Some results / ideas on the effect of flows

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

2. 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 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 A.G. Peeters et al., Phys. Plasmas 12, 072515 (2005)

3. 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 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 (+) A.G. Peeters et al., PPCF 48 (2006) B413

4. 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 Growth rates corrected for the ExB shearing as a function of the parallel velocity shear (assuming a purely toroidally rotating plasma) A.G. Peeters et al., PPCF 48 (2006) B413

5. 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 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 D. Strintzi, unpublished

6. 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