An iterative algorithm of coupling the Kinetic Code for Plasma Periphery (KIPP) with SOLPS

Abstract Power exhaust is one of the critical issues for future fusion devices, e.g. ITER. The calculation of power deposition is critical for the divertor design. SOLPS is the main tool for predictions of the Scrape-off Layer (SOL) and divertor conditions in the future fusion device ITER, where parallel kinetic effects in the SOL will play an important role. SOLPS uses a collisional fluid model which does not take kinetic effects into account. The present work has enabled SOLPS in its 1D version to incorporate electron kinetic effects by coupling it with the Kinetic Code for Plasma Periphery (KIPP). An iterative algorithm, which is made as an automatic process, is investigated in this work.

[1]  Bruce I. Cohen,et al.  A suitable boundary condition for bounded plasma simulation without sheath resolution , 1993 .

[2]  F. Najmabadi,et al.  Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas , 1986 .

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

[4]  J. Virmont,et al.  Nonlocal heat transport due to steep temperature gradients , 1983 .

[5]  J. Contributors,et al.  Experimental sheath heat transmission factors in diverted plasmas in JET , 2013 .

[6]  P. Stangeby.  A problem in the interpretation of tokamak Langmuir probes when a fast electron component is present , 1995 .

[7]  Guy Schurtz,et al.  A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes , 2000 .

[8]  David Tskhakaya,et al.  On Recent Massively Parallelized PIC Simulations of the SOL , 2012 .

[9]  Boris B. Kadomtsev,et al.  Reviews of Plasma Physics , 2012 .

[10]  Francis F. Chen,et al.  Introduction to Plasma Physics and Controlled Fusion , 2015 .

[11]  S. I. Braginskii.  Reviews of Plasma Physics , 1965 .

[12]  W. Fundamenski,et al.  Interpretation of divertor Langmuir probe measurements during the ELMs at JET , 2011, Journal of nuclear materials. Journal des materiaux nucleaires.

[13]  Williams,et al.  Nonlocal electron heat transport by not quite Maxwell-Boltzmann distributions. , 1986, Physical review letters.

[14]  R. K. Wakerling,et al.  The characteristics of electrical discharges in magnetic fields , 1949 .

[15]  D. N. Hill,et al.  An evaluation of kinetic effects in the DIII-D divertor , 1998 .

[16]  Y. Igitkhanov,et al.  Non-local transport effects on the tokamak SOL plasma parameters , 1990 .

[17]  M. Shoucri,et al.  Fully kinetic simulation of coupled plasma and neutral particles in scrape-off layer plasmas of fusion devices , 1999, Journal of Plasma Physics.

[18]  T. Soboleva,et al.  Influence of Kinetic Effects on Particle and Energy Flows in the ITER Divertor , 1994 .

[19]  J. Wesson.  Effect of temperature gradient on plasma sheath , 1995 .

[20]  B. J. Muga,et al.  Particle-in-Cell Method , 1970 .

[21]  B. Leblanc,et al.  Modification of the electron energy distribution function during lithium experiments on the National Spherical Torus Experiment , 2012 .

[22]  A. Taroni,et al.  The Particle and Heat Drift Fluxes and their Implementation into the EDGE2D Transport Code , 1996 .

[23]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[24]  Milo R. Dorr,et al.  Progress with the COGENT Edge Kinetic Code: Implementing the Fokker‐Planck Collision Operator , 2014 .

[25]  A. Loarte,et al.  Predicted effects of parallel temperature gradients on the overestimation of TCV divertor target Langmuir probe Te measurements , 2003 .

[26]  D. Coster,et al.  On Kinetic Effects during Parallel Transport in the SOL , 2008 .

[27]  R. Chodura.  Basic Problems in Edge Plasma Modelling , 1988 .

[29]  M. Dorf.  Continuum Kinetic Modeling of the Tokamak Plasma Edge , 2015 .

[31]  P. Catto,et al.  Long Mean Free Path Modifications of Electron Heat Conduction , 1998 .

[32]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[33]  S. Krasheninnikov.  On nonlocal electron heat conduction , 1993 .

[34]  J. Contributors,et al.  Modelling of tungsten re-deposition coefficient , 2015 .

[35]  P. Stangeby,et al.  Errors in measuring electron temperatures using a single Langmuir probe in a magnetic field , 1987 .

[36]  A. M. Mirza,et al.  Heat transport formula in strongly inhomogeneous plasmas , 1989 .

[37]  D. Coster,et al.  Kinetic simulations of electron heat flux in the scrape-off layer , 2017 .

[38]  Daniel F. Martin,et al.  Progress with the COGENT Edge Kinetic Code: Collision Operator Options , 2012 .

[39]  P. Stangeby.  Langmuir-, and bolometer-probe interpretation for plasmas with two electron components , 1984 .

[40]  T. Takizuka,et al.  A binary collision model for plasma simulation with a particle code , 1977 .

