat small Within the error bars no clear change in stiffness. BUT: maybe the runs are not well converged, or the shearing is too small to bring out the effect Normalized ion heat flux as a function of the ion temperature gradient length. Red without shearing, blue with 1.1e4, and black with 2.2e4 s-1 ExB shearing D. Strintzi, unpublished