Benchmarking of Lower Hybrid Current Drive Codes with Application to ITER-Relevant Regimes

Transcription

1 1 Bnchmarking of Lowr Hybrid Currnt Driv Cods with Application to ITER-Rlvant Rgims P.T. Bonoli 1), R.W. Harvy 2), C. Kssl 3), F. Imbaux 4), T. Oikawa 5), M. Schnidr 4), E. Barbato 6), J. Dckr 4), G. Giruzzi 4), C.B. Forst 7), S. Id 5), Y. Pysson 4), A.E. Schmidt 1), A.C.C. Sips 8), A.P. Smirnov 2), and J.C. Wright 1) 1) Plasma Scinc and Fusion Cntr, MIT, Cambridg, MA 2139, USA. 2) CompX, Dl Mar, CA 9214, USA. 3) Princton Plasma Physics Laboratory, Princton, NJ 8543, USA. 4) Association EURATOM-CEA, CEA, Cadarach, FRANCE. 5) Naka Fusion Rsarch Establishmnt, JAERI, Ibaraki-kn, JAPAN. 6) Associazion EURATOM-ENEA, Frascati (Roma), ITALY. 7) Univrsity of Wisconsin, Madison, WI 5376, USA. 8) Max Planck Institut für Plasmaphysik, Garching, GERMANY. Abstract. This papr discusss th rsults of a bnchmark xrcis in which th prdictions of svral simulation modls for lowr hybrid currnt driv (LHCD) wr compard using paramtrs typical of th stady stat oprating scnario in th ITER dvic (th so-calld Scnario 4). Th most complt LHCD simulation modls that wr usd combind 2D vlocity spac Fokkr Planck solvrs with toroidal ray tracing packags. Ths modls also prdictd th highst LHCD fficincis with MA of drivn currnt for 3 MW of coupld LHRF powr. Cods that solvd th Fokkr Planck quation using a Grn s function approach and thn computd th drivn LH currnt using a wav inducd RF flux basd on 1D paralll vlocity damping along ray trajctoris wr found to prdict LH currnts 35-4% lowr than th 2D Fokkr Planck modls. This discrpancy is undrstood in trms of th approximat natur of th 1D wav inducd flux that fails to proprly captur 2D vlocity spac ffcts that occur in LHCD owing to th significant distortion of th lctron distribution function. W also usd an orbit-following Mont Carlo cod to study th possibl parasitic damping of LH wavs on fusion gnratd alpha particls. Th ffct of magntic fild rippl and fast ion anomalous transport on th alpha population was considrd. It was found that for a larg anomalous diffusion cofficint (1m 2 /s), th absorption on fusion alphas can b as high as 7.7% using a LHRF sourc frquncy of 3.7 GHz. This rsult givs som confidnc in th sourc frquncy choic of 5. GHz in ordr to minimiz th possibility of this parasitic intraction. 1. Introduction Lowr hybrid (LH) wavs hav th attractiv proprty of damping strongly via lctron Landau rsonanc on rlativly fast tail lctrons at (2.5 3) v t, whr v t = (2T /m ) 1/2 is th lctron thrmal spd. Consquntly ths wavs ar wll-suitd to driving currnt in th plasma priphry whr th lctron tmpratur is lowr, making lowr hybrid currnt driv (LHCD) a promising tchniqu for off axis (r/a.6) currnt profil control in ractor grad plasmas. A cntral objctiv of LHCD on ITER is to supplmnt th bootstrap currnt in ordr to accss attractiv stady-stat oprating rgims, namly thos with modrat or rvrsd shar, high bootstrap fraction ( 7%), high β n (~ 3) and good confinmnt (H ITER-89 ~ 2.5) [1]. Indd, off-axis lowr hybrid currnt driv has alrady bn shown to b an ffctiv tool for optimizing th currnt profil for accss to advancd tokamak oprating mods in th JET [2] and JT-6U [3] tokamaks. In addition, th RF sourc frquncy can b chosn high nough to minimiz th parasitic intraction of LH wavs with fusion-gnratd alpha particls. Th rlativly high phas spd also minimizs dltrious ffcts du to particl trapping which can bcom important in th priphry.

