TN-01_UpdateStateArtEdgeModelling
=================================

.. meta::
   :description: technical note

   :keywords: Report,2047357-TN-D2.5+M2.9,Update,on,state,of,the,art,in,edge,modelling,M.,Barnes1,,M.,R.,Hardman2,,J.,Omotani3,and,F.,I.,Parra4,1,Rudolf,Peierls,Centre,for,Theoretical,Physics,,University,of,Oxford,,Clarendon,Laboratory,,Parks,Road,,Oxford,OX1,3PU,,United,Kingdom,2,Tokamak,Energy,Ltd,,173,Brook,Drive,,Milton,Park,,OX14,4SD,,United,Kingdom,3,Culham,Centre,for,Fusion,Energy,,Culham,Science,Centre,,Abingdon,,Oxon,,OX14,3DB,,United,Kingdom,4,Princeton,Plasma,Physics,Laboratory,,P.O.,Box,451,,Princeton,,New,Jersey,08540,,United,States,E-mail:,michael.barnes@physics.ox.ac.uk,1.,Introduction,The,edge,region,of,magnetic,conﬁnement,fusion,plasmas,presents,numerous,modelling,large,variations,challenges.,There,are,abrupt,changes,in,magnetic,ﬁeld,topology,,in,plasma,collisionality,,multiple,ion,species,in,diﬀerent,ionisation,states,,signiﬁcant,interactions,with,neutral,particles,and,several,boundary,layers,surrounding,the,material,wall.,As,a,result,,a,plethora,of,analytical,and,numerical,models,have,been,developed,to,study,diﬀerent,aspects,of,the,edge,plasma,physics.,In,a,previous,report,[1],,we,provided,an,overview,of,the,relevant,physics,parameters,in,the,edge,and,discussed,the,various,approaches,taken,to,model,the,plasma,there.,Here,we,provide,an,update,to,this,report,,focusing,on,recent,progress,in,edge,modelling.,2.,Overview,of,edge,codes,While,there,are,many,diﬀerent,models,–,and,associated,codes,–,used,to,study,the,plasma,edge,,they,can,all,be,placed,into,a,handful,of,categories.,At,one,end,of,the,spectrum,are,Monte,Carlo,codes,(e.g.,,DEGAS2,,EIRENE,,GTNEUT,,NEUT2D),used,to,study,neutral,dynamics.,These,codes,employ,a,kinetic,treatment,for,neutrals,due,to,their,long,collisional,mean-free-path.,They,are,often,used,in,combination,with,multi-,component,ﬂuid,codes,(e.g.,,SOLPS,,EDGE2D,,EMC3,,SOLEDGE-2D,,TECXY),that,employ,a,ﬂuid-diﬀusive,model,for,transport.,These,codes,are,typically,used,to,study,transport,parallel,to,the,magnetic,ﬁeld,with,a,high,degree,of,sophistication,regarding,aspects,of,the,problem,such,as,the,wall,geometry,,multi-component,plasma,eﬀects,and,plasma-neutral,interactions.,However,,they,are,inherently,2D,,ruling,out,the,possibility,of,studying,turbulent,dynamics.,Instead,,they,use,a,crude,anomalous,diﬀusivity,ﬁtted,to,experimental,data,to,model,the,cross-ﬁeld,transport.,Most,codes,built,to,study,edge,turbulence,,including,cross-ﬁeld,transport,,are,ﬂuid,codes,(e.g.,,HERMES,[2],,GBS,[3],,1,Update,on,state,of,the,art,in,edge,modelling,2,GDB,[4],,GRILLIX,[5],,HESEL,[6],,TOKAM3X,[7]),based,on,a,drift-reduced,version,of,Braginskii’s,equations.,These,codes,are,typically,quite,mature,,with,a,high,degree,of,ﬂexibility,regarding,the,magnetic,geometry,–,including,the,ability,to,model,X-point,conﬁgurations.,However,,they,often,do,not,treat,multiple,ion,species,or,interactions,with,kinetic,neutrals,,and,ultimately,are,limited,in,applicability,to,plasmas,at,relatively,high,density,and/or,low,temperature.,Even,in,such,modes,of,operation,,they,cannot,capture,kinetic,eﬀects,such,as,the,prompt,loss,of,particles,at,the,material,wall.,This,brings,us,to,the,other,end,of,the,spectrum,,where,there,is,a,growing,list,of,drift,kinetic,and,gyrokinetic,codes,adapted,for,edge,conditions,(e.g.,,XGC,[8],,Gkeyll,[9],,GENE,[10],,COGENT,[11]).,In,principle,these,kinetic,codes,should,provide,a,more,complete,picture,of,edge,plasma,dynamics.,However,,they,come,with,extreme,computational,expense,,and,they,are,less,developed,,both,in,terms,of,the,analytical,models,on,which,they,are,based,and,in,terms,of,the,range,of,physics,currently,implemented.,3.,Recent,progress,in,edge,modelling,As,we,are,focused,on,developing,and,implementing,a,model,for,plasma,turbulence,in,the,edge,of,magnetic,conﬁnement,fusion,devices,,we,restrict,our,attention,here,to,advances,Instead,of,giving,a,list,of,improvements,in,ﬂuid,and,kinetic,models,for,turbulence.,made,to,every,code,over,the,last,couple,of,years,,we,will,focus,on,developments,that,have,pushed,forward,what,is,possible,in,edge,modelling,,with,an,emphasis,on,kinetic,treatments.,On,the,analytical,theory,front,,there,have,been,at,least,a,few,notable,advances,made:,•,Our,own,work,has,led,to,the,development,of,a,novel,set,of,moment-kinetic,equations,[12],that,combine,aspects,of,ﬂuid,and,drift,kinetic,approaches.,This,approach,makes,it,easier,to,transition,from,a,kinetic,to,a,ﬂuid,treatment,and,has,the,advantage,that,the,velocity,coordinate,is,everywhere,(and,at,all,times),deﬁned,in,terms,of,the,local,thermal,speed.,•,Research,elsewhere,has,made,ﬂuid,modelling,of,kinetic,eﬀects,more,accurate:,An,extension,of,the,original,Landau-ﬂuid,closure,[13],has,been,developed,to,treat,non-,Maxwellian,particle,distribution,functions,[14].,This,model,is,intended,for,use,in,the,ﬂuid,code,HERMES,(BOUT++),[15],to,improve,its,treatment,of,plasma,dynamics,near,the,wall,,where,,as,mentioned,above,,the,particle,distribution,function,develops,cutoﬀs,in,the,velocity,space,due,to,particle,losses.,•,Finally,,it,has,been,shown,that,inclusion,of,kinetic,electron,and,ﬁnite,ion,orbit,width,eﬀects,leads,to,a,collapse,of,the,Debye,sheath,at,much,smaller,angles,between,the,magnetic,ﬁeld,and,wall,than,previously,anticipated,based,on,ﬂuid,analysis,[16]:,In,particular,,this,angle,is,found,to,scale,like,the,electron-ion,mass,ratio,rather,than,its,square,root.,This,is,a,further,argument,in,favour,of,developing,kinetic,codes,for,the,treatment,of,edge,plasma,dynamics.,Update,on,state,of,the,art,in,edge,modelling,3,The,main,advances,to