Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics
type: Item
instance of: scholarly article
title: Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics
zbMATH Open document ID: 1167.35033
author: Anne Nouri
author: Philippe Ghendrih
author: Yanick Sarazin
author: Claudia Negulescu
published in: Kinetic and Related Models
publication date: 2009-03-04T00:00:00Z
review text: 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 interaction leads to non-linear constraints along the magnetic field. First, the authors present the physics and the equations governing the evolution of the electric potential of a turbulent plasma flow. They examine the specific conditions introduced by the contact to the wall material and their impact on the system of equations. The reduction of the 3D electrostatic potential equation to a 2D equation is analyzed as well as the linearization procedure that allows one to cast the problem in a variational framework. Further, the mathematical nonlinear evolution problem for the electric potential is summarized. The existence and uniqueness of the solution of the linearized problem is proven. Finally, the existence and uniqueness of the solution to the original nonlinear evolution equation is examined. The results are obtained under an appropriate smallness condition on the source term of the equation, as well as by requiring more regularity of the source term and the initial condition. The working model is two-dimensional in space and time evolving.
reviewed by: Claudia-Veronika Meister
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 76F25
Mathematics Subject Classification ID: 76F70
Mathematics Subject Classification ID: 76M30
Mathematics Subject Classification ID: 76X05
zbMATH DE Number: 5522919
zbMATH Keywords: plasma
zbMATH Keywords: controlled fusion
zbMATH Keywords: fluid model
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: existence of solution
zbMATH Keywords: uniqueness of solution
zbMATH Keywords: energy estimate
MaRDI profile type: Publication
full work available at URL: krm.2008.1.619
OpenAlex ID: W2031923663
DOI: 10.3934/KRM.2008.1.619
description: scientific article; zbMATH DE number 5522919