December  2008, 1(4): 619-639. doi: 10.3934/krm.2008.1.619

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

1. 

CMI/LATP (UMR 6632), Université de Provence, 39, rue Joliot Curie, 13453 Marseille Cedex 13, France, France

2. 

CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France, France

Received  June 2008 Revised  September 2008 Published  October 2008

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.
Citation: Claudia Negulescu, Anne Nouri, Philippe Ghendrih, Yanick Sarazin. Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics. Kinetic and Related Models, 2008, 1 (4) : 619-639. doi: 10.3934/krm.2008.1.619
[1]

J. F. Padial. Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion. Conference Publications, 2011, 2011 (Special) : 1176-1185. doi: 10.3934/proc.2011.2011.1176

[2]

Yizhao Qin, Yuxia Guo, Peng-Fei Yao. Energy decay and global smooth solutions for a free boundary fluid-nonlinear elastic structure interface model with boundary dissipation. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1555-1593. doi: 10.3934/dcds.2020086

[3]

Jun Zhou. Global existence and energy decay estimate of solutions for a class of nonlinear higher-order wave equation with general nonlinear dissipation and source term. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1175-1185. doi: 10.3934/dcdss.2017064

[4]

Daniel Franco, Donal O'Regan. Existence of solutions to second order problems with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 273-280. doi: 10.3934/proc.2003.2003.273

[5]

Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control and Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018

[6]

Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2001-2029. doi: 10.3934/cpaa.2013.12.2001

[7]

Inger Daniels, Catherine Lebiedzik. Existence and uniqueness of a structural acoustic model involving a nonlinear shell. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 243-252. doi: 10.3934/dcdss.2008.1.243

[8]

Ariane Piovezan Entringer, José Luiz Boldrini. A phase field $\alpha$-Navier-Stokes vesicle-fluid interaction model: Existence and uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 397-422. doi: 10.3934/dcdsb.2015.20.397

[9]

Tan H. Cao, Boris S. Mordukhovich. Optimality conditions for a controlled sweeping process with applications to the crowd motion model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 267-306. doi: 10.3934/dcdsb.2017014

[10]

Mohan Mallick, Sarath Sasi, R. Shivaji, S. Sundar. Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2022, 21 (2) : 705-726. doi: 10.3934/cpaa.2021195

[11]

Rachel Clipp, Brooke Steele. An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 61-74. doi: 10.3934/mbe.2012.9.61

[12]

Nguyen Thanh Long, Hoang Hai Ha, Le Thi Phuong Ngoc, Nguyen Anh Triet. Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (1) : 455-492. doi: 10.3934/cpaa.2020023

[13]

Marco Di Francesco, Alexander Lorz, Peter A. Markowich. Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1437-1453. doi: 10.3934/dcds.2010.28.1437

[14]

Daoyi Xu, Weisong Zhou. Existence-uniqueness and exponential estimate of pathwise solutions of retarded stochastic evolution systems with time smooth diffusion coefficients. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2161-2180. doi: 10.3934/dcds.2017093

[15]

Tong Yang, Fahuai Yi. Global existence and uniqueness for a hyperbolic system with free boundary. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 763-780. doi: 10.3934/dcds.2001.7.763

[16]

Trad Alotaibi, D. D. Hai, R. Shivaji. Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4655-4666. doi: 10.3934/cpaa.2020131

[17]

Luigi C. Berselli. An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case.. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 199-219. doi: 10.3934/dcdss.2010.3.199

[18]

Hideo Takaoka. Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6351-6378. doi: 10.3934/dcds.2020283

[19]

Dominique Blanchard, Nicolas Bruyère, Olivier Guibé. Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2213-2227. doi: 10.3934/cpaa.2013.12.2213

[20]

L.R. Ritter, Akif Ibragimov, Jay R. Walton, Catherine J. McNeal. Stability analysis using an energy estimate approach of a reaction-diffusion model of atherogenesis. Conference Publications, 2009, 2009 (Special) : 630-639. doi: 10.3934/proc.2009.2009.630

2020 Impact Factor: 1.432

Metrics

  • PDF downloads (55)
  • HTML views (0)
  • Cited by (4)

[Back to Top]