WORK&PACKAGE&ENABLING&RESEARCH&& 2014&scientific/technical&report&template& Report&due&by&31&December&2014&&

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1 WORK&PACKAGE&ENABLING&RESEARCH&& 2014&scientific/technical&report&template& Report&due&by&31&December&2014&& & WPENR&2014& &report&form& Project&title&& (as&in&task&agreement)& Principal&Investigator& Institute&of&Principal&Investigator& Project&reference&number&& (asin&task&agreement)& Theoryandsimulationofenergeticparticledynamicsandensuing collectivebehaviorsinfusionplasmas.[shorttitle:nonlinear EnergeticparticleDynamics(NLED)] FulvioZonca ENEAC.R.FrascatiItaly WP14%ER%01/ENEA%01 Filenameshouldbeoftheformat:WP14_ER_report_RU%nnwhereRU%nnisforexampleIPP%01. Purpose&and&use&of&report& Therearetwomainpurposes: 1. Measureofachievementoftheproject sgoalswithevidence 2. Scientificoutputimpactandpossibleexploitation Thereportsshouldbeasbriefandclearaspossiblereferringtopublicationsandotherinformationfor details. However there should be enough information to support statements that deliverables have beenachieved.asanindicationthe& full& report& should& not& exceed& 10& pagesandshorterreportsare preferred.pleasekeeptothereportformatanddonotattachadditionalinformation.ifthereareoneor twoparticularlysignificantfiguresthatareneededtodemonstratetheresultsthesecanbeincludedin thetables. The reports will be assessed by the EUROfusion STAC and will be made available to the PMU and thereby relevant Task Force and project leaders in case follow%up in the main Work Programme is appropriate(theycanrequestfurtherdetailsifneeded). Timeline:& 31December2014: Scientific/technical report (this form) delivered to the PMU EarlyJanuary2015: LateFebruary: Friday27February: AllERreportspassedtoSTAC.TheremaybequestionsofclarificationfromSTAC tothepisduringjanuary/earlyfebruary STACassessmentoftheERprogrammedeliveredtoPMU WP14MonitoringreportdeliveredtoCommissionbyPMU. Mid%March2015: STAC report on ER delivered to General Assembly including any recommendationsforfollow%upinthemainworkprogramme(2015orlater). & WP14%ER%01/ENEA%01 1

2 1.&Main&scientific&output&V&summary& Summarisethemainachievementsoftheprojectandtheirpotentialimpact(1%2pages).Donotlistthe deliverableshere(itissuggestedyoufirstcompletethedeliverablestableinsection4below). Thegeneraltheoreticalframeworkfortheself%consistentdescriptionofshearanddriftAlfvénwaves (SAWs/DAWs)excitedbyenergeticparticles(EPs)andensuingtransportprocessesinfusionplasmas hasbeencompletedandassessed[1%4].thisframeworkisapplicabletolinearaswellasnonlinear studies;andincludessingle%andmulti%modedescriptions[12]therebyilluminatingspatiotemporal structures cross%scale couplings resonant excitations self%consistent phase%space dynamics and transport processes and spectral transfers [34]. Applications of this general framework to the interpretationofexperimentalobservationsandnumericalsimulationresults[1%7]demonstrateits practical usefulness in providing/enhancing insights into the underlying fundamental dynamics. In particularthecrucialroleofrealisticplasmaprofilesandequilibriummagneticconfigurationsare understoodintermsofwave%epfiniteinteractionlengthvs.perpendicularfluctuationwavelength; andintermsofwave%epfiniteinteractiontimevs.wave%particletrappingtime[4].thiscanalsobe understoodintermsofcompetitionofresonancedetuningandradialdecouplinginthepresenceof