Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modeling

Abstract The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region – the part of the plasma interacting with the wall of the device – is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral plasma region. In particular, we are interested in introducing an efficient Asymptotic-Preserving (AP) numerical scheme capable to cope with the strong anisotropy of the problem as well as the non-linear boundary conditions, and this with acceptable computational costs. This work constitutes the numerical follow-up of the more mathematical paper by C. Negulescu, A. Nouri, Ph. Ghendrih, Y. Sarazin, Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics.

[1]  Fabrice Deluzet,et al.  Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations , 2010, 1008.3405.

[2]  Claudia Negulescu.  Asymptotic-preserving schemes. Modeling, simulation and mathematical analysis of magnetically confined plasmas , 2013 .

[3]  Claudia Negulescu,et al.  Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics , 2008 .

[4]  P. Stangeby.  The Plasma Boundary of Magnetic Fusion Devices , 2000 .

[5]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[6]  A. Stegmeir.  GRILLIX: A 3D turbulence code for magnetic fusion devices based on a field line map , 2015 .

[7]  G. Fishpool,et al.  Characterization of 3D filament dynamics in a MAST SOL flux tube geometry , 2013, 1307.5234.

[8]  Shi Jin,et al.  A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources , 2009, J. Comput. Phys..

[9]  Luc Mieussens,et al.  A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit , 2008, SIAM J. Sci. Comput..

[10]  P. Degond.  Asymptotic-Preserving Schemes for Fluid Models of Plasmas , 2011, 1104.1869.

[11]  Fabrice Deluzet,et al.  An Asymptotic Preserving Scheme for Strongly Anisotropic Elliptic Problems , 2009, Multiscale Model. Simul..

[12]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[13]  N. Crouseilles,et al.  An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits. , 2011 .

[14]  N. Fedorczak,et al.  Multi-scale self-organisation of edge plasma turbulent transport in 3D global simulations , 2015 .

[15]  Claudia Negulescu,et al.  Highly anisotropic temperature balance equation and its asymptotic-preserving resolution , 2012, 1203.6739.

[16]  Guido Ciraolo,et al.  The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries , 2016, J. Comput. Phys..

[17]  MAGNETICALLY CONFINED PLASMAS,et al.  Asymptotic-Preserving Schemes , 2010 .

[18]  Shi Jin,et al.  Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations , 1999, SIAM J. Sci. Comput..

[19]  Claudia Negulescu,et al.  Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time , 2014 .

[20]  Federico David Halpern,et al.  Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation , 2012 .

[21]  Shi Jin.  ASYMPTOTIC PRESERVING (AP) SCHEMES FOR MULTISCALE KINETIC AND HYPERBOLIC EQUATIONS: A REVIEW , 2010 .

[22]  Claudia Negulescu,et al.  An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro-Macro decomposition , 2011, J. Comput. Phys..

[23]  J. Demmel,et al.  Solving Sparse Linear Systems with Sparse Backward Error , 2015 .

[24]  S. I. Braginskii.  Transport Processes in a Plasma , 1965 .

[25]  Claudia Negulescu,et al.  Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations , 2012, J. Comput. Phys..

[26]  李幼升,et al.  Ph , 1989 .