Predictive modelling of ELMy H-modes with a new theory-motivated model for ELMs

Abstract

A new model for the type I ELMy H-mode based on linear ballooning stability theory is presented. The model can be written as a linear differential equation for the amplitude of an unstable ballooning mode and is coupled to a system of transport equations. The differential equation for the ballooning mode amplitude has two terms-one representing the growth rate of the perturbation and one controlling the decay rate of the mode and driving the mode amplitude towards the level of background fluctuations. A critical pressure gradient limit is used to control whether the growth rate differs from zero. When coupled to a JETTO transport simulation, the model qualitatively reproduces the experimental dynamics of a type I ELMy H-mode, including an edge localized mode (ELM) frequency that increases with the external heating power. This paper also discusses why the linear ballooning model, in the first place, produces discrete oscillations when coupled to a transport simulation rather than a stationary state with a slightly enhanced ballooning mode amplitude.

Integrated pedestal and core modeling of Joint European Torus (JET) triangularity scan discharges

“…1-3,5,8 -16 Evidence of access to second stability in high triangularity discharges has been observed in a number of tokamaks, for example, DIII-D, 1,2,11 Joint European Torus ͑JET͒, 8 Japan Tokamak-60U ͑JT-60U͒ 3,11, 16 and Alcator C-Mod. 5 The objective of this paper is to carry out predictive modeling of discharges with different values of triangularity and to examine if the models used for the core and pedestal region are consistent with the pedestal pressure gradient being limited to the first stability region for plasmas with low triangularity or gaining access to second stability for the plasmas with high triangularity.…”

Integrated ELM Modelling

“…Inspired by the model above, and starting from Eq. (3), a model describing the limit cycle behaviour of an unstable ballooning mode was derived and subsequently used in simulations with the (standard) JETTO transport code [38,39]. Later, the approach was extended to peeling modes.…”

Role ofE ×B Shear Flow in Transport Barrier Oscillations

“…Indeed, if the coupling term with the shear flow is replaced by a shift of the instability threshold, no relaxations oscillations are observed except if the instability term is further modified (e.g. by a Heavyside function [7]). …”

“…A relaxation is characterized by an increase of turbulent transport through the barrier and a decrease of the pressure inside the barrier. Currently, transport barrier relaxations are modelled by phenomenologically constructed dynamical equations for the amplitudes of relevant modes ([4] - [7]). …”