generallynon%perturbativewave%epinteractions[3%7]. The general theoretical framework also addresses the interactions of SAW/DAW including drift waveturbulence(dwt)withzonalstructures(zs;i.e.zonalflowsandfields)andphasespacezonal structures (PSZS) [34]. Such interactions of SAW/DAW/DWT with ZS/PSZS involve cross%scale couplingsmeso%scaledynamicsandnon%localtransport[3;zarzosoetal.prl& (2013); Dumont et al. PPCF (2013)]. This problem has been investigated especially for the interplayofdwtwiththegeodesicacousticmode(gam)excitedbyeps(egam)[89].whilegams haveafavorableimpactondwtreductionduringthel%htransitionelectrostaticegamsimulations ingyselapointtoamorecomplicatedpicture.itwasfoundinparticularthategamscouldenhance DWT in some situations [Zarzoso et al. PRL& (2013); Dumont et al. PPCF (2013)].ProjectactivitieshaveclarifiedhowGAMsandEGAMsrelatetoeachother[8]andprogress ingyro%kineticsimulationshasbeenmadeonhowegamsanddwtinteractbothinelectrostatic andelectromagneticregimes[9].theseresultshavebeenobtainedbydetailedinvestigationsofthe GAM/EGAM linear dispersion relation [89] showing the important role of the EP distribution functioninconfigurationandvelocityspaceaswellastherelevanceofkineticelectrontreatmentin electromagnetic simulations yielding a reduction of the EGAM growth rate. Good agreement betweenanalytictheoryandnemorbnumericalsimulationresultshasbeenfound[9].meanwhile furtherunderstandingofthemeso%scaledynamicsintheegam%itginteractionhasdemonstrated theavalanche%likenatureofradialitgpropagation[9]. AnextensiveandsuccessfulbenchmarkingactivityofNLEDprojectcodeshasbeencarriedouton well%definedlineartestcases[671011].inparticularthexhmgccodehasbeenusedtostudythe linearpropertiesofbetainducedalfvéneigenmodes(baes);i.e.realfrequenciesgrowthratesand modestructuresofepdrivenbaeshavebeeninvestigatedbyvaryingtheepdensity.linearfeatures of those modes have been compared with numerical simulation results from the gyro%kinetic eigenvaluesolverligkaandfoundtobeingoodagreement[67].thestabilityofann=6toroidal AE(TAE)hasbeenalsoconsideredfortheITPA%TAEbenchmarkcaseassumingβ e =2 10 %4 andno EPs[10].ThemodefrequenciesmeasuredwithNEMORBEUTERPEXHMGCandLIGKAhavebeen found to be in good qualitative agreement even though small differences between the different valuesarefound;thereasonofthediscrepancyisstilltobeinvestigated[10].thenemorbcodehas also been used for linear simulations of an n = 6 reversed shear AE (RSAE) with simple model profiles.thenumericalresultsarein good agreement with analytical theory predictions [10]. The benchmarkbetweenhymagycandhmgccodeshasbeenperformedfortwotestcases[11];and enrichedbybenchmarkagainsthymagyc%hmgc"obtainedbycouplingthefullgyro%kineticsolverin HYMAGYC with the MHD field solver in HMGC. For the first test case (characterized by a circular shiftedmagnetic%surfaceequilibriumwitha/r 0 =0.1andaparabolicsafetyfactorprofilewithq 0 =1.1 q a =1.9 mode number n=2 and m=1234) a qualitative agreement between results of the three codesisobtained.forthesecondtestcase(itpa%taewithalowermagneticshearq 0 =1.71q a =1.87 WP14%ER%01/ENEA%01 2