,kinetic,simulations,of,edge,turbulence,come,via,adding,in,more,physics,eﬀects,to,existing,codes,,many,of,which,already,exist,in,some,form,in,one,or,more,of,the,ﬂuid,turbulence,codes:,•,At,least,a,couple,of,the,continuum,kinetic,codes,have,made,changes,to,their,treatment,of,magnetic,geometry,to,allow,for,simulations,with,X-points.,These,include,COGENT,[17],,a,ﬁnite,volume,code,with,a,simpliﬁed,ﬂuid,model,for,electron,dynamics,,and,GENE-X,[18],,a,new,code,spun,oﬀ,from,GENE,that,is,electrostatic,with,Dougherty,collision,operator,[19],,has,no,neutrals,,imposes,simplistic,boundary,conditions,,and,uses,low-order,ﬁnite,diﬀerences.,GENE-X,uses,a,ﬂux,coordinate,independent,approach,to,allow,for,treatment,of,the,X,point,,while,COGENT,employs,a,somewhat,similar,multiblock,approach,that,is,locally,ﬁeld-aligned.,These,continuum,codes,join,their,PIC,counterpart,,XGC,,in,their,ability,to,treat,diverted,plasmas.,•,Some,edge,codes,have,been,extended,to,include,electromagnetic,ﬂuctuations.,These,include,the,kinetic,code,Gkeyll,[22],and,the,ﬂuid,code,GBS,[23].,Simulations,using,Gkeyll,in,helical,geometry,without,neutrals,[22],indicate,that,electromagnetic,eﬀects,could,lead,to,a,modest,broadening,of,the,electron,heat,ﬂux,in,the,scrape-oﬀ,layer,due,to,enhanced,cross-ﬁeld,transport,,while,inclusion,of,magnetic,shear,[20],led,to,a,more,signiﬁcant,reduction,in,transport.,•,A,kinetic,treatment,of,neutrals,was,also,added,to,both,GBS,[24],and,to,Gkeyll,[21].,In,the,case,of,Gkeyll,,this,is,restricted,to,atomic,neutrals,with,electron-impact,ionization,and,charge,exchange,collisions:,there,is,no,treatment,of,radiation,,recombination,,or,neutral-neutral,collisions;,and,a,Maxwellian,approximation,is,used,when,treating,ion-neutral,collisiions.,For,GBS,,the,treatment,additionally,includes,neutral,molecules.,4.,Areas,for,further,improvement,Most,of,the,physics,eﬀects,of,importance,in,the,edge,have,been,included,in,at,least,one,of,the,existing,kinetic,codes,,but,as,evidenced,above,,each,code,is,missing,at,least,some,of,the,key,ingredients.,Eﬀorts,are,currently,underway,to,add,many,these,ingredients,to,extant,codes.,However,,there,are,at,least,a,few,clear,areas,where,code,models,could,be,improved:,•,To,our,knowledge,each,of,the,kinetic,codes,mentioned,above,employs,some,form,of,simpliﬁed,model,for,electron,dynamics,,be,it,an,assumed,Boltzmann,response,,a,reduced,ﬂuid,model,or,a,linearised,Poisson,equation,(Boussinesq,approximation),with,the,electrostatic,potential,solved,using,the,polarisation,density.,The,latter,approximation,is,not,strictly,consistent,with,the,drift,ordering,in,the,edge.,•,Related,to,the,above,,we,are,not,aware,of,a,rigorous,procedure,for,determining,the,ﬁnite,Larmor,radius,corrections,needed,for,a,gyrokinetic,model,of,the,plasma,in,the,edge.,Update,on,state,of,the,art,in,edge,modelling,4,•,The,wall,boundary,conditions,employed,are,of,varying,levels,of,sophistication,but,require,further,guidance,from,theory,to,be,complete.,We,are,aware,of,eﬀorts,underway,to,extend,existing,kinetic,models,for,the,various,sheaths,surrounding,the,wall,so,that,they,can,be,used,in,kinetic,codes.,Our,approach,is,to,ﬁrst,treat,the,issue,with,electron,physics,and,obtaining,the,electrostatic,potential,before,moving,on,to,bridge,the,gap,between,the,open,and,closed,ﬁeld,line,regions,of,the,plasma.,The,moment,kinetic,approach,we,have,developed,should,provide,a,natural,avenue,for,obtaining,the,electrostatic,potential,self-consistently.,As,for,including,a,separatrix,,our,current,philosophy,is,that,the,most,eﬃcient,approach,would,be,to,make,use,of,ﬁeld-line-following,coordinates,where,possible,and,to,use,analytical,theory,to,match,between,these,regions,and,a,non-ﬁeld-aligned,grid,just,around,the,separatrix.,Update,on,state,of,the,art,in,edge,modelling,5,[1],F.,I.,Parra,,M.,Barnes,,and,M.,R.,Hardman.,Physics,in,the,edge,of,fusion,devices.,Excalibur/Neptune,Report,,3:2047357–TN–03–01,M1.2,,2021.,[2],B.,D.,Dudson,and,J.,Leddy.,Hermes:,global,plasma,edge,ﬂuid,turbulence,simulations.,Plasma,Phys.,Control.,Fusion,,59:054010,,2017.,[3],P.,Ricci,,F.,D.,Halpern,,S.,Jolliet,,J.,Loizu,,A.,Mosetto,,A.,Fasoli,,I.,Furno,,and,C.,Theiler.,Simulation,of,plasma,turbulence,in,scrape-oﬀ,layer,conditions:,the,gbs,code,,simulation,results,and,code,validation.,Plasma,Phys.,Control.,Fusion,,54:124047,,2012.,[4],B.,Zhu,,M.,Francisquez,,and,B.,N.,Rogers.,Gdb:,A,global,3d,two-ﬂuid,model,of,plasma,turbulence,and,transport,in,the,tokamak,edge.,Comp.,Phys.,Comm.,,232:46,,2018.,[5],A.,Stegmeir,,D.,Coster,,A.,Ross,,O.,Maj,,K.,Lackner,,and,E.,Poli.,Grillix:,a,3d,turbulence,code,based,on,the,ﬂux-coordinate,independent,approach.,Plasma,Phys.,Control.,Fusion,,60:035005,,2018.,[6],J.,J.,Rasmussen,,A.,H.,Nielsen,,J.,Madsen,,V.,Naulin,,and,G.,S.,Xu.,Numerical,modeling,of,the,transition,from,low,to,high,conﬁnement,in,magnetically,conﬁned,plasma.,Plasma,Phys.,Control.,Fusion,,58:014031,,2015.,[7],P.,Tamain,,H.,Buﬀerand,,G.,Ciraolo,,C.,Colin,,D.,Galassi,,Ph.,Ghendrih,,F.,Schwander,,and,E.,Serre.,The,tokam3x,code,for,edge,turbulence,ﬂuid,simulations,of,tokamak,plasmas,in,versatile,magnetic,geometries.,J.,Comp.,Phys.,,321:606,,2016.,[8],C.,S.,Chang,,S.,Ku,,and,H.,Weitzner.,Numerical,study,of,neoclassical,plasma,pedestal,in,a,tokamak,geometry.,Phys.,Plasmas,,11:2649,,2004.,[9],E.,L.,Shi,,G.,W.,Hammett,,T.,Stoltzfus-Dueck,,and,A.,Hakim.,Gyrokinetic,continuum,simulation,of,turbulence,in,a,straight,open-ﬁeld-line,plasma.,J.,Plasma,Phys.,,83:905830304,,2017.,[10],Q.,Pan,,D.,Told,,E.,L.,Shi,,G.,W.,Hammett,,and,F.,Jenko.,Full-f,version,of,gene,for,turbulence,in,open-ﬁeld-line,systems.,Phys.,Plasmas,,25:062303,,2018.,[11],M