2 2 Givn ths physics considrations, w hav undrtakn a dtaild bnchmarking xrcis in which w compard th prdictions of svral advancd simulation modls for lowr hybrid currnt driv using a tst cas basd on a proposd stady stat oprating mod (Scnario #4) for th ITER dvic [4]. Th plan of this papr is as follows. In Sction 2 w rviw th physics modls usd in th diffrnt LHCD simulation modls that compris our bnchmarking xrcis. In Sction 3 w prsnt paramtrs usd for th bnchmark xrcis and comparisons of th drivn currnt profils and LHRF dposition profils prdictd by th diffrnt simulation modls. W also discuss rasons for th diffrnt prdictions among th various modls. In Sction 4 w xamin th ffcts of parasitic absorption of th LH wavs on fusion gnratd alpha particls using an orbit following Mont Carlo cod. Finally in Sction 5 w giv conclusions and suggstions for futur work. 2. Lowr Hybrid Currnt Driv Physics Modls Th most advancd modls that w hav usd ar th CQL3D-GENRAY [5, 6] and DELPHINE [7] cods which combin a 3D (v, v //, r) Fokkr Planck calculation [s Eq.(1)] with a toroidal ray tracing packag. Th moduls itrat to comput a slf-consistnt nonthrmal lctron distribution function. Ths modls hav th advantag that thy proprly captur th complt 2D vlocity spac physics in th collision oprator C(f, p //, p ), including th f t f f 1 f ( p// ) + C( f, p//, p ) + E// + Γsδ ( p// ) + rχ F p p r r = Drf p// // // r (1) ffcts of pitch angl scattring and momntum consrving corrctions in th background collision oprator. For th purposs of th prsnt bnchmark xrcis, ths cods find th stady stat solution to Eq. (1) nglcting th DC lctric fild trm (E // ) and th fast lctron diffusivity oprator. Both CQL3D and DELPHINE includ th ffct of particl trapping which is important vn for off-axis LHCD. Particl trapping in DELPHINE is computd using analytic bounc intgrals basd on circular concntric flux surfacs whras CQL3D prforms numrical bounc avraging in th actual noncircular tokamak gomtry. Although th 2D and 3D solutions of Eq. (1) can b computationally xpnsiv, th drivn LH currnt is straightforward to comput from a simpl vlocity momnt intgral. W hav also includd th LSC [8] and ACCOME [9] simulation modls in th bnchmark study. Ths cods mploy a Grn s function tratmnt [1] of th Fokkr Planck quation from which th drivn currnt is formulatd by convolving th rsulting rspons function (χ) with th wav-inducd RF flux (Γ rf ): J rf = d 3 χ p Γ rf, p Γ rf = D QL f p. (2) This approach is computationally fast and th rspons function (χ) includs 2D vlocity spac ffcts, particl trapping, and momntum consrving corrctions in th collision oprator. Howvr, th mthod rlis on an stimat for th wav inducd RF flux which is computd in both LSC and ACCOME from a 1D paralll vlocity spac solution of Eq. (1). Th LSC modl attmpts to account for 2D vlocity spac ffcts in th dissipatd powr first rportd in Rf. [11] by rplacing th lading cofficint [(2+Z ff )/2] of th collision oprator

3 3 in Eq. (1) with [(1+Z ff )/5]. A similar tchniqu is also usd in th FRTC cod [12] whr [(2+Z ff )/2] is rplacd by [(5+Z ff )/1]. Th ACCOME LHCD modl usd in th bnchmark includs 2D vlocity spac ffcts in th collision oprator by assuming th prpndicular dpndnc of th lctron distribution function is Maxwllian with an ffctiv prpndicular lctron tmpratur (T ) du to Fuchs [13]. Equation (1) is thn intgratd ovr prpndicular momntum rtaining an arbitrary T in th collision oprator intgrals [14]. Ths mthods mployd in LSC, FRTC, and ACCOME for trating th 2D powr dissipation ar found to b inadquat, spcially for ITER whr th quasilinar platau bcoms narrow rlativ to prsnt day xprimnts. 