1 HW/P-1 Kintic Intgratd Modling of Hating and Currnt riv in okamak Plasmas A. Fukuyama 1), H. Nuga 1), S. Murakami 1) 1) Graduat School of Enginring, Kyoto Univrsity, Kyoto, Japan -mail contact of main author: fukuyama@nuclng.kyoto-u.ac.jp Abstract. In ordr to slf-consistntly dscrib hating and currnt driv and various influncs of nrgtic particls in tokamak plasmas, w hav bn dvloping a kintic intgratd modling cod ASK3G. his modling is basd on th bhavior of th momntum distribution function of ach particl spcis. h tim volution of th momntum distribution function is dscribd by a nwly-xtndd Fokkr-Planck componnt ASK/FP and th influnc of nrgtic particls on global stability is studid by a full wav componnt ASK/WM. Slf-consistnt analysis of multi-schm hating in a IER plasma is dmonstratd for th first tim including radial transport and fusion raction rat calculatd from th momntum distribution function. h linar stability of global ign mods in th prsnc of nrgtic particls is also discussd. 1. Introduction In ordr to accuratly prdict th bhavior of fusion plasmas and to dvlop rliabl schms controlling thm, dvlopmnt of intgratd simulation cods for burning plasmas is urgntly ndd. Fusion ractions and xtrnal plasma hating and control gnrat nrgtic particls and modify th momntum distribution functions of plasma spcis. h xistnc of ths nrgtic particls may driv global instabilitis, such as rsistiv wall mods, intrnal kink mods, Alfvén ignmods and so on. h occurrnc of global instabilitis usually rdistribut th nrgtic particls. Prvious analyss of momntum distribution functions usually assum background spcis with Maxwllian distribution and th tmpratur of th bulk componnt cannot b changd during th analyss. hs assumptions ar not satisfid in a strong hating cas whr th bulk tmpratur changs rapidly. hrfor intgratd cor-transport simulation basd on th momntum distribution is rquird for.. Kintic Intgratd Modling of okamak Plasmas For ths purposs, w hav bn dvloping a kintic intgratd simulation cod, ASK3G, basd on th tim volution of th momntum distribution functions. It is an xtnsion of th intgratd tokamak modling cod ASK [1] which includs th componnts for MH quilibrium, diffusiv transport, ray tracing, full wav and th Fokkr-Planck analyss. In ASK3G, th Fokkr-Planck componnt ASK/FP dscribs th bhavior of th bulk componnt including th radial transport, and slf-consistntly simulats strong hating cass whr th momntum distribution function is strongly modifid. h modification is takn into account in th full wav componnt ASK/WM which dscribs th ICRF hating and low-frquncy global instabilitis. Figur 1 illustrats th prsnt structur of th intgratd cod, ASK, and associatd cods. h ASK3 is an xtnsion to th analysis of thr-dimnsional (3) hlical configurations,
HW/P-1 composd of ASK componnts and thr additional transport componnts. hy ar dsignd to xchang prdfind standard data through unifid application intrfac. Fig. 1. Prsnt structur of ASK and ASK3 h cor transport phnomna hav bn simulatd by various lvls of transport modling as shown in Fig.. h ASK cod includs thr kinds of componnts for transport analysis. h convntional transport componnt ASK/R is basd on th diffusiv transport quations for dnsitis, toroidal momntum, tmpratur, and poloidal magntic flux. ASK/X [] is basd on dynamic transport modling which solvs flux-surfac-avragd multi-fluid quations including th quations of motion. It dscribs th tim volution of th radial lctric fild and plasma rotation profils slf-consistntly. h Fokkr-Planck cod ASK/FP has bn xtndd for th kintic intgrat modling; th radial transport is includd and high prformanc is obtaind by paralll procssing. h highr dimnsional kintic modlings usually dscrib plasma turbulnc and rquir much mor computr rsourcs. 3. Multi-spcis Fokkr-Planck analysis h rlativistic bounc-avragd Fokkr-Planck componnt ASK/FP [3] has bn nwly xtndd to dscrib th tim volution of th multispcis momntum distribution function f s (p, θ, ) whr s, p, θ and ar particl spcis, magnitud of momntum, pitch angl and normalizd minor radius, rspctivly. In this modling, axisymmtry, tim scal longr than th particl bounc tim, and zro bounc orbit width ar assumd. h Fokkr-Planck quation includs nonlinar Coulomb collision, quasilinar wav-particl intraction, paralll lctric fild acclration, radial diffusion, and particl sourc. Figurs and 5 show typical simulation rsults for multi-schm hating in IER plasma. W assumd a radial diffusion cofficint rr () =.1(1 + 9 ) [ m /s] and an inward pinch trm
