Nonlinear Dynamics in the Tokamak Edge

Abstract

The nonlinear character of the tokamak edge results from a unique combination of parameters, leading to a wide dynamical range for most processes. The energetically consistent gyrokinetic equilibrium is emphasised. Edge turbulence computed gyrokinetically exhibits energetic contact to mesoscale MHD and does not follow linear scaling. Gyrofluid studies show self consistent profiles, currents and flows which are kicked out of equilibrium to varying degree. L-mode turbulence and ELM crash phenomenology are both examples of energetic contact between turbulence and MHD, with opposite causality. The overall equilibrium is a statistical saturation rather than a state to which the plasma dissipatively converges. Basic situation of the tokamak edgeThe physical situation of the tokamak edge is defined by its parameters. These have several specific relationships that may eventually explain why such processes as the L-to-H transition [1][2][3] are unique to the edge while many current scenarios to explain them do not have edge-specific character. Nonlinearity is the central theme of any physical process in the edge of a confined plasma, resulting from the combination of low to moderate temperatures and steep gradients. One usually thinks of turbulence in this context, but another process also involves nonlinearity in a major way: the establishment through damped oscillations and flow relaxation of an axisymmetric quasisteady state which then evolves on a slow timescale given by transport. The approach to equilibrium rather than the time-independent balances by themselves is relevant because turbulence in the edge leads to a statistical balance rather than a converged equilibrium. Disparity in time constants becomes relevant and the strictness of the equilibrium balances varies accordingly. Nonlinear time dependent computation is the only way to approach this situation theoretically. The establishment of strict consistency in the model equations becomes a necessary prerequisite. Ultimately, approximation in a model is allowed but lack of consistency will lead to numerical difficulties, or worse, a result which may be explainable but is not the real one. The emphasis in this paper will be on nonlinear gyrokinetics and the kinetic equilibrium because that is newer. Some results on nonlinear consequence in delta-f gyrokinetic edge turbulence computations are given, and finally the character of the edge as found in nonlinear gyrofluid computations is summarised. These findings are relevant because their character should be directly addressed by attempts by global nonlinear gyrokinetic modelling to simulate nonlinear dynamics in the edge of confined plasmas. Parameter SituationThe tokamak edge is characterised by steep gradients in the radial profile at least one of the main state variables (density, electron and ion temperature). This much is well known. However there is a consequence for the parameter situation which is less appreciated. One often thinks in terms of lowest quantities and corrections which are small according to...

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