Hermes: global plasma edge fluid turbulence simulations

The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the self-consistent evolution of plasma fluctuations, global profiles and flows, but the numerical tools capable of doing this in realistic (diverted) geometry are only now being developed. Here a 5-field reduced 2-fluid plasma model for the study of instabilities and turbulence in magnetised plasmas is presented, built on the BOUT++ framework. This cold ion model allows the evolution of global profiles, electric fields and flows on transport timescales, with flux-driven cross-field transport determined self-consistently by electromagnetic turbulence. Developments in the model formulation and numerical implementation are described, and simulations are performed in poloidally limited and diverted tokamak configurations.

[1]  N. Walkden,et al.  The effects of shape and amplitude on the velocity of scrape-off layer filaments , 2015, 1506.02814.

[2]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[3]  D. Reiser.  Revisited global drift fluid model for linear devices , 2012 .

[4]  P. B. Snyder,et al.  BOUT++: A framework for parallel plasma fluid simulations , 2008, Comput. Phys. Commun..

[5]  B. Scott.  The nonlinear drift wave instability and its role in tokamak edge turbulence , 2002 .

[6]  A. Hindmarsh,et al.  Application of parallel implicit methods to edge-plasma numerical simulations , 2002 .

[7]  I. Nedzelskiy,et al.  Improved confinement events triggered by emissive electrode biasing on the tokamak ISTTOK , 2004 .

[8]  Dimits.  Fluid simulations of tokamak turbulence in quasiballooning coordinates. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Fabio Riva,et al.  The GBS code for tokamak scrape-off layer simulations , 2016, J. Comput. Phys..

[10]  James Myra,et al.  Convective transport by intermittent blob-filaments: Comparison of theory and experiment , 2011 .

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

[12]  D. Ryutov,et al.  Two-dimensional electric fields and drifts near the magnetic separatrix in divertor tokamaks , 1999 .

[13]  Virginie Grandgirard,et al.  TOKAM-3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks , 2010, J. Comput. Phys..

[14]  Stephen C. Jardin,et al.  Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states , 2009, J. Comput. Phys..

[15]  G. Huysmans,et al.  MHD stability in X-point geometry: simulation of ELMs , 2007 .

[16]  Massimiliano Mattei,et al.  Advances in the physics basis for the European DEMO design , 2015 .

[17]  G. Corrigan,et al.  Modelling of SOL Flows and Target Asymmetries in JET Field Reversal Experiments with EDGE2D Code , 2000 .

[18]  Steven J. Plimpton,et al.  Nonlinear magnetohydrodynamics simulation using high-order finite elements , 2004 .

[19]  A. Mikhailovskii,et al.  Transport Equations of Plasma in a Curvilinear Magnetic Field , 1984 .

[20]  A. S. Kukushkin,et al.  Finalizing the ITER divertor design: The key role of SOLPS modeling , 2011 .

[21]  S. Voskoboynikov,et al.  Simulation of tokamak edge plasma including self-consistent electric fields , 2001 .

[22]  John M. Dawson,et al.  Geodesic Acoustic Waves in Hydromagnetic Systems , 1968 .

[23]  P. Snyder,et al.  Boundary Plasma Turbulence Simulations for Tokamaks , 2008 .

[24]  Bill Scott,et al.  Shifted metric procedure for flux tube treatments of toroidal geometry: Avoiding grid deformation , 2001 .

[25]  P. Diamond,et al.  Recent progress towards a physics-based understanding of the H-mode transition , 2016 .

[26]  B. Scott.  Three-Dimensional Computation of Drift Alfven Turbulence , 1997 .

[27]  L. C. Woods.  Physics of plasmas , 2003 .

[28]  Federico David Halpern,et al.  Boundary conditions for plasma fluid models at the magnetic presheath entrance , 2012 .

[29]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[30]  N. Hershkowitz,et al.  Models, assumptions, and experimental tests of flows near boundaries in magnetized plasmas , 2016 .

[31]  Deng Zhou.  Geodesic acoustic modes in tokamak plasmas with a radial equilibrium electric field , 2015 .

[32]  G. Dif-Pradalier,et al.  Magnetic geometry and particle source drive of supersonic divertor regimes , 2014 .

[33]  X. Garbet,et al.  Thermodynamical and microscopic properties of turbulent transport in the edge plasma , 2012 .

[34]  J. Angus,et al.  Modeling of large amplitude plasma blobs in three-dimensions , 2014 .

[35]  X. Xu,et al.  BOUT++: Recent and current developments , 2014, Journal of Plasma Physics.

[36]  P. Barabaschi,et al.  Fusion electricity: a roadmap to the realization of fusion energy , 2012 .

[37]  Volker Naulin,et al.  Turbulent transport and the plasma edge , 2007 .

[38]  A..  Fusion Engineering and Design A volumetric neutron source for fusion nuclear technology testing and development , 2004 .

[39]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[40]  P. Catto,et al.  Drift-ordered fluid equations for field-aligned modes in low-β collisional plasma with equilibrium pressure pedestals , 2003 .

[41]  Bruce D. Scott.  The character of transport caused by E×B drift turbulence , 2003 .

[42]  K. Bodi,et al.  Transition to supersonic flows in the edge plasma , 2011 .

[43]  Jayson Luc Peterson,et al.  Positivity Preservation and Advection Algorithms with Applications to Edge Plasma Turbulence , 2013, SIAM J. Sci. Comput..

[44]  Makoto Nakamura,et al.  Self-consistent treatment of the sheath boundary conditions by introducing anisotropic ion temperatures and virtual divertor model , 2016, J. Comput. Phys..

[45]  F. Wagner,et al.  A quarter-century of H-mode studies , 2007 .

[46]  Adil Hassam,et al.  Three‐dimensional fluid simulations of the nonlinear drift‐resistive ballooning modes in tokamak edge plasmas , 1993 .

[47]  M. Groth,et al.  Influence of the E  ×  B drift in high recycling divertors on target asymmetries , 2015 .

[48]  B. Braams,et al.  Plasma Edge Physics with B2‐Eirene , 2006 .

[49]  Bruce D. Scott,et al.  Free-energy conservation in local gyrofluid models , 2005 .

[50]  R. Merlino.  Understanding Langmuir probe current-voltage characteristics , 2007 .

[51]  D. Pfirsch,et al.  Collisional drift fluid equations and implications for drift waves , 1996 .

[52]  李幼升,et al.  Ph , 1989 .

[53]  K. Vafai,et al.  Numerical methods in heat transfer , 1986 .

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

[55]  W. D’haeseleer,et al.  Flux Coordinates and Magnetic Field Structure , 1991 .

[56]  Philippe Ghendrih,et al.  The Plasma Boundary of Magnetic Fusion Devices , 2001 .

[57]  R. Chodura,et al.  Plasma–wall transition in an oblique magnetic field , 1982 .

[58]  S. J. Wukitch,et al.  H-mode pedestal and threshold studies over an expanded operating space on Alcator C-Mod , 2006 .

[59]  J. Madsen,et al.  Verification of BOUT++ by the method of manufactured solutions , 2016, 1602.06747.

[60]  F. Parra,et al.  Electrostatic turbulence in tokamaks on transport time scales , 2008 .