On the Study of Higher Harmonics of Heat Pulse Propagation in the Modulated-Heating Experiments

The dynamical response of temperature perturbation in the heat pulse propagation experiment is investigated, where the heating power is modulated with the waveform of a periodic step function. The higher harmonics (in the temporal Fourier components) in the heat pulse is studied, taking into account a sudden jump in the gradient-flux relation that has been shown experimentally [S. Inagaki et al., Nucl. Fusion 53, 113006 (2013)]. The higher harmonics in the transport domain (where heating power is absent) are composed of two elements. One is the diffusive contribution, and the other is the component, which is induced by the jump in the hysteresis of gradient-flux relation. While the amplitude of the former shows an exponential decay with respect to the increment of the harmonic number m (for m-th harmonics), the latter has the much weaker decay (algebraic dependence) on m. The radial wavenumber of heat-pulse propagation becomes smaller as m increases, if the jump in the hysteresis exists. The higher harmonics, which are driven by the nonlinearity in the gradient-flux relation, are also discussed. The model in the framework of diffusive picture (with nonlinearity in the transport coefficient) does not explain experimental observations on the radial profile of perturbation.