3. Rsults of LHCD Cod Bnchmark Study 3.1 Plasma quilibrium and LHRF Paramtrs Th plasma quilibrium usd for th LHCD cod bnchmark is shown in FIG. 1. Th quilibrium flux contours shown in Fig. 1(a) corrspond to th stady stat Scnario 4 [4] with R = 6.35m, a = 1.85m, B = 5.3 T, κ sp = 1.97, δ sp =.58, and β N = 2.57 (%-m-t/ma). Th total plasma currnt in this cas is 9 MA with wak rvrsd shar [q() = 3.44, q(min) = 2.58, and q(a) = 6.42]. Th lctron tmpratur and dnsity profils ar shown in Fig. 1(b) with cntral valus of 24 kv and m -3 rspctivly. Idntical tmpratur profils wr usd for th dutrons, tritons, and B 4 with cntral valus of 25.2 kv in ach cas. Th rlativ concntrations (n i / n ) of dutrium, tritium, and bryllium wr rspctivly (.416,.416,.42). A constant profil of Z ff was assumd with Z ff = Th 2D Fokkr Planck solvr (CQL3D) rquirs an up-down symmtric quilibrium. Thus th MHD quilibrium in Fig. 1(a) was first symmtrizd and translatd to th Z= plan and this rprsntation was thn usd by all th cods. 25 T n Z(m) T [kv], n [1 19 m -3 ] Normalizd toroidal flux R (m) FIG. 1(a): Magntic flux surfac gomtry for th stady stat ITER Scnario 4. FIG. 1(b): Elctron tmpratur and dnsity profils for th stady stat ITER Scnario 4.

4 4 Th LHRF sourc frquncy was takn to b 5. GHz and th coupld LH powr was 3 MW. In CQL3D-GENRAY, DELPHINE, and ACCOME ray trajctoris wr launchd from thr vrtical positions, Z = [-.4m, +.1m, +.6m] to modl th finit poloidal xtnt of th LH launchr. Th LSC ray tracing cod only allows rays to b launchd from a singl location, which was chosn to Z = +.1m in this cas. Th coupld LH powr spctrum was charactrizd in trms of th paralll rfractiv indx (n // = k // c / ω) as: 2 sin ( x) 2π S( n// ) = S, x = ( n 2 // n x n// max n // min // ). (3) Th cntral paralll rfractiv indx in th co-currnt driv (CD) dirction was varid with n // = (1.9, 2., 2.1), and in ach cas w took n //min = n // -.1, and n //max = n // +.1. Th cntral n // in th countr-cd dirction was fixd at n // = 3.8 during this scan. Th amplituds S wr chosn so that th powr in th forward lob dividd by th total powr was.87. This corrsponds to a dirctionality that is highr than th proposd passiv activ multi-junction launchr for ITER [4]. 3.2 Rsults of th LHCD Cod Bnchmark Study Th main rsults of th LHCD cod bnchmark study ar summarizd in Fig. 2. In that figur w hav plottd th prdictd LH currnt dnsity in th lft hand panls and th corrsponding LH powr dnsity in th right hand panls for th CQL3D-GENRAY, DELPHINE, ACCOME, and LSC simulations, moving from th top to th bottom of th pag. Th intgratd LH currnt has bn includd in th lft hand panls. A gnral trnd that is first apparnt is that th prdictd powr dissipation for th forward lob is pakd at a normalizd ( r/a) of.6 in th CQL3D, DELPHINE, and ACCOME simulations. Th forward lob in th LSC simulation damps a bit farthr out in radius at r/a.65. This could b causd by diffrncs in th MHD quilibrium and / or plasma profils usd with LSC, as compard to thos in Fig. 1. This would hav occurrd bcaus th LSC rsults shown in Fig. 2 ar part of a tim dpndnt ITER simulation [15] whr th plasma was bing volvd using th tokamak simulation cod TSC [16]. In all four simulations th rvrs powr lob at high n // (= 3.8) can b sn to damp at a lowr tmpratur at r/a >.9. An vn mor dramatic indication that th quilibrium profil data was diffrnt in th LSC simulation is th high lvl of forward powr that is dampd off-axis at r/a =.9 for th n // = 1.9 spctrum. Prsumably th ray trajctoris corrsponding to n // = 1.9 ncountrd a wav accssibility limit bfor damping most of thir powr via lctron Landau rsonanc and propagatd back to th plasma dg, undrwnt a radial rflction at that point