3 mode number n=6 and poloidal harmonics m=7 18) increasing the energetic particles density valuesthehymagycresultsshowmoresignificantdifferencesw.r.t.theothertwocodes.further checksareunderinvestigationforthehymagyccode[11]. Linearstudiesofthee%fishboneinstabilityhavebeencarriedonforstandard(peakedon%axis)and inverted(peakedoff%axis)densityprofileofthesupra%thermalelectronsusingxhmgc[12].asetof simulations to enlighten the effect of kinetic bulk ions and bulk electrons (besides the energetic electrons)hasalsobeencompleted.equilibriacharacterizedbyinvertedormonotonicaboveand below unity q profiles have been considered and results agree with theoretical expectations and show the importance of the EP distribution function for the mode evolution which is clearly destabilizedbythebarelytrapped/circulatingsupra%thermalparticles[12].fortheseanalyses[13]it is crucial to use a realistic model equilibrium distribution function [C. Di Troia PPCF (2012);1415] which has been adopted for both NEMORB and XHMGC. Nonlinear numerical simulationsofanon%axispeakedenergeticelectrondensityprofilehavebeenperformed[g.vladet al.nuclearfusion (2013)]andresultshavebeensuccessfullyverifiedagainsttheoretical predictionswithparticularemphasisonsaturationmechanismandontheroleofphase%lockingand self%consistent interplay of nonlinear mode dynamics and EP transport [416]. Studies of off%axis peakedenergeticelectrondensityprofileshavebeenpostponeduntilcompletionofcorresponding linearstabilityanalyses. Alinearglobalgyro%kineticstabilityanalysisincludingmultiplebackgroundionspecies(D T He ash Be) and EP species (α NBI%D) was carried out with the LIGKA code aimed at studying EP transportduetoaesinaniter15ma standard scenario[17%21].themodestructuresanddamping rateswereusedfornon%linearperturbativestudiesemployingthehagiscode.itwasfoundthat kinetic effects (trapped kinetic ions inclusion of diamagnetic effects dilution and impurities) typicallyreducethedampingofaesandthusleadtoamoreunstablespectrumofmodes;e.g.for TAEsbetween5<n<35.AlsohigherorderTAEbranches(i.e.m+1/m+2;m+2/m+3...)canbevery weaklydamped.afterasuccessfullinearbenchmarkofhagisandligkafortheepdrivenon%linear simulationswerecarriedout.thefirstresultsshowveryclearlythattheproblemcannotbetreated with a local quasi%linear model: although the linear phases in single%mode vs. multi%mode simulationsareverysimilarthenon%linearphasedifferssignificantlyduetonon%linearphasespace coupling effects. The saturation amplitudes are considerably higher (up to almost one order of magnitude) and linearly subdominant modes can become dominant in the non%linear phase. Convergenceandsensitivitystudiesareinprogress. Multi%modeinducedEPtransporthasbeenanalyzedforamulti%beamgeneralizationoftheO'Neil problem[22].inparticulartheproblemofn"supra%thermalbeamshasbeenaddressedinvestigating the self%consistent EP response in the presence of the complete spectrum of resonantly excited Langmuir waves degenerate with the corresponding beam modes. Velocity space transport correspondstoeptransportintherealspaceduetooverlappingaesnearmarginalstabilityaslong astheresonanceseparationissmallcomparedtotheradialmodewidth.bynumericalevaluationof the Finite Time Lyapunov Exponent (FTLE) field we have studied EP transport processes and LagrangianCoherentStructures.ThecomparisonwiththecaseofmultipleAEsintoroidalgeometry isinprogress[22]. Fortheinvestigationofspatiotemporalstructuresofself%consistentSAW/DAWinteractionswithEPs [1%7]atest%particlenumericaltoolbasedonHamiltonianmappingtechniquesbeendevelopedina generalform[5]readilyusablewithfullygyro%kineticcodesand/orself%consistentorperturbative