Ideal magnetohydrodynamic constraints on the pedestal temperature in tokamaks

Abstract

The ideal magnetohydrodynamic (MHD) stability limits for the edge transport barrier (ETB) region in tokamaks are explored, concentrating in particular on the intermediate to high toroidal mode number, n, modes. These calculations take full account of the effect of the edge bootstrap current on the stability of both ballooning and peeling modes. Because the current plays an important role in MHD stability, the temperature and density independently influence stability and, in particular, the pressure gradient that the ETB can support. The stability calculations therefore provide limits to the achievable temperature pedestal associated with the transport barrier which are not simply pressure pedestal limits, as is often assumed. One important result is that increasing triangularity is predicted to be beneficial in providing access to a higher temperature pedestal at fixed pedestal width, at least up to triangularity ∼0.5. Another significant result is that the finite n corrections, which are stabilizing for ballooning modes, are important for narrow pedestal widths and permit significantly higher temperature pedestals than one would obtain using the leading order (n = ∞) ballooning theory. Specific calculations for equilibria characteristic of ITER and FIRE suggest that temperature pedestals in the region of a few kiloelectronvolts should be achievable, but the precise value depends on the pedestal width, a prediction for which is beyond the scope of this paper.

Edge-localized mode avoidance and pedestal structure in I-mode plasmas

“…I-mode pressure pedestals are observed at a weaker peak pressure gradient than that found in ELMy H-modes, and scale more weakly than the ∇p ∼ I 2 p trend expected from ballooning stability; similarly, the pedestals are not constrained on the β p -limited line exhibited by ELMy H-modes. Numerical modeling of peeling-ballooning MHD stability using the ELITE code [30,47] indicates that I-mode pedestals are far from the computed stability boundary, consistent with the observed lack of large ELMs. However, small, intermittent ELM events have been observed under certain conditions in I-mode.…”

“…ELM triggering in H-mode has been identified with the interaction between pressure-driven ballooning and current-driven kink/peeling MHD instabilities in the pedestal [29][30][31]. Detailed numerical studies of the MHD instabilities associated with ELM drive are accomplished through the ELITE code [30,47]. This method is also used for the MHD stability component of the predictive EPED model [26][27][28].…”

Ion energies and currents of type I and mitigated ELMs in the ASDEX Upgrade far scrape-off layer

“…These measurements agree that each ELM consists of a number of field aligned filaments, expelled at different toroidal locations on the plasma low field side into the scrape-off layer (SOL). Qualitatively similar ELM features have been reproduced by non-linear MHD simulations [15][16][17]. As they propagate across the SOL, propelled by electrostatic interchange motions [18], some filaments break into smaller fragments before hitting the first wall as observed in [5].…”

Predictive modeling of pedestal structure in KSTAR using EPED model

“…We utilize the HELENA code to construct these equilibria. Typically, the plasma density or temperature profile which includes the steep pedestal profile information is generated by using the following analytical formula: 17 f ðwÞ ¼ f sep þ a f 0 ftanh½2ð1 À w mid Þ=D Àtanh½2ðw À w mid Þ=Dg þa f 1 Hð1 À w=w mid Þ½1 À ðw=w mid Þ a f 1 a f 2 ;…”