3 HW/P-1 Fluid modl iffusiv transport quation: n(, t), v φ (, t), (, t) ynamic transport quation: n(, t), u(, r), (, t) Kintic modl Bounc-avragd drift-kintic quation: f (p, θ p,, t) Axisymmtric gyrokintic quation: f (p, θ p,, χ, t) Gyrokintic quation: f (p, θ p,, χ, ζ, t) Full kintic quation: f (p, θ p, φ g,, χ, ζ, t) R X FP XGC G5, GKV PARASOL Fig.. Lvl of transport modling to kp th initial dnsity profil. h ICRF wavs hat tritons by scond-harmonic cyclotron damping and lctrons by Landau damping. utrons ar hatd by NBI and alpha particls ar gnratd by fusion raction. Figur illustrats th contours of f s at various radial position, 1 s aftr hating starts. Initial lctron dnsity and tmpratur on th magntic axis ar 1 m 3 and kv. Figurs 5 indicat th radial profils at t = 1 s of th absorbd powr dnsity of ach particl spcis, avrag kintic nrgy of lctrons, and, collisionally transfrrd powr dnsity, and tim volution of collisionally transfrrd powr. h distribution f s is calculatd on 5 magntic surfacs by full-implicit paralll solvr on 5 CPU cors. h total absorbd powr is. MW for lctrons, 1.17 MW for, 31. MW for and 1.3 MW for alpha particls. h fusion raction rat is calculatd with f s of racting particls. At t = ms, th alpha particl dnsity is only.5% of th lctron dnsity. h tritons producd by raction affct f nar th normalizd momntum p 1, about 1 MV. Collisional powr transfr btwn spcis is also calculatd slf-consistntly by using th nonlinar collision oprator which consrvs momntum and nrgy with rasonabl numrical accuracy. Fig. 3. Powr transfr among plasma spcis In th calculation shown in Fig., th radial diffusion broadns th collisional powr transfr profil, spcially hatd by ICRF wavs. h rgion of triton tmpratur incras bcoms broadr and is shiftd inward du to th inward pinch. W found that th hating and currnt
HW/P-1.5 Elctron - - - 1 - - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - 1 - - - - - - - - - - - - - - - - - - - - - - - - - 1-1 - - 1 - - - 1-1.5-1 -1.5 H -1.5-1.5 1 - - - - - Fig.. Radial dpndnc of momntum distribution functions for lctron,,, H. driv profils ar snsitiv to th radial transport modl. W hav introducd svral kinds of turbulnt diffusion cofficint and inward pinch, without nrgy dpndnc, with 1/ 1 + p dpndnc, fixd radial profil, and turbulnt transport modls usd in transport simulations. Validation of th radial transport modl with xprimntally obsrvd radial profils of nrgtic particls is undr way.. Full wav analysis including th influnc of nrgtic particls h ICRF wav lctric fild is calculatd by th full wav componnt ASK/WM [] in th cas shown in Fig. 1. Using th kintic dilctric tnsor calculatd by numrical intgration in momntum spac, ASK/WM can dal with arbitrary f s in analyzing ICRF hating and currnt driv. h nrgtic particls also affct th stability of Alfv n ign mods and low-frquncy global ign mods. Sinc th prsnt kintic dilctric tnsor modl assums a uniform plasma, mods coupld with drift wavs cannot b corrctly dscribd. hrfor w hav dvlopd a drift-kintic dilctric tnsor modl for arbitrary f s. Using this nwly-dvlopd modl, w hav analyzd th linar stability of low-frquncy Alfv n ign mods coupld with drift wavs drivn by nrgtic particls. h analysis of global ign mod usually studid with MH modl,.g. rsistiv wall mods and intrnal kink mods, is also undr way including th influnc of nrgtic particls. Acknowldgmnts his work is supportd in part by Grant-in-Aid for Scintific Rsarch (S) (17) from JSPS.
5 HW/P-1 (a) Pabs [MW/m 3 ] 1..5 1. (b) [kv] 5 3 1.5 1. (c).5 (d) 5 PC [MW/m ] 3 -.5.5 1. Pc [MW] -5 t [ms] 1 Fig. 5. Radial profils of (a) absorbd powr dnsity, (b) avrag kintic nrgy, (c) collisionally transfrrd powr dnsity, and tim volution of collisional powr transfr Rfrncs [1] FUKUYAMA A t al., Proc. of th IAEA FEC (Villamoura, ) IAEA-CSP-5/C/H/P-3. [] HONA M, FUKUYAMA A, J. Comp. Phys., 7, (). [3] NUGA H, FUKUYAMA A, J. Plasma and Fusion Rs. Sris,, 15 (9) [] FUKUYAMA, A., t al.: Proc. of 1th IAEA FEC (Chngdu, ) IAEA-CN-19/H/P-1.