and wr absorbd clos to th plasma dg. Som furthr indication that rays launchd nar n // = 1.9 ar barly abl to damp bfor bcoming inaccssibl can b sn in Fig. 3. Thr w hav plottd rays from th CQL3D-GENRAY simulation in th rang1.8 n // 2. (shown as grn to blu) and in th rang -3.9 n // -3.7 (shown as rd to purpl). A fw of th dark blu rays blow n // = 1.9 ar not absorbd and instad bcom inaccssibl and propagat to th plasma dg. Although most of th forward powr in th CQL3D-GENRAY simulation was dampd at r/a.6, th ray bhavior in Fig. 3 dos suggst that th wav propagation and absorption is snsitiv to dtails of th magntic quilibrium and profils, spcially whn th LH wavs ar propagating nar th accssibility limit [in this cas n //acc 1.6, assuming B 4.1T and

5 5 J LH (MA / m 2 ) 1..5 I LH = 1.99 MA I LH = 1.69 MA I LH = 1.44 MA CQL3D S LH (MW/m 3 ) N // = 1.9 N // = 2. N // = 2.1 CQL3D J LH (MA / m 2 ) 1.4 n // =1.9, I LH =1.8 MA n // =2., I LH =2.5 MA n // =2.1, I LH =2.6 MA DELPHINE S LH (MW/m 3 ) n = 1.9 // n = 2. // n = 2.1 // DELPHINE j LH (MA / m 2 ) I LH = 1.25 MA I LH = 1.21 MA I LH = 1.8 MA I LH =.95 MA ACCOME S LH (MW/m 3 ) n // = 1.9 n // = 2. n // = 2.1 n // = 2.2 ACCOME jlh (MA/m2) LSC ILH =.87 MA =.98 = 1.1 = PLH (MW/m3) LSC n = 1.9 = 2. = 2.1 = FIG. 2: Summary of LHCD simulations from CQL3D, DELPHINE, ACCOME, and LSC.

6 6 Z(m) R (m) FIG. 3: LH ray trajctoris from CQL3D-GENRAY simulation, plottd in th poloidal cross-sction. n m -3 nar r/a =.95]. Th DELPHINE simulation in Fig. 2 also shows som fraction of forward powr bing dampd nar th dg for n // = 1.9, although not as much as in th LSC simulation, consistnt with th fact that DELPHINE usd th quilibrium and profils shown in Fig.1. A scond gnral trnd sn in Fig.2 is that th mor complt 2D (vlocity spac) cods prdict highr currnts [( ) MA for CQL3D and DELPHINE] than th cods mploying a rspons function ray tracing approach [( ) MA for ACCOME and LSC]. This discrpancy is thought to b du to th fact that th 2D vlocity spac dissipation is not modld proprly by th 1D paralll vlocity spac wav damping usd in Eqs. (2) with th rspons function approach. In ordr to dmonstrat thr can b significant distortion of th distribution function in 2D vlocity spac, vn for a rlativly narrow quasilinar platau w hav plottd f (v, v // ) from th CQL3D simulation for n // = 1.9, at a radial location nar th maximum in th absorption profil (r/a =.65) (s Fig. 4). Dspit th narrow platau width thr is still noticabl distortion of f du to pitch angl scattring of lctrons into th prpndicular dirction. Morovr, th trappd-passing boundary in th co-cd dirction (solid black lin in Fig. 4) now lis quit clos to all platau lctrons that ar pitch-angl scattrd into th prpndicular plan. In fact, w know that trapping is an important ffct in ths simulations. W hav r-run th CQL3D cas for n // = 1.9 with trapping turnd off and found that th LH currnt incrasd by 4% from 1.99 MA to 2.8 MA, with th profil of drivn currnt rmaining th sam. Thus it is possibl in ths simulations that dtails of how trappd particls ar tratd in th various modls can b important. Som indication that this may b th cas is th diffrnc in drivn LH currnt in th CQL3D and DELPHINE modl prdictions. Rcall from Fig. 2 that DELPHINE prdicts up to 2.5 MA of LH currnt for n // = 2., compard to 1.69 MA for CQL3D. Som of this diffrnc could b du to th diffrnt tratmnts of particl trapping in th two modls, whr DELPHINE mploys analytic bounc intgrals in circular flux surfac gomtry whras CQL3D prforms a numrical bounc avraging in th noncircular FIG. 4: Nonthrmal lctron distribution contours from th CQL3D simulation for n // = 1.9, at r/a =.65.

