Abstract
This article assesses current understanding of hysteresis in transport relations, and its impact on the field. The rapid changes of fluxes compared to slow changes of plasma parameters are overviewed for both core and edge plasmas. The modulation ECH experiment is explained, in which the heating power cycles on-and-off periodically, revealing hysteresis and fast changes in the gradient–flux relation. The key finding is that hystereses were observed simultaneously in both the the gradient–flux and gradient–fluctuation relations. Hysteresis with rapid timescale exists in the channels of energy, electron and impurity densities, and plausibly in momentum. Advanced methods of data analysis are explained. Transport hysteresis can be studied by observing the higher harmonics of temperature perturbation in heating modulation experiments. The hysteresis introduces the term , which depends on the harmonic number m in an algebraic manner (not exponential decay). Next, the causes of hysteresis and its fast timescale are discussed. The nonlocal-in-space coupling works here, but does not suffice. One mechanism for ‘the heating heats turbulence’ is that the external source S in phase space for heating has its fluctuation in turbulent plasma. This coupling can induce the direct input of heating power into fluctuations. The height of the jump in transport hysteresis is smaller for heavier hydrogen isotopes, and could be one of the origins of isotope effects on confinement. Finally, the impacts of transport hysteresis on the control system are assessed. Control systems must be designed so as to protect the system from sudden plasma loss.
Highlights
Introduction and background of the problemIn the history of the study of confinement in toroidal plasmas, the approach of analyzing the response to periodic modulation of heating power has been applied routinely
There have been many experimental reports that the gradient–flux relation has a hysteresis, and the heat flux may directly depend on the heating power
This view shows a contrast to the conventional ‘diffusive model’ of the transport, in which the heat flux is expressed in terms of the local plasma parameters and their gradients
Summary
In the history of the study of confinement in toroidal plasmas, the approach of analyzing the response to periodic modulation of heating power has been applied routinely (for a review see e.g. [1]). There have been many experimental reports (e.g. on W7-AS [3], on DIII-D [4]) that the gradient–flux relation has a hysteresis (depending on switching on/off of ECH heating), and the heat flux may directly depend on the heating power (figure 1 [4, 5]) This view shows a contrast to the conventional ‘diffusive model’ of the transport, in which the heat flux is expressed in terms of the local plasma parameters and their gradients. Transport hysteresis can explain the disparity of heat pulse between inward- and outward- propagations [9], which cannot be explained by a local diffusive model This hysteresis can have a profound impact on our evaluation of the dynamical response of burning plasmas. The understanding of these observations is necessary for the accurate prediction of burning plasma, and in designing the temporal control system to prevent dynamic changes of core plasma
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