Abstract
Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated ECH experiments both in tokamaks and stellarators. This is most apparent for modulated experiments in the Large Helical Device (LHD) and in Wendelstein 7 advanced stellarator (W7-AS). In this paper we show that: (1) this power dependence can be reproduced by linear models and as such hysteresis (in flux) has no relationship to hysteresis as defined in the literature; (2) observations of ‘hysteresis’ (in flux) and a direct response to power can be perfectly reproduced by introducing an error in the estimated deposition profile as long as the errors redistribute the heat over a large radius; (3) non-local models depending directly on the heating power can also explain the experimentally observed Lissajous curves (hysteresis); (4) how non-locality and deposition errors can be recognized in experiments and how they affect estimates of transport coefficients; (5) from a linear perturbation transport experiment, it is not possible to discern deposition errors from non-local fast transport components (mathematically equivalent). However, when studied over different operating points non-linear-non-local transport models can be derived which should be distinguishable from errors in the deposition profile. To show all this, transport needs to be analyzed by separating the transport in a slow (diffusive) time-scale and a fast (heating/non-local) time-scale, which can only be done in the presence of perturbations.
Highlights
In this paper we show that: (1) this power dependence can be reproduced by linear models and as such hysteresis has no relationship to hysteresis as defined in the literature; (2) observations of ‘hysteresis’ and a direct response to power can be perfectly reproduced by introducing an error in the estimated deposition profile as long as the errors redistribute the heat over a large radius; (3) non-local models depending directly on the heating power can explain the experimentally observed Lissajous curves; (4) how non-locality and deposition errors can be recognized in experiments and how they affect estimates of transport coefficients; (5) from a linear perturbation transport experiment, it is not possible to discern deposition errors from non-local fast transport components
Experiments in 1988 at the tokamak de Fontenay-aux-Roses (TFR) performed by the FOM ECRH team showed that electron transport in fusion plasmas can have a fast response to applied heating power [1], which is much faster than the settling of the temperature profiles
From the literature we conclude that Te (ρ, t) andqe (ρ, t) can be considered as a linear response to a ECH perturbation P (ρ, t). This is a crucial step in the analysis as the transport phenomena that can reproduce the Lissajous curves must be reproducible by a linear model
Summary
Experiments in 1988 at the tokamak de Fontenay-aux-Roses (TFR) performed by the FOM ECRH team showed that electron transport in fusion plasmas can have a fast response to applied heating power [1], which is much faster than the settling of the temperature profiles. This important observation has been extensively studied and is known as ballistic transport [2]. Recent simulations suggests that it can be explained by local transport mechanisms [7] Based on these studies, the concept of hysteresis could be partially coupled to observations in tokamaks [5, 8]
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