The problem of the propagation of a harmonic temperature perturbation in a plasma with both diffusive and nondiffusive energy transport is addressed. The energy flux is modeled by two (radially varying) effective coefficients for the diffusive and nondiffusive transport, and the effects of perturbed energy sinks and of cylindrical geometry are taken into account. A simple, local relationship is found between the two transport coefficients and the gradients of the phase and amplitude of the temperature perturbation. This relationship can be used for the interpretation of heating modulation experiments, provided data at different modulation frequencies are available. Since a harmonic density perturbation in a plasma follows a similar linearized transport equation, a similar model can be applied also to density modulation experiments.

The electron heat transport is investigated in ASDEX Upgrade using electron cyclotron heating (ECH) combining steady-state and power modulation schemes. Experiments in which the electron heat flux has been varied in the confinement region while the edge was kept constant were performed. They demonstrate that ∇ Te and ∇ Te/Te can be varied by a factor of 3 and 2, respectively. They allow a detailed determination of the transport characteristics by comparing steady-state and modulation data with modelling. The analyses clearly show the existence of a threshold (∇ Te/Te)crit above which transport increases. Both steady-state and modulation experiments agree with such a transport model. The experiments have been carried out at low density in the L-mode to ensure low electron–ion coupling and good conditions for studying electron heat transport. The experiments were carried out at two different values of plasma current and show that transport increases at low current, as well-known from global scaling laws for confinement time. In the pure off-axis cases the region inside the ECH deposition is just at the (∇ Te/Te)crit threshold, which allows it to be measured directly from the profile of ∇ Te/Te deduced from the experimental Te profile. Using this technique, it appears that the turbulence threshold agrees with that expected from the trapped electron mode driven turbulence. It has the correct absolute value and seems to have the correct radial dependence that is determined by the trapped electron fraction and by the density gradient. It almost does not vary with other plasma parameters. In contrast, the threshold calculated for electron temperature gradient modes is higher than the experimental values of ∇ Te/Te and this turbulence is therefore not expected to be excited under these experimental conditions.

Experiments on electron heat transport were performed in the tokamak ASDEX Upgrade, mainly in ohmically heated plasmas, applying either edge cooling by impurity injection or edge heat pulses with ECH. Repetitive pulses within one plasma discharge were made allowing Fourier transformation of the temperature perturbation. This yields a good signal to noise ratio up to high harmonics and allows a detailed investigation of the pulse propagation. For densities lower than 1:8 10 19 m ,3 , an increase of the central electron temperature was found as the response to the edge cooling via impurity injection similar to observations made in other tokamaks. The inversion does not appear instantaneously, but with a time delay roughly compatible with diffusion. Modeling of the propagation of the cold pulses in the framework of the IFS-PPPL model yields qualitative agreement. However the predicted increase of the ion temperature is not observed experimentally on the fast time scale. The response to ECH heat pulses is not perfectly symmetrical to cold pulse experiments, but the similarities suggest a common underlying physical mechanism. No inversion of the heat pulse is found, instead the initial pulse from the edge is associated with a second, much slower heat pulse in the centre which is similar (and not symmetrical) to that of the cold pulses. It is found that the central increase is related to the arrival of the pulse close to the inversion radius and not to the initial pulse.

Experiments with strong localized electron cyclotron heating (ECH) in the RTP tokamak show that electron heat transport is governed by alternating layers of good and bad thermal conduction. For central deposition hot T e filaments are observed inside the q = 1 radius. Moving the ECH resonance from the centre to the edge of the plasma results in discrete steps of the central electron temperature. The transitions occur when the minimum q value crosses q = 1, 2, 5/2 or 3, and correspond to the loss of a transport barrier situated close to the rational q value. Close to the transitions a new type of sawtooth activity is observed, characterized by the formation of sharp off-axis maxima on the T e profile, which collapse abruptly. The formation of the off-axis maxima is attributed to heat deposition precisely 'on top of' a transport barrier.

Perturbative and steady-state heat transport of FTU tokamak in current ramp-up discharges are investigated by means of modulated electron cyclotron heating (MECH). Perturbative and steady-state transport experiments are coherent with an electron heat transport which switches from low to high values when electron temperature gradient length reaches a threshold value 1/L T c . The threshold value 1/L T c is shown to be proportional to the ratio s/q.The experimental findings are compared to predictions of an empirical model based on the assumption of a threshold gradient length, L T c (1/L T = |∇T e /T e |), in the electron temperature T e below which electron thermal diffusivity, χ e , switches from low to high values. Plasma responses to steady state and MECH are modelled assuming the electron diffusivity as χ PB = χ 0 + αT