7 7 tokamak gomtry. In addition, CQL3D formulats a bounc avragd quasilinar oprator, whras DELPHINE taks a mor simplifid approach in which th RF oprator is not bounc avragd [7]. 4. Lowr Hybrid Wav Absorption on Fusion Alpha-Particls Th qustion of parasitic absorption of LH wavs on fusion gnratd alpha-particls is an important issu for ITER as it dirctly impacts th choic of sourc frquncy. Although th choic of frquncy is partly drivn by th nd to avoid paramtric dcay of th LH pump wav [17], th mor critical nd for ITER is to kp th LH wav phas spd high nough so as to minimiz th intraction with nrgtic alpha particls. Th spatial profil of fusion alpha particls is important to know whn assssing this intraction. Rcntly [18] work has bn don to assss th ffcts of toroidal fild (TF) coil rippl and anomalous ion transport on th spatial profil of fast alpha-particls in th stady stat ITER Scnario 4. A simulation modl that combins th SPOT [19] orbit following Mont Carlo cod with th DELPHINE Fokkr Planck ray tracing packag [7] was modifid [18] to includ oprators in th Mont Carlo packag to account for spatial diffusion ffcts du to TF rippl and anomalous ion transport. Th simulatd fast alpha dnsity profils obtaind with th modifid Mont Carlo cod ar shown in Fig. 5. Th rfrnc alpha dnsity profil without rippl or anomalous transport ffcts is shown in blu in Fig.5. Th spatial profil obtaind by including a stochastic diffusion cofficint in th Mont Carlo oprator to FIG. 5: Alpha-particl dnsity (m -3 ) profils for ITER Scnario 4 with magntic fild rippl ffct (grn), with anomalous transport (rd), and rfrnc cas (blu). modl th TF rippl is shown as th grn curv in Fig. 5. Finally, th spatial profil rsulting from an anomalous ion diffusion cofficint of 1 m 2 /s in th Mont Carlo oprator is shown as th rd curv. Clarly, th anomalous ion diffusion has th biggst ffct on th spatial profil of alpha particls with th TF fild rippl having littl ffct in th rgion whr LH wavs would b xpctd to damp, i.. at r/a.6. Th spatial profils of alpha particl dnsity in Fig. 5 wr usd in th DELPHINE cod with a LH sourc frquncy of 3.7 GHz. Th prcntag of powr lost parasitically by th LH wavs to th alpha-particls was thn found to b 1.8%, 1.9%, and 7.7% for th rfrnc alpha profil, th profil with magntic rippl, and th profil with anomalous transport, rspctivly. Although th lvl of parasitic absorption was found to b non-ngligibl (7.7%) with th alpha profil rsulting from anomalous diffusion, it should b pointd out that th diffusion cofficint magnitud usd in this cas probably rprsnts an uppr limit. 5. Summary and Conclusions In this papr four simulation modls for LHCD wr bnchmarkd against ach othr on a plasma quilibrium rprsntativ of th stady stat ITER Scnario 4. It was found that th mor complt 2D (vlocity spac) Fokkr Planck ray tracing modls prdictd th highst drivn currnts ( MA). It was found that th simulation modls basd on a rspons function ray tracing approach prdictd significantly lss LH currnt and that this could b du to impropr tratmnt of 2D vlocity spac ffcts in th wav absorption. Diffrncs in