.,Dorf,,M.,Dorr,,J.,A.,Hittinger,,R.,H.,Cohen,,and,T.,D.,Rognlien.,Continuum,kinetic,modeling,of,the,tokamak,plasma,edge.,Phys.,Plasmas,,23:56102,,2016.,[12],F.,I.,Parra,,M.,Barnes,,and,M.,R.,Hardman.,2d,drift,kinetic,model,with,wall,boundary,conditions.,Excalibur/Neptune,Report,,7:2047357–TN–07–02,M1.4,,2021.,[13],G.,W.,Hammett,and,F.,W.,Perkins.,Fluid,models,for,landau,damping,with,application,to,the,ion-temperature-gradient,instability.,Phys.,Rev.,Lett.,,64:3019,,1990.,[14],K.,Fan,,X.,Xu,,B.,Zhu,,and,P.,Li.,Kinetic,landau-ﬂuid,closures,of,non-maxwellian,distributions.,Phys.,Plasmas,,29:042116,,2022.,[15],B.,D.,Dudson,,M.,V.,Umansky,,X.,Q.,Xu,,P.,B.,Snyder,,and,H.,R.,Wilson.,Bout++:,A,framework,for,parallel,plasma,ﬂuid,simulations.,Comp.,Phys.,Comm.,,180:1467,,2009.,[16],R.,J.,Ewart,,F.,I.,Parra,,and,A.,Geraldini.,Sheath,collapse,at,critical,shallow,angle,due,to,kinetic,eﬀects.,Plasma,Phys.,Control.,Fusion,,64:015010,,2022.,[17],M.,Dorf,and,M.,Dorr.,Continuum,gyrokinetic,simulations,of,edge,plasmas,in,single-null,geometries.,Phys.,Plasmas,,28:032508,,2021.,[18],D.,Michels,,A.,Stegmeir,,P.,Ulbl,,D.,Jarema,,and,F.,Jenko.,Gene-x:,A,full-f,gyrokinetic,turbulence,code,based,on,the,ﬂux-coordinate,independent,approach.,Comp.,Phys.,Comm.,,264:107986,,2021.,[19],P.,Ulbl,,D.,Michels,,and,F.,Jenko.,Implementation,and,veriﬁcation,of,a,conservative,,multi-,species,,gyro-averaged,,full-f,,lenard-bernstein/dougherty,collision,operator,in,the,gyrokinetic,code,gene-x.,Contr.,Plasm.,Phys.,,62:e202100180,,2021.,[20],N.,R.,Mandell,,G.,W.,Hammett,,A.,Hakim,,and,M.,Francisquez.,Reduction,of,transport,due,to,magnetic,shear,in,gyrokinetic,simulations,of,the,scrape-oﬀ,layer.,Plasma,Phys.,Control.,Fusion,,64:085006,,2022.,[21],T.,N.,Bernard,,F.,D.,Halpern,,M.,Francisquez,,N.,R.,Mandell,,J.,Juno,,G.,W.,Hammett,,A.,Hakim,,G.,J.,Wilkie,,and,J.,Guterl.,Kinetic,modeling,of,neutral,transport,for,a,continuum,gyrokinetic,code.,Phys.,Plasmas,,29:052501,,2022.,[22],N.,R.,Mandell,,G.,W.,Hammett,,A.,Hakim,,and,M.,Francisquez.,Turbulent,broadening,of,electron,Update,on,state,of,the,art,in,edge,modelling,6,heat-ﬂux,width,in,electromagnetic,gyrokinetic,simulations,of,a,helical,scrape-oﬀ,layer,model.,Phys.,Plasmas,,29:042504,,2022.,[23],M.,Giacomin,,P.,Ricci,,A.,Coroado,,G.,Fourestey,,D.,Galassi,,E.,Lanti,,D.,Mancini,,N.,Richart,,L.,N.,Stenger,,and,N.,Varini.,The,gbs,code,for,the,self-consistent,simulation,of,plasma,turbulence,and,kinetic,neutral,dynamics,in,the,tokamak,boundary.,J.,Comp.,Phys.,,463:111294,,2022.,[24],A.,Coroado,and,P.,Ricci.,A,self-consistent,multi-component,model,of,plasma,turbulence,and,kinetic,neutral,dynamics,for,the,simulation,of,the,tokamak,boundary.,Nucl.,Fusion,,62:036015,,2022.

:pdfembed:`src:_static/TN-01_UpdateStateArtEdgeModelling.pdf, height:1600, width:1100, align:middle`