hybrid MHD%particle codes. A first draft of a User Guide has been also made available. Physical quantities(epphasespacevariableswave%epphaseandpowerexchangeetc.)aremonitoredfora propersampleoftestparticlesrepresentingthewholeresonantepsbehaviourinaself%consistent simulation.self%consistentdynamicsofpszscanbeinvestigatedinthiswayanddetailedinformation onthemodesaturationmechanismscanbeobtainedfromaquantitativeanalysisoftestparticle behaviour. Radial mode structures are found to vary in the nonlinear regime [5%7]. As part of nonlinearbenchmarkingstudiesmadepossiblebythetest%particlediagnostictool[5]theeffectof radial mode structure evolution on saturation mechanism has been investigated comparing simulationresultsofxhmgcwiththoseofthehagiscode.nonlinearwave%particleinteractionwas WP14%ER%01/ENEA%01 3

4 calculatedforafixedmodestructureprovidedbyxhmgc.non%perturbativeepresponsesandfinite radial fluctuation structures in nonuniform plasmas were found increasingly more important for increasing EP drive [67]. As further application of the Hamiltonian mapping diagnostics [5] nonlinear benchmark of different codes XHMGC LIGKA%HAGIS and CKA%EUTERPE has been systematically carried out [6723]. In particular the formation of PSZS has been observed with commonfeaturesforallthecodes.bothxhmgcandligka%hagisshowresonancesplittingwithin PSZS and the consequent resonant particle density flattening. Both codes show that the radial extensionofthedensityflatteningissetatsaturationbythemodewidth(radial"decoupling)rather thanbythefinitewave%epinteractionlength(resonance"detuning).applicationofthismethodtothe benchmarkofnemorbcodeisinprogress;andthattoeuterpeisinanadvancedstage[2331]. A fluid%electron/ gyro%kinetic%ion model for electromagnetic gyro%kinetic simulations called FLU% EUTERPEhasbeenimplementedinthefullygyro%kineticEUTERPEcode.Thismodeloffersimproved numericalrobustnessavoidingthecancellationproblemandlooseningthetimesteprequirement compared with fully gyro%kinetic electromagnetic codes. The cost of these improvements is the neglectofelectronkineticeffectsandtherequirementtoadopttruncatedfluidclosures.ithasbeen appliedtomodeltheinternalkinkmodeintokamaksofincreasinglyrealisticgeometryfromalarge aspectratiocircularcasetoacasewithaspectratio3.0andelongation1.85comparabletocurrent largetokamakexperiments.boththefluidkinkandtheeffectofgyro%kineticbulkionsonthekink modehavebeenstudied.finallytheeffectofgyro%kineticfastionshasbeenconsideredpermitting simulationsofthelinearstageofthefishbonecycle.bothkinkmodestabilisationbyfastparticles andthen=1energeticparticlemodehavebeenobserved. On the algorithmic side anew scheme for fully kinetic electromagnetic PIC simulations has been successfully developed and tested as well as a phase space diagnostics for non%linear mode saturation. ThefullykineticversionofthecodehasbeenappliedtotheinteractionofTAEandkineticAlfvén wave(kaw)inatokamakgeometrywhereaglobaltae%kawstructurehasbeenidentifiedwhich appearstobemoreunstablewithrespecttothefastionsthanasimple(fluid%like)taemode. ThehybridschemehasbeenappliedtothecalculationofthestabilityanalysisofaHELIASreactor configuration.theeffectofthefinitefast%ionorbitwidthandthefinitefast%iongyroradiustherole oftheequilibriumradialelectricfieldaswellastheeffectofanisotropicfastparticledistribution functions(loss%coneandicrh%typedistributions)havebeenstudiedinwendelstein7%xstellarator geometry. 