8 8 th drivn currnt wr also found among th 2D modl prdictions and may b rlatd to diffrncs in how th modls trat particl trapping and bounc avraging of th RF oprator. In th futur, CQL3D and DELPHINE will b run on th sam tst cas with particl trapping ffcts shut off. Also, th 2D modls should b compard with th prdictions of othr advancd Fokkr Planck tratmnts such as th DKE cod [2]. Th snsitivity obsrvd in th LHRF dposition profils at n //=1.9 for cods using slightly diffrnt quilibria will ncssitat a dirct comparison of LH ray trajctoris from th diffrnt ray tracing cods in futur work. Also in futur work th ffct of rducd dirctionality in th LH couplr spctrum will b quantifid. Finally, th orbit following Mont Carlo cod SPOT was modifid to includ th ffcts of spatial diffusion on fast alpha particls du to TF coil rippl and anomalous ion transport. It was found that an anomalous diffusion cofficint of 1m 2 /s could caus nough spatial diffusion in th alpha dnsity profil to incras th parasitic damping of LH wavs at 3.7 GHz from 1.8% (with no transport) to 7.7%. Futur work should includ simulations with SPOT and DELPHINE at 5 GHz in ordr to confirm that th parasitic damping drops to ngligibl lvls at th highr frquncy. [1] JARDIN, S.C. t al, Fusion Enginring and Dsign 38, 27 (1997). [2] SÖLDNER, F.X. t al., Plasma Physics and Controlld Fusion 39, B353-B369 (1997). [3] IDE, S., NAITO, O., OIKAWA, T. t al., 17th IAEA Confrnc on Fusion Enrgy (Yokohama, Japan, 1998), (IAEA, Vinna, 1998) Vol. 2 p [4] ITER Tchnical Basis Documnt (IAEA, Vinna, 21) Doc. No. GAO FDR R1., Sction [5] HARVEY, R.W. and McCOY, M.G., Procdings of th IAEA Tchnical Committ Mting on Advancs in Simulation and Modling of Thrmonuclar Plasmas, Montral, 1992, p , IAEA, Vinna (1993); US DOC-NTCC Doc. No. DE [6] SMIRNOV, A.P. and HARVEY, R.W., Bull. Am. Phys. Soc. 4,1837 (1995). [7] IMBEAUX, F. and PEYSSON, Y., Plasma Physics and Controlld Fusion 47, 241 (25). [8] IGNAT, D.W., Nuclar Fusion (1994). [9] DEVOTO, R.S., t al., Nuclar Fusion 32, 773 (1992). [1] KARNEY, C.F.F. and FISCH, N.J., Physics of Fluids 28, 116(1985). [11] KARNEY, C.F.F. and FISCH, N.J., Physics of Fluids 22, 1817 (1979). [12] TALA, T.J.J. t al., Nuclar Fusion 4, 1635 (2). [13] FUCHS, V. t al., Physics of Fluids 28, 3619 (1985). [14] BONOLI, P.T. and ENGLADE, R.C., Physics of Fluids 29, 2937 (1986). [15] KESSEL, C. t al., 21 st IAEA Fusion Enrgy Confrnc, (Chngdu, China, Octobr 16 21, 26) Papr IT/P1-7. [16] JARDIN, S.C. t al., J.L., Journal of Computational Physics (1986). [17] PORKOLAB, M., Physics of Fluids 2, 258 (1977). [18] SCHNEIDER, M., ERIKSSON, L.-G., BASIUK, V., and IMBEAUX, F., 33 rd EPS Confrnc on Plasma Physics and Controlld Fusion (Roma, Italy, Jun 19-23, 26). [19] SCHNEIDER, M. t al., Plasma Physics and Controlld Fusion 47, 287 (25). [2] DECKER, J. and PEYSSON, Y., Tchnical Rport EUR-CEA-FC-1736 EURATOM CEA Cadarach, Dcmbr, 24. This work was supportd in part by th US DoE undr contract Nos. DE-FC2 99ER54512 and DE-FC2-1ER54649.