Edge localized mode activity as a limit cycle in tokamak plasmas

Abstract

A model of edge localized modes in tokamak plasmas is presented. A limit-cycle solution is found in the transport equation (time-dependent Ginzburg-Landau type), which has a hysteresis curve for the gradient versus the flux. A periodic oscillation of the particle outflux and an L-H intermediate state are predicted near the L~H transition boundary. A mesophase in spatial structure appears near the edge. PACS numbers: 52.25.Fi, 52.35.Kt Edge localized modes (ELMs) are a regularly observed phenomenon characterized by the sudden drop of the edge density or temperature with a burst of particles or heat during the H phase in tokamak plasmas [ll. When the density or temperature near the plasma edge exceeds a certain threshold value, an £-to //-mode transition takes place [21. The ELMs usually follow the L-to-// transition and show a variety in the magnitude and frequency of the bursts and appear in some restricted parameter space of the H phase [1,3-8]. Their experimental characterization has recently begun [3,5]. The H mode with small and frequent ELMs is a candidate for standard operation in experimental tokamak reactors. Research to obtain the ELM y-H mode by an external control (e.g., ELM in the JFT-2M tokamak [7]) is an urgent task. This type of ELM, which we analyze here, has the characteristics that the period and the duration of the burst have similar values, as is shown in Fig. 1, and that it appears near the L-H transition boundary [7]. There are other ELMs (called "giant ELMs") which are associated with large-amplitude bursts, and appear at some critical pressure near the edge [1,3-8]. Key physical mechanisms for discriminating the various ELMs are not yet known. To explain the ELMs a comparison with critical-/? analysis due to the MHD ballooning mode [3,5] has been applied. The analyses have shown that some ELMs (particularly the small and frequent ones) can occur far below the critical pressure gradient. Resistive MHD analysis[3] of a surface peeling mode may explain some ELMs; however, the assumed current-pressure profiles are not yet experimentally identified. There remains a question for MHD models, since some ELM activities are insensitive to the q value. Namely, the observed soft-x-ray emission profiles of ELMs do not shift when the surface q value is varied from 2.4 to 5.6 [2]. Therefore ELMs are not considered to be located at a certain rational surface. The period and duration of small and frequent ELMs are left unsolved in the MHD analysis.A model of ELMs as a cyclic oscillation between L and H phases due to impurity accumulation has been proposed [9]. Up to now, however, the impurity accumulation has been considered to be an associated phenomenon [3,10].In this paper we propose a more complete model of small and frequent ELMs, shown in Fig. 1. The L-H transition has been observed to yield a hysteresis curve for the thermodynamic forces (e.g., the density/temperature gradients) versus the associated flows [2,3]. Previous theories [11,12] have predicted a sudden change in loss flux through the radia...

Axisymmetric oscillations at L–H transitions in JET: M-mode

“…Similar phenomena have been reported and discussed at JET and elsewhere [2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], usually concentrating on electrostatic fluctuation measurements in similar frequency ranges. This is a rapidly advancing field, references [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] may not include all the latest or relevant results, but are representative.…”

“…This is a rapidly advancing field, references [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] may not include all the latest or relevant results, but are representative. Reference [20] presents a good global view of previous studies.…”

Bifurcation theory of a one-dimensional transport model for the L-H transition

“…To model the evolution of the transport self-consistently it is necessary to include the evolution of the radial electric field explicitly 7,8,28 e…”

“…This growth of a larger transport barrier may be a natural description of the occurrence of a very-high-confinement mode (VH-mode) as observed in DIII-D 17 and JET, 18 and it could occur naturally in some reaction diffusion systems with a certain general structure, the so-called S-curve models. 7,13,19 This paper is organised as follows. First of all, the 1-dimensional L-H transition model is described in Sec.…”

Bifurcation theory for the L-H transition in magnetically confined fusion plasmas

“…4. To describe the dynamics during possible transitions of the transport, the evolution of the radial electric field 8,15,16 must be taken into account, via Ampères law which balances temporal changes of the radial electric field with the radial currents,…”