Zero-dimensional model for the critical condition for the L–H transition in the flux–gradient relation

Abstract

In this paper, the physics of the L- to H-mode transition is discussed, focusing on the mechanism induced by the localized mean radial electric field. In addition to the neoclassical effect, an additional source of the electric field is introduced. The influence of turbulence-driven Reynolds stress is taken into account here. The case where the zonal flows are not excited is analysed. Even if the spontaneous zonal flows by turbulence cannot be excited, the bifurcation of the mean radial electric field can occur, if the electric field is strong enough eρpEr/Ti ∼ −1. Hard transition of the electric field takes place. The enhancement of electric field above this critical value can induce a bifurcation in the gradient–flux relation, i.e. the disappearance of the L-mode branch. The critical condition of the heat flux for the onset of transition is obtained.

On the Origin of Steep and Localized Radial Electric Field in the Transport Barrier at Plasma Edge

“…allows multiple solutions of E r , that appear as distinct states. For given flux, bifurcations are predicted to occur [37][38][39][40]. The other element is the toroidal effect on the dielectric constant.…”

On the spatial structure of solitary radial electric field at the plasma edge in toroidal confinement devices

“…The impacts of magnetic field ripples on the edge barrier in tokamaks have attracted attentions, particularly in conjunction with symmetry-breaking-magnetic perturbation for ELM control [47]. As has been [40,48], the influence of small ripples is complicated, and may introduce a new bifurcation in addition to the one, which is discussed in this article. The issue requires future intensive studies.…”

“…In addition, even in the process of L-H transition, the magnitude of solitary electric field was found to jump without substantial change of ion pressure gradient [11]. This jump was discussed based on the electric field bifurcation model [40]. The physics of electric field bifurcation has been studied in helical plasmas as well [41][42][43].…”

A structural bifurcation of transport in toroidal plasmas

“…The influence of the inhomogeneous radial electric field on the turbulence intensity then modifies the mean pressure gradient, so as to close the connection of nonlinear interactions. This system was studied in [18] in the limit of a point model, and a 1D structure is investigated here. The stationary state under a given heat flux (constant in space and time) is analysed.…”