Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics

,Claudia Negulescu,Anne Nouri,Yanick Sarazin,,Cea, Irfm, F-13108 Saint-Paul-Lez-Durance ,Philippe Ghendrih

doi:10.3934/krm.2008.1.619

Abstract

The electric potential plays a key role in the confinement properties of tokamak plasmas, with the subsequent impact on the performances of fusion reactors. Understanding its structure in the peripheral plasma -- interacting with solid materials -- is of crucial importance, since it governs the boundary conditions for the burning core plasma. This paper aims at highlighting the dedicated impact of the plasma-wall boundary layer on this peripheral region. Especially, the physics of plasma-wall interactions leads to non-linear constraints along the magnetic field. In this framework, the existence and uniqueness of the electric potential profile are mathematically investigated. The working model is two-dimensional in space and time evolving.

Highlights

The growing need for new sources of energy is one of the drives of the ITER project [13]
In particular the peripheral plasma is widely studied, due to its crucial role to control the interaction of the plasma with the surrounding wall material, and to define the boundary conditions of the core plasma
Since the large scale radial structure of the electric potential leads to the large scale poloidal flows associated to the electric drift effects, we focus on the analysis of the mean potential depending only on the radial direction and the parallel one, which introduces nonlinear boundary conditions

Summary

Introduction

The growing need for new sources of energy is one of the drives of the ITER project [13]. The present paper is dedicated to the mathematical analysis of the slowly varying electric potential that leads to poloidal flows in the edge plasma. These radially sheared flows play an essential role in the saturation of turbulence [16]. They are suspected to the essential ingredient in the triggering of the so-called H-mode, where the plasma spontaneously develops an edge transport barrier characterised by reduced turbulence and associated transport [4] These poloidal flows are basically driven by equilibrium constraints, including boundary conditions in the SOL, and by the turbulence itself via non linear interactions [5].

Generation of the fluctuating electric field

The mathematical problem

Existence and uniqueness of the linear problem

Existence and uniqueness of the nonlinear problem

Findings

Conclusion