2.&Publications/presentations& Listthosewhichhavehadasubstantialcomponentfromtheworkoftheprojectmarkingthosewhich areentirelyfromtheworkoftheproject. Givetitlefirstauthorjournal/conference/othervenue Unless&otherwise&stated&publications/presentations&below&are&intended&to&be&entirely&from&the& work&of&the&project.& & [1] F. Zonca and L. Chen Theory" on" excitations" of" drift" Alfvén" waves" by" energetic" particles." I." Variational"formulation.Phys.Plasmas (2014).PDF(50%NLEDsupport) [2]F.ZoncaandL.ChenTheory"on"excitations"of"drift"Alfvén"waves"by"energetic"particles."II."The" general"fishboneglike"dispersion"relation.phys.plasmas (2014).pdf(50%nledsupport) [3] F. Zonca et al. Energetic" particles" and" multigscale" dynamics" in" fusion" plasmas. Plenary invited presentation at the 41.st EPS Conference on Plasma Physics Berlin Germany June 23 % 27 June (2014);andPlasmaPhys.Contr.Fusion (2015).PDF(80%NLEDsupport) [4]F.Zoncaetal.Nonlinear"dynamics"of"phase"space"zonal"structures"and"energetic"particle"physics" in"fusion"plasmas.tobepublishedinnew.j.phys(2015).pdf(80%nledsupport) WP14%ER%01/ENEA%01 4

5 [5]S.Briguglioetal.Analysis"of"the"nonlinear"behavior"of"shearGAlfvén"modes"in"tokamaks"based"on" Hamiltonian"mapping"techniquesPhysicsofPlasmas (2014).PDF [6]X.Wangetal.Studies"of"nonlinear"dynamics"of"waveGparticle"interactions"in"Tokamak"plasmas" based" on" Hamiltonian" mapping" techniques. Invited presentation at the Joint Varenna % Lausanne InternationalWorkshoponTheoryofFusionPlasmasVarennaItalySeptember1%5(2014).PDF [7]X.Wangetal.Structure"of"waveGparticle"interactions"in"nonlinear"beta"induced"Alfvén"eigenmode" dynamics." Invited talk to be presented at the 7 th IAEA Technical Meeting on Plasma Instabilities FrascatiItalyMarch4%62015.PDF [8] J.%B. Girardo et al. Relation" between" energetic" and" standard" geodesic" acoustic" modes Phys." Plasmas" (2014).PDF(50%NLEDsupport) [9]D.Zarzosoetal.Analytic"dispersion"relation"of"energetic"particle"driven"geodesic"acoustic"modes" and"simulations"with"nemorb"nucl.fusion (2014).pdf(50%nledsupport) [10]A.Biancalanietal.Global"Gyrokinetic"Modeling"of"Geodesic"Acoustic"Modes"and"Shear"Alfvén" Instabilities"in"ASDEX"Upgrade."Presentedatthe25 th IAEAFusionEnergyConferenceSaint PetersburgRussiaOct PaperEX/P1%18.PDF [11]G.Fogacciaetal.Linear"benchmark"activity"of"HYMAGYC"code.&Tobepresentedatthe7 th IAEA TechnicalMeetingonPlasmaInstabilitiesFrascatiItalyMarch4%62015.PDF& [12]V.Fuscoetal.Analysis"of"the"electron"fishbone"instability"with"the"XHMGC"code.&Tobe presentedatthe7 th IAEATechnicalMeetingonPlasmaInstabilitiesFrascatiItalyMarch4% PDF [13]C.DiTroiaetal.Effects"of"ECRHGlike"and"LHHGlike"anisotropies"in"phase"space"on"electron" fishbone"resonant"excitation.&tobepresentedatthe7 th IAEATechnicalMeetingonPlasma InstabilitiesFrascatiItalyMarch4%62015.PDF [14]C.DiTroiaandA.BiancalaniBayesian"derivation"of"plasma"equilibrium"distribution"function"for" tokamak"scenarios.&presentedatthe25 th IAEAFusionEnergyConferenceSaintPetersburgRussia Oct PaperTH/P7%6.PDF [15]C.DiTroia.Bayesian"derivation"of"plasma"equilibrium"distribution"function"for"tokamak" scenarios"and"the"associated"landau"collision"operator.