Simulation of internal transport barriers by means of the canonical profile transport model
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Simulation of Internal Transport Barriers by Means of the Canonical Profile Transport Model Yu. N. Dnestrovskij*, S. V. Cherkasov*, A. Yu. Dnestrovskij*, S. E. Lysenko*, and M. J. Walsh** *Nuclear Fusion Institute, Russian Research Centre Kurchatov Institute, Moscow, 123182 Russia **EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK Received March 11, 2005
Abstract—Models with critical gradients are widely used to describe energy balance in L-mode discharges. The so-called first critical gradient can be found from the canonical temperature profile. Here, it is suggested that discharge regimes with transport barriers can be described based on the idea of the second critical gradient. If, in a certain plasma region, the pressure gradient exceeds the second critical gradient, then the plasma bifurcates into a new state and a transport barrier forms in this region. This idea was implemented in a modified canonical profile transport model that makes it possible to describe the energy and particle balance in tokamak plasmas with arbitrary cross sections and aspect ratios. The magnitude of the second critical gradient was chosen by comparing the results calculated for several tokamak discharges with the experimental data. It is found that the second critical gradient is related to the magnetic shear s. The criterion of the transport barrier formation has the form (a2/r)d/dr ln(p/pc) > z0(r), where r is the radial coordinate, a is the plasma minor radius, p is the plasma pressure, pc is the canonical pressure profile, and the dimensionless function z0(r) = C0 + C1s (with C0i ~ 1, C0e ~ 3, and C1i, e ~ 2) describes the difference between the first and second critical gradients. Simulations show that this criterion is close to that obtained experimentally in JET. The model constructed here is used to simulate internal transport barriers in the JET, TFTR, DIII-D, and MAST tokamaks. The possible dependence of the second critical gradient on the plasma parameters is discussed. PACS numbers: 52.55.Fa DOI: 10.1134/S1063780X06010016
1. INTRODUCTION
aspect ratios. The model includes a set of equations for the electron and ion temperatures, Te and Ti; the plasma density n; and the potential of the poloidal magnetic field, ψ. The plasma equilibrium and the radial coordinate ρ are determined from the solution to the Grad– Shafranov equation. The first critical gradient is described by means of the theory of canonical profiles. The canonical profile of the function µ = 1/q (hereafter, denoted by µc) can be found from the solution to the Euler equation for the plasma free energy functional [1],
The energy balance in L-mode tokamak discharges is often described by models with critical gradients. The so-called first critical gradients can be determined from the theory of canonical profiles [1]. When the temperature and density gradients are steeper than the first critical gradients, transport in plasmas is greatly enhanced because of the excitation of drift modes and because of an increase in the
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