October Milano Core-Pedestal Energy Confinement. Empirical Scaling Laws and "stiff" profiles. A. Jacchia 1, F. De Luca 2 1 Consiglio Nazionale delle Ricerche - Istituto di Fisica del Plasma EURATOM - ENEA - CNR Association, via R.Cozzi, Milano Italy 2 Dipartimento di Fisica, Università degli Studi di Milano via Celoria, Milano Italy

Local transport Local T, n.. profiles Theory Match profiles with Interpretative-Predictive Codes Empirical Scaling laws Mean-integral quantities Statistical analysis Extrapolation to Unexplored regimes ?link? Local heat transport & Empirical scaling

A two-term model of the confinement in Elmy H–modes J.G.Cordey et al "A two-term model of the confinement in Elmy H-modes" Nucl. Fusion 43 (2003) 670 D.C. McDonald et al "Recent progress on the development and analysis of the ITPA global H-mode using the confinement databases" Nucl. Fusion 47(2007) Pedestal Scalar Database V3.2 (March 2002) - T e ~T i JET, ASDEX-U, D3D, JT60,CMOD, MAST, JFT2M

W core = W- W ped is based on the assumption that the total energy can be expressed as sum of independent quantities. Profile stiffness (consistency) links core and boundary behaviour. ETG, ITG modes control i.e. the steepness of electron and ion temperature profiles. Core-Pedestal relationship in the presence of stiff temperature profiles

Stiffness in JET T e,i profiles

Stiffness in FTU EC heated L-mode T e profiles stiff in the region 0.2 <  < 0.6. n e ~10 20 & T e ~T i. All profiles show same in the ‘confinement’ region independently of where and how much power is injected.

"Stiff energy"- minimal model

W vs W ped of the Pedestal database

Regressing (OLS fitting) W, W ped and W core =W-W ped using the PSDBv3.2 assuming that W and W ped are function of the global variables: I, R, P, n, B, k, , m, f q = q 95 /q cyl no differences within error bars in the scaling of W and W core = W-W ped are found because of the simple relationtionship between the two figures. Thermal Conduction Model Empirical Scaling of W, W ped & W core

Stiffness does not mean unmodifiable T profiles an example from Asdex-Upgrade H-modes If ICH heating does not modify R/L T = A hence confinement time degradation (vs P) physics is located in the pedestal; ECH heating modifies R/L T =A and core confinement drops.

R/L w scaling - statistical approach with thermal conduction model on PDB

R/L w scaling with thermal conduction model on PDB data with no systematic error in W ped No Errore sistematico

Conclusions Statistical approach to core confinement is possible and needed but profile stiffness must be accounted for. An improved model for the "stiff energy" is possible but this requires a more complex DB. DB should contain ETG - ITG relevant plasma parameters such for instance Te,i at  ~0.5. Global confinement and local heat transport studies must be compared and common features understood to gain insight in prime principle physics.

Published results… Mathfit-Wpedcalcolato.m

Offset due to systematic errors in W ped ?

Energy Confinement time time evolution At t=3 s ECH on Energy confinement time drops from  0 =140 ms to  1 =103 ms Scaling of  not consistent with P -0.6 June 2007

W(t) modelling Hand fit Wmhd solving d/dt W= (P 0 +P 1 )-W/    t<3.045 s d/dt W= (P 0 +P 1 )-W/    t>3.045 s Quite fast switch of  45 ms after the ECH switch on (less than 20 ms). Threshold in T e /T i ? Rotation? Not enough time resolution.. June 2007

2.5 more MW of NBI added at t=5.5s in shot NBI heating induces confinement time degradation. No change in T e /T i Change in  less sharp. Scaling of  consistent with P June 2007

W/W ped Scaling should give critical gradient length of the core