&submittedtonucl.fusion. [16]F.Zoncaetal.Role"of"phase"locking"in"nonlinear"dynamics"of"fishbones"and"EPMs."Paper BP Bull.Am.Phys.Soc.59No.15(2014).PDF [17] S. D. Pinches and Ph. Lauber et al. Energetic" Ions" in" ITER" Plasmas. Submitted to Physics of Plasmas2014.(20%NLEDsupport)" [18]Ph.Lauberetal.Kinetic"Models"for"Energetic"Particle"Physics"in"Tokamaks"G"Verification" Validation"and"Predictions"for"ITER.PresentedattheJointVarenna%LausanneInternational WorkshoponTheoryofFusionPlasmasVarennaItalySeptember1%5(2014).PDF(50%NLED support). [19]Ph.Lauber.Local"and"Global"Kinetic"Stability"Analysis"of"Alfvén"Eigenmodes"in"the"15"MA"ITER" Scenario.SubmittedtoPlasmaPhysicsandControlledFusion2014.(70%NLEDsupport) [20]M.Schnelleretal.Study"of"Nonlinear"Fast"Particle"Transport"and"Losses"in"the"Presence"of" Alfvén"Waves.PresentedattheJointVarenna%LausanneInternationalWorkshoponTheoryof FusionPlasmasVarennaItalySeptember1%5(2014).PDF(80%NLEDsupport) [21]M.Schnelleretal.Study"of"Nonlinear"Fast"Particle"Transport"in"the"Presence"of"Alfvén"Waves"for" the"iter"15"ma"scenario.presentedatthe25 th IAEAFusionEnergyConferenceSaintPetersburg RussiaOct PaperTH/P2%06.PDF(80%NLEDsupport) [22]N.CarlevaroG.Montanietal.Transport"features"in"a"multiGresonance"beamGplasma"system."To bepresentedatthe7 th IAEATechnicalMeetingonPlasmaInstabilitiesFrascatiItalyMarch4% PDF [23]S.Briguglioetal.Nonlinear"dynamics"of"the"n=6"TAE:"comparison"between"HMGC"HAGIS"and" EUTERPE"results.Presentedatthe13thMeetingoftheITPAEnergeticParticleTopicalGroup(Joint MeetingofITPAMHDDisruptions&ControlandEnergeticParticlePhysicsTopicalGroups)Oct21% PadovaItaly.PDF [24]A.Mishchenkoetal.Gyrokinetic"particleGinGcell"simulations"of"Alfvén"eigenmodes"in"presence"of" continuum"effectsphys.plasmas (2014).pdf WP14%ER%01/ENEA%01 5

6 [25]A.Mishchenkoetal.New"variables"for"gyrokinetic"electromagnetic"simulationsPhys.Plasmas (2014).PDF(60%NLEDsupport) [26] M. Cole et al. Fluid" electron" gyrokinetic" ion" simulations" of" linear" internal" kink" and" energetic" particle"modesphys.plasmas (2014).pdf [27]A.Mishchenkoetal.Pullback"transformation"in"gyrokinetic"electromagnetic"simulationsPhys. Plasmas (2014).PDF(60%NLEDsupport) [28] A. Mishchenko et al. Global" hybridggyrokinetic" simulations" of" fastgparticle" effects" on" Alfvén" Eigenmodes"in"stellaratorsNucl.Fusion (2014).PDF [29]A.Mishchenkoetal.Global"gyrokinetic"particleGinGcell"simulations"of"Alfvénic"modes.Presented at the 25 th IAEA Fusion Energy Conference Saint Petersburg Russia Oct Paper TH/P4%49.PDF(70%NLEDsupport) [30]M.Coleetal.A"hierarchy"of"models"for"numerical"simulation"of"global"modes.Presentedatthe Joint Varenna % Lausanne International Workshop on Theory of Fusion Plasmas Varenna Italy September1%5(2014).PDF [31] A. Könies et al. A" nonglinear" Hybrid" MHDGgyrokinetic" Model" with" fixed" mode" structure" in" stellarator"geometry.presentedatthe12thmeetingoftheitpaenergeticparticletopicalgroup Mar.31 Apr.32014MadridSpain.PDF [32] M. Cole et al. Fluid" electron" kinetic" ion" simulations" of" Alfvénic" instabilities. Presented at the 12thMeetingoftheITPAEnergeticParticleTopicalGroupMar.31 Apr.32014MadridSpain. PDF 3.&Exploitation&of&the&project&results&(optional)& Ifyouthinkanyoftheresultsoroutputs(suchascodes)shouldbeincludedinortransferredtothe mainworkpackagesinthefutureprovideabriefcommentincludingwhichworkpackage(s)andthe reasons.