Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes

Abstract

A model based on magnetohydrodynamic (MHD) stability of the tokamak plasma edge region is presented, which describes characteristics of edge localized modes (ELMs) and the pedestal. The model emphasizes the dual role played by large bootstrap currents driven by the sharp pressure gradients in the pedestal region. Pedestal currents reduce the edge magnetic shear, stabilizing high toroidal mode number (n) ballooning modes, while at the same time providing drive for intermediate to low n peeling modes. The result is that coupled peeling–ballooning modes at intermediate n (3<n<20) are often the limiting instability which constrains the pedestal and triggers ELMs. These modes are characterized in shaped tokamak equilibria using an efficient new numerical code, and simplified models are developed for pedestal limits and the ELM cycle. Results are compared to several experiments, and nonideal MHD effects are briefly discussed.

Two-dimensional imaging of edge-localized modes in KSTAR plasmas unperturbed and perturbed by n=1 external magnetic fields

“…Even with the conservative values n e & 1 Â 10 19 m À3 and T e & 0:5 keV for the pedestal top, the estimated optical depth is s > 1 at the left side of the filamentary region, i.e., the pedestal top region because the ELMs are generally believed to develop at the steepest pressure gradient. 2,4 Combined with the observed coherent rotation of the entire filaments in the poloidal direction, this supports the validity of the ECE local measurement for all filament regions. On the other hand, the fluctuation dT rad =hT rad i will contain the finite density effect in the case of marginal optical depth, 12,13 i.e.,dT rad =hT rad i ¼ ð1 þ A 2 ÞdT e =hT e i þ A 2 dn e =hn e i, where A 2 ¼ ð1 À rÞse Às =ð1 À e Às Þð1 À re Às Þ and r is the wall reflection coefficient.…”

“…The initial growth of the multiple ELM filaments is exponential in time and strongly localized in the edge region, which is in qualitative agreement with the linear peeling-ballooning model. 2 The saturated state is meta-stable but eventually transforms into the final crash phase through a short transient phase. The large ELM crash event is a series of filament bursts, which are inherently 3D and nonaxisymmetric events localized both poloidally and toroidally.…”

Transition to ELM-free improved H-mode by lithium deposition on NSTX graphite divertor surfaces

“…Numerical simulations have identified peeling and/or ballooning modes as candidate instabilities generating filamentary structures that burst outward across flux surfaces during periodic non-linear growth phases [2,3]. Because ELMs carry a substantial transient heat and particle load into the scrape-off layer (SOL), they will present serious power-handling problems to future fusion devices.…”

Bootstrap current for the edge pedestal plasma in a diverted tokamak geometry

“…[1][2][3][4][5][6] Existing studies of the bootstrap current and the construction of analytic formulas being used in the equilibrium and stability analyses have been mainly focused on the core plasma. [7][8][9][10] Recently, the importance of the bootstrap current has been re-emphasized through its critical role played in the stability, equilibrium, and turbulence studies of the steep gradient edge pedestal 13,14 in H-mode (high confinement mode) operation. A steep pressure gradient in the edge pedestal yields a large localized bootstrap current.…”