TTF M. Ottaviani Euratom TORE SUPRA Overview of progress in transport theory and in the understanding of the scaling laws M. Ottaviani EURATOM-CEA, Cadarache Acknowledgements: B. Labit, G. Manfredi

TTF M. Ottaviani Euratom TORE SUPRA Outline Brief review of transport studies, scaling laws, similarity experiments, difficulties. The gyroradius scaling problem Beta dependence issues Electron heat transport. ETG? Profile effects, stiffness, safety factor (current) dependence Conclusions

TTF M. Ottaviani Euratom TORE SUPRA Scaling laws, ITER

TTF M. Ottaviani Euratom TORE SUPRA Difficulties with the scaling laws

TTF M. Ottaviani Euratom TORE SUPRA Similarity experiments Similarity experiments (espec. DIII-D), that vary one adimensional parameter at a time, shed some light but do not resolve the issue. The scaling of the ion conductivity from power balance changes from Bohm (or worse) in L-mode to g-Bohm in H-mode Electrons always gyro-Bohm (different physics?) Measured turbulence microscopic characteristics essentially gyro-Bohm (DIII-D, IAEA 2000) Limitations as in 0-D scaling apply (espec. error bars 30%)

TTF M. Ottaviani Euratom TORE SUPRA Gyroradius scaling

TTF M. Ottaviani Euratom TORE SUPRA Global ITG fluid simulations (Manfredi-Ottaviani)

TTF M. Ottaviani Euratom TORE SUPRA ITG correlation functions and pol. spectra Rho-star=1/50,1/100,1/200. Gyro-Bohm scaling Peak of the corr. funct. at around 0.3

TTF M. Ottaviani Euratom TORE SUPRA ITG gyrokinetic simulations, Lin et al. Recent (2002) gyrokinetic simulations also converge to gyro-Bohm scaling at sufficiently small rho-star. Microscopic features same as in fluid simulations

TTF M. Ottaviani Euratom TORE SUPRA Convergence to gyro-Bohm: a possible explanation

TTF M. Ottaviani Euratom TORE SUPRA Gyroradius scaling: conclusions Numerical simulations of ITG tubulence now agree that convergence to gyro-Bohm scaling occurs in the limit of small gyroradius. Recent ETG simulations (Labit-Ottaviani) also show the same behaviour, although convergence is more difficult due to the radial extension of ETG vortices. Thus:

TTF M. Ottaviani Euratom TORE SUPRA BETA: not a scaling parameter Alfven ITG (AITG) from Zonca et al. (1998): new e.m. branch. The maximum growth rate depends on beta.

TTF M. Ottaviani Euratom TORE SUPRA AITG: global gyrokinetic eigenvalue analysis (Falchetto-Vaclavik, EPS 2002)

TTF M. Ottaviani Euratom TORE SUPRA Nonlinear results From Scott, NJP (2002) Beta scan from the DALFTI Model (drift-Alfven with ion temperature dynamics)

TTF M. Ottaviani Euratom TORE SUPRA FWEH in Tore Supra The Tore Supra FW transport database is optimally represented by an offset linear formula, independent of the density q e  n  e T  e (1/ L Te -1/ L c ), with   1.5,  = 0, and R / L c = 5 (  1) + 10 (  2) |s| / q

TTF M. Ottaviani Euratom TORE SUPRA Renewed interest in ETG

TTF M. Ottaviani Euratom TORE SUPRA ETG transport resuscitated From Jenko et al, Gyrokinetic flux tube simulations of ETG tubulence show enhancement of at least an order of magnitude over the equivalent ITG transport. This is enough to compensate the reduction due to the mass ratio The ETG adiabatic response does not allow strong zonal flow generation: STREAMERS

TTF M. Ottaviani Euratom TORE SUPRA ETG fluid simulations (Labit-Ottaviani) Phenomenology: Contour plots and 2D correlation functions

TTF M. Ottaviani Euratom TORE SUPRA Fluid ETG: beta scan Weak dependence on beta Transport from the magnetic flutter negligible Not a definite scaling

TTF M. Ottaviani Euratom TORE SUPRA Fluid ETG: power(gradient) scan Transport somewhat below the required level to match observations

TTF M. Ottaviani Euratom TORE SUPRA Test particles in model streamers Zero frequency: ballistic transport. Bohm timescale With typical frequency, in the rest frame of the wave: ZERO TRANSPORT

TTF M. Ottaviani Euratom TORE SUPRA Beta scaling: conclusions Beta: not a scaling parameter. Not a power-law dependence Expect degradation near the ideal limit, otherwise the dependence is probably weak

TTF M. Ottaviani Euratom TORE SUPRA Profile effects: resiliency, stiffness Tore Supra (left), Asdex (right). Almost-independence of the temperature gradient scale-length on the input power

TTF M. Ottaviani Euratom TORE SUPRA Automatic stiffness model

TTF M. Ottaviani Euratom TORE SUPRA Stiffness ? Stiffness as seen from power balance analysis can be the consequence of the dominance of a specific physics in a certain region of the discharge Criticality effects better seen by tailoring the power deposition profiles Also from pulse propagation/modulation, but interpretation more problematic

TTF M. Ottaviani Euratom TORE SUPRA More on profile effects

TTF M. Ottaviani Euratom TORE SUPRA Conclusions Gyro-Bohm scaling finally well established numerically. It remains to be clarified why it does not turn out in certain experiments (Not enough asymptotic + profile/flow effects? Proximity to threshold?) Possible action: force gyro-Bohm scaling in transport analysis. Adds a constraint to the exponents. Reduce uncertainty? Beta not a scaling parameter. Degradation near the ballooning limit from Alfvenic dynamics. ETG perhaps a good explanation for electron heat transport. Pluses: independence of the electron transport on the mode of operation; exptl. threshold matches theory. More work needed to understand the size of the ETG transport. Current scaling not a true scaling, comes from threshold Stiffness of the temperature scalelength can come from the dominance of a given physics in the transport region, not from threshold.