[41]  D. Tskhakaya.  Kinetic Modelling of the Plasma Recombination , 2016 .

[42]  Jet Efda Contributors,et al.  Kinetic simulations of the parallel transport in the JET scrape-off layer , 2009 .

[43]  Réal R. J. Gagné,et al.  Splitting schemes for the numerical solution of a two-dimensional Vlasov equation , 1978 .

[44]  T. Takizuka,et al.  Effect of Source and Sink on Heat Transport in the SOL , 2010 .

[45]  R. Chodura.  Non-Local Heat Conduction Along a Scrape-Off Layer with Strong Recycling , 1990 .

[46]  R. Chodura.  Kinetic Effects in the Scrape off Layer , 1992 .

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

[48]  T. Takizuka,et al.  Kinetic Modelling of Divertor Fluxes during ELMs in ITER and Effect of In/Out Divertor Plasma Asymmetries , 2016 .

[49]  D. Coster,et al.  Kinetic modelling of temperature equilibration rates in the plasma , 2013 .

[50]  T. Takizuka,et al.  Kinetic Particle Simulation Study of Parallel Heat Transport in Scrape-off Layer Plasmas over a Wide Range of Collisionalities , 2010 .

[51]  T. Takizuka,et al.  PIC Simulation Study of Heat Transport Kinetic Factors in Scrape‐Off Layer Plasmas , 2012 .

[52]  D. Coster,et al.  Extensions to the SOLPS edge plasma simulation code to include additional surface interaction posibilities , 2006 .

[53]  W. Fundamenski.  Parallel heat flux limits in the tokamak scrape-off layer , 2005 .

[54]  D. Coster.  Whole device ELM simulations , 2009 .

[55]  T. Takizuka.  Development of the PARASOL Code and Full Particle Simulation of Tokamak Plasma with an Open-Field SOL-Divertor Region Using PARASOL , 2011 .

[56]  A. M. Mirza,et al.  Delocalized heat flux for low Z plasmas , 1990 .

[57]  Robert James Goldston.  Energy confinement scaling in Tokamaks: some implications of recent experiments with Ohmic and strong auxiliary heating , 1984 .

[58]  M. Groth,et al.  1D kinetic modelling of the JET SOL with tungsten divertor plates , 2013, Journal of nuclear materials. Journal des materiaux nucleaires.

[59]  A. Bergmann,et al.  Implementation into B2 of a 21-moment description for the parallel transport , 1996 .

[60]  B. Dudson,et al.  Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer , 2013, 1302.0676.

[61]  Y. Igitkhanov,et al.  Implication of Kinetic Effects for Fluid Codes , 1994 .

[62]  F. Najmabadi,et al.  Generalized parallel heat transport equations in collisional to weakly collisional plasmas , 1988 .

[63]  T. Takizuka.  Kinetic effects in edge plasma: kinetic modeling for edge plasma and detached divertor , 2017 .

[64]  R. Cohen,et al.  Kinetic Modelling of Detached and ELMy SOL Plasmas , 1996 .

[65]  R. Cohen,et al.  Kinetic effects in tokamak scrape-off layer plasmas , 1996 .

[66]  Ronald H. Cohen,et al.  Kinetic effects on particle and heat fluxes in detached plasmas , 1996 .

[67]  D. Tskhakaya,et al.  One-dimensional plasma sheath model in front of the divertor plates , 2017 .

[68]  F. Najmabadi,et al.  Effects of pressure anisotropy on plasma transport , 1986 .

[69]  Benchmarks of KIPP: Vlasov‐Fokker‐Planck Code for Parallel Plasma Transport in the SOL and Divertor , 2014 .

[70]  M. Groth,et al.  Assessment of the effect of parallel temperature gradients in the JET SOL on Te measured by divertor target Langmuir probes , 2015 .

[71]  Implementation of Non-local Transport Model into 2D Fluid Code , 1994 .

[72]  David Tskhakaya,et al.  Optimization of PIC codes by improved memory management , 2007, J. Comput. Phys..

[73]  D. P. Coster,et al.  Development and Benchmarking of a New Kinetic Code for Plasma Periphery (KIPP) , 2012 .

[74]  P. Catto,et al.  Electron heat conduction modifications due to long mean free path effects , 2000 .

[75]  D. Tskhakaya,et al.  Stability of the Tonks–Langmuir discharge pre-sheath , 2016 .

[76]  A. Kukushkin,et al.  Application of BGK Collision Operator for Kinetic Correction of Fluid Models , 1994 .

[77]  T. Takizuka,et al.  Particle simulation of divertor plasma , 1984 .

[78]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[79]  E Weinan,et al.  The heterogeneous multiscale method* , 2012, Acta Numerica.

[80]  R. Chodura.  Nonlocal Heat flux in the Scrape-Off Layer of a High-Temperature Plasma , 1988 .

[81]  D. P. Coster.  Reduced Physics Models in SOLPS for Reactor Scoping Studies , 2016 .