(1pagemaximum) Applications of the general theoretical framework [1%4] to interpretation of experimental observations and numerical simulation results can provide/enhance insights into the underlying fundamentaldynamicsofsaw/dawinteractionswithepsinfusionplasmas.practicalexamplesof experimentalapplicationsarediscussedin[2].examplesofapplicationswithnumericalsimulation resultsaregivenin[4%7].theverygeneralnatureoftheframeworkmakesitapplicabletoessentially allactivitiesrelatedtoinvestigationsofsaw/dawinteractionswithepsinfusionplasmas. KineticmodestructurescomputedwithLIGKA[17%21]canbeprovidedtoothergroupswith perturbativecodesthatfocuse.g.onthecombinationoftaeinducedtransportand3dplasmaedge effects(rippletbmelmcoils)forwallloadstudies. InprincipletheHamiltonianmappingdiagnostictool[5]couldbetransferredtotheCode DevelopmentforIntegratedModellingWorkPackage(WP%CD)tobeinterfacedwithParticle%in%Cell and/orhybridmhd%particlecodesforinitial%valuecodesfortheinvestigationofmicro%turbulence and/orenergeticparticleeffectsonalfvénmodes.note(cf.#4)thatafirstdraftofauserguidehas alsobeenmadeavailable. WP14%ER%01/ENEA%01 6

7 WP14%ER%01/ENEA% &Project&deliverables& GiventhenatureofEnablingResearchitisnaturalthatnotalldeliverableswillbefullymetinallcases. Deliverable&(verbatim&from&project&description)&&&&&&&&&&&&&&&&&&&&&& Note:&Last&item&in&list&(*)&is&in&addition&to&those&from& project&description& Achieved:& Fully/Partly/Not& Evidence&for&achievement&brief&reason&for&partial&or&nonKachievement& Linearbenchmarks:ITPA%TAEbenchmark(benchmarkof HYMAGYCagainstXHMGCNEMORBandLIGKA);other benchmarkcasesconcerningtaesandbaeswheretheep drivehasbeenshowntomodifythemodestructurewill beadded Fully ThelinearbenchmarkofXHMGCandLIGKAforBAEhasbeensuccessfully completed[67].thebenchmarkofnemorbagainsteuterpeand XHMGChasbeensuccessfullyperformedintheframeworkoftheITPA testcaseandintheabsenceofeps[10].benchmarkofhymagycagainst XHMGConafirsttestcasehasbeenachieved[11].TheITPA%TAE benchmarkneedssomefurtherchecks. Linearanalysisofe%fishboneinstabilityforon/offaxis peakedenergeticelectrondensityprofileanddifferent anisotropyoftheepdistributionfunction(xhmgc) Fully Linearanalysisforon%axispeakedenergeticelectrondensityprofilehas beencompleted[12].analysisofoff%axispeakedprofilerequiressome moreinvestigationtoclearlyidentifythecharacteristicsofwave%particle interaction[1213]. Perturbativeanalysisofmulti%modescenariosincluding realisticdamping Fully/Partly FullyreferstolinearkineticstabilityanalysisofTAEsinburningITER plasma.partlytonon%linearperturbativeanalysis:firstresultsavailable convergenceandsensitivityanalysisinprogress[17%21] AnalysisofEPtransportinmulti%resonance1DVlasov system:comparisonwiththecaseofmultipleaesin toroidalgeometry Partly TheanalysisofEPtransportinmulti%resonance1DVlasovsystemis completed[22].thecomparisonwiththecaseofmultipleaesintoroidal geometryisinprogress(manpowerrequestedforthisstudywas underestimatedintheprojectproposal). Developmentofstandardizedtest%particlephase%space diagnosticstoolsbasedonhamiltonianmapping techniqueswhicharefocusedonidentifyingelucidating andquantitativelydescribingthenonlinearprocesses underlyingsaturationoffluctuationamplitudesandep transport Fully Thetoolshavebeenfullydeveloped[5]andappliedtodifferentcodes developedbydifferentresearchgroups[6723];input/output standardizationcanbeimproved.afirstdraftofauserguidehasalso beenmadeavailable.

