ITER Performance Study with the Presence of Internal Transport Barrier

Transcription

1 J. Plasma Fuson Rs. SERIES, Vol. 8 (9) IER Prformanc Study wth th Prsnc of Intrnal ransport arrr hawatcha Onjun Plasma and Fuson Rsarch Unt, Srndhorn Intrnatonal Insttut of chnology, hammasat Unvrsty, Pathum han, haland (Rcvd: 5 Sptmbr 8 / Accptd: 11 Aprl 9) Slf-consstnt modlng of th Intrnatonal hrmonuclar Exprmntal Ractor (IER) has bn carrd out usng th 1.5D ALDUR ntgratd prdctv modlng cod. In ths smulatons, th boundary s takn to b at th top of th pdstal, whr th pdstal valus ar dscrbd usng a thortcal-basd pdstal modl. hs pdstal tmpratur modl s basd on magntc and flow shar stablzaton wdth scalng and balloonng mod prssur gradnt modl. h pdstal tmpratur modl s usd togthr wth a Mxd /g cor transport modl, whch can nclud th I ffct. It s found that th formaton of an I has a strong mpact on both tmpratur profls, spcally nar th cntr of th plasma. Wth th I ffct s ncludd, th cntral on tmpratur ncrass sgnfcantly. h ncras of cntral tmpratur rsults n a sgnfcant mprovmnt of alpha powr producton and, consquntly, fuson prformanc. It s obsrvd that n most of th plasma cor, th on thrmal dffusvty s smallr wth an I ncludd than n thos wthout th I n th IER smulatons. hs rducton n th dffusvty rsults n strongr gradnts and, consquntly, hghr valus of th cntral tmpratur. Kywords: Plasma, Fuson, IER, I, E, Pdstal 1. Introducton h Intrnatonal hrmonuclar Exprmntal Ractor (IER) s an ntrnatonal collaboratv ffort wth an am to dmonstrat th scntfc and tchnologcal fasblty of nuclar fuson usng th magntc confnmnt fuson concpt [1]. h goal of IER s to produc plasmas wth a suffcntly hgh nrgy dnsty for a long nough tm to achv sustand hgh-prformanc fuson burnng. Producng fuson ractons whch satsfy such a condton nsd a tokamak rqurs th ablty to both hat and contan hgh-tmpratur plasmas. Du to th fact that hgh confnmnt mod (H-mod) dschargs n tokamaks gnrally provd xcllnt nrgy confnmnt and hav accptabl partcl transport rats for mpurty control, many fuson xprmnts such as IER ar dsgnd to oprat n th H-mod rgm. h mprovd prformanc of H-mod manly rsults from th formaton of th dg transport barrr (E) [], calld th pdstal. It s also known that prformanc of H-mod plasma can b furthr mprovd wth th prsnc of a transport barrr nsd plasma, calld th ntrnal transport barrr (I) [3]. h prsnc of I n H-mod plasma rsults a complcatd scnaro and ylds an mprov prformanc of that plasma. h projctons of IER hav bn carrd out n many scnaros usng varous ntgratd modlng cods [4-8]. For xampl, th ALDUR ntgratd prdctv modlng cod [9] was usd to prdct th prformanc of IER for th standard H-mod scnaro [4, 6-8]. h prformanc of IER was valuatd n trm of fuson Q. Not that fuson Q s th rato of a fuson powr wth an appld hatng powr. A rang of th prformanc s author s -mal:thawatcha@st.tu.ac.th 347 prdctd. It was found that th prdctd prformanc of IER usng ALDUR cod wth th Mxd ohm/gyroohm (Mxd /g) transport cod s rlatvly low compard to thos usng othr transport cods [6-8]. It s worth notng that Mxd /g was dvlopd usng th JE plasma. In thos prvous works [6-8], th ffct of I was not ncludd n th smulatons. As a rsult, t s ntrstng to xplor th H-mod scnaro of IER whn I s prsnt. In ths work, th prlmnary study of th IER n th H-mod scnaro wth th prsnc of I s carrd out. h H-mod s rprsntd by th formaton of E. h E s dscrbd by a pdstal modl basd on magntc and flow shar stablzaton, and balloonng mod nstablty. For th I, th I s formd by th supprsson of cor anomalous transport. hs papr s organzd as follows: brf dscrptons for a ALDUR ntgratd prdctv modlng cod, anomalous transport modls, and pdstal modls ar gvn n scton. h IER prdcton usng a ALDUR ntgratd prdctv modlng cod s dscrbd n scton 3, whl concluson s gvn n scton 4.. ALDUR Cod h ALDUR ntgratd prdctv modlng cod s usd to comput th tm voluton of plasma profls ncludng lctron and on tmpraturs, dutrum and trtum dnsts, hlum and mpurty dnsts, magntc q, nutrals, and fast ons. hs tm-volvng profls ar computd n th ALDUR ntgratd prdctv modlng cod by combnng th ffcts of many physcal procsss slf-consstntly, ncludng th ffcts of transport, plasma 9 by h Japan Socty of Plasma Scnc and Nuclar Fuson Rsarch

2 . Onjun, IER Prformanc Study wth th Prsnc of Intrnal ransport arrr hatng, partcl nflux, boundary condtons, th plasma qulbrum shap, and sawtooth oscllatons. Fuson hatng and hlum ash accumulaton ar also computd slf-consstntly. h ALDUR smulatons hav bn ntnsvly compard aganst varous plasma xprmnts, whch yld an ovr all agrmnt wthn 1% rlatv RMS dvaton [1, 11]. In ALDUR cod, fuson hatng powr s dtrmnd by th nuclar racton rats and a Fokkr Planck packag to comput th slowng down spctrum of fast alpha partcls on ach flux surfac n th plasma. h fuson hatng componnt of th ALDUR cod also computs th rat of th producton of thrmal hlum ons and th rat of th dplton of dutrum and trtum ons wthn th plasma cor. h ffