Energy transport and electron temperature profile stiffness with localized ECRH
Off-axis ECRH clearly reveals electron temperature profile stiffness in FTU, particularly when absorption is located in the confinement region, i.e. outside sawteeth inversion radius (r/a > 0.2), but inside the radiation dominated periphery (r/a< 0.6). The typical marker of electron temperature profile stiffness, observed in all similar experiments on ASDEX-UG, D III-D, Tore Supra, TCV, is a step in the radial dependence of the electron thermal diffusivity. The step is usually positioned at the ECW absorption radius, particularly when the ECRH power density is much in excess than the ohmic input. The step amplitude is just enough to keep the temperature profile smooth, which shows a gradient length LT=-T/dT/dr almost unchanged from ohmic to ECRH, independently on ECRH intensity and localization.
Modulated ECH (MECH) has been applied to study electron temperature profile stiffness in FTU plasmas during current ramp-up. MECH experiments at current flat-top on ASDEX-UG have shown that the heat wave propagates much faster outwards than inwards, confirming the step-wise behaviour of thermal diffusivity at the EC absorption radius. The experiments during current ramp-up were performed on FTU by using ECRH at a power level much lower than ohmic heating, in order to limit as much as possible the impact of ECRH on profile shapes. In addition, target plasmas with very different shapes were obtained with the control of the breakdown and density build-up phases. Fig.1 shows two typical targets, one with peaked temperature (and current density) profiles, the other one with flat-hollow profiles, characterized by a typical Double Tearing Modes occurrences. Heat wave propagation is very sensitive, much more than power balance analysis, to discontinuities in thermal conductivity. In addition, by looking at the amplitude and phase radial distribution of electron temperature oscillations it can be excluded that the apparent drop in diffusivity is due mostly to a heat pinch.
Fig.1 Evolution in time of the electron
temperature on axis and at the deposition radius (up), and of the temperature
profile (bottom) for two discharges characterized by very different profile
shapes. The heat wave is launched at the EC wave absorption radius, which
is well inside the flat region in one case (shot #20144), and in the steep
region in the other one (shot #20146).
The experiments have shown that in these conditions
the low-high diffusivity transition layer is not strictly positioned at the
absorption radius, and that it depends to some extent on the profile shape.
For a given position of the absorption layer (r/a¼0.25), in case of peaked
discharges the narrow EC deposition occurs mostly in the high diffusivity
region, while for flat-hollow discharges it is located well inside the low
diffusivity, central volume. The step in diffusivity appears therefore to
be dependent on the gradient profile shape, consistently with the assumption
that the maximum temperature gradient length is limited below a critical value.
The critical gradient length model gives in fact a good description of most experimental findings on profile stiffness in steady-state. The results of MECH experiments on current ramp-up can be consistently included within this frame, as shown in Fig.2. First, the plasma column appears divided in two regions with different confinement properties. Second, the radial position of the step in both transient and steady state electron thermal diffusivity almost coincide. Third, the low-high diffusivity transition layer is located where the effective gradient length, decreasing with increasing radius, stabilizes around a critical value.
Fig.2 The figure summarizes the key elements showing consistency between critical gradient modelling and experimental data. The effective gradient length (open dots) saturates (at ¼10) as a critical value derived from ETG turbulence (x) is overcome (at r=5÷7 cm). Both steady-state and transient thermal diffusivity switch from low to high values at almost the same radial position.
All these features can be interpreted assuming
that electron thermal transport is enhanced into the plasma where 1/LT
exceeds a critical value 1/LT,c, this last depending
on local plasma parameters.
Assuming as the critical gradient length LT,c the value of the actual LT at the transition layer, data from different discharges can be correlated to the corresponding local magnetic shear, as also observed on Tore Supra. FTU data shows a dependence of LT,c on the s/q parameter very similar to Tore Supra results, in spite of the different electron heating method (ECRH for FTU, Fast Wave in the ion cyclotron frequency range for T.S.). This dependence is consistent with theoretical predictions based on Electron Temperature Gradient turbulence.
Considering that ECRH is an extremely well suited tool for experimental studies on energy confinement, strong experimental effort is continuing on FTU on this issue of electron temperature profile resiliency.