8 Deliverable&(verbatim&from&project&description)&&&&&&&&&&&&&&&&&&&&&& Note:&Last&item&in&list&(*)&is&in&addition&to&those&from& project&description& Achieved:& Fully/Partly/Not& Evidence&for&achievement&brief&reason&for&partial&or&nonKachievement& Non%linearbenchmarks:benchmarkofXHMGCNEMORB andhagisusingthenewlydevelopedcommondiagnostics Studyofnonlinearsaturationmechanismsofe%fishbone mode(xhmgctphm) FurtherdevelopmentandapplicationofNEMORBto investigateglobalelectromagneticinstabilities FurtherdevelopmentandapplicationoftheEUTERPEcode familytoinvestigateglobalelectromagneticinstabilitiesin stellaratorgeometry Fully/Partly Partly Partly Fully BenchmarkofXHMGCandHAGIShasbeenessentiallycompleted(Fully); benchmarkofnemorbisinprogress(partly);additionalbenchmarkof EUTERPEisinanadvancedstage(Fully/Partly).See[6723]. Nonlinearnumericalsimulationsofon%axispeakedenergeticelectron densityprofilehavebeenperformed[g.vladetal.nuclearfusion (2013)]andresultshavebeenverifiedagainsttheoretical predictions[416].studiesofoff%axispeakedenergeticelectrondensity profileshavebeenpostponeduntilcompletionofcorrespondinglinear stabilityanalyses. GoodagreementbetweenanalytictheoryandNEMORBnumerical simulationresultsofgam/egamhasbeenfound[9].inadditiontothe benchmarkstudiesofnemorbagainsteuterpeandxhmgcrsae drivenbyepshavealsobeeninvestigatedwithnemorbprovingits capabilitytodealwithglobalelectromagneticinstabilities[10]. 2d&application:& %gyro%kineticsimulationoftaecouplingwiththecontinuum[24]& new&models: %FLUID%EUTERPEhasbeendeveloped[263032] %non%linearhybridmodelcka%euterpefor3dgeometryderivedcoded andbenchmarked[31;unpublished] application: %Simulationsofgyro%kineticenergeticionsinteractingwithAlfvén eigenmodesfromidealmhd[2829] algorithm:& %mixedvariablesformulationofthepicsimulationschemefor electromagneticperturbations[2527] WP14%ER%01/ENEA%01 8

9 Deliverable&(verbatim&from&project&description)&&&&&&&&&&&&&&&&&&&&&& Note:&Last&item&in&list&(*)&is&in&addition&to&those&from& project&description& Achieved:& Fully/Partly/Not& Evidence&for&achievement&brief&reason&for&partial&or&nonKachievement& (*)LinearandnonlinearanalysisoftheGAM/EGAM system.interplayofgam/egamwithdwt Fully AnalyticalstudyoftheGAMdispersionrelation;identificationoftwo typesofegams;assessmentoftheimportanceofvariouseffects:finite Larmorradiusfiniteorbitwidthandkineticelectrons[89]. AnalyticalderivationofamodeldescribingthecouplingbetweenEGAM anditgturbulence;definitionofphysicalcriteriaforefficientcoupling [89]. WP14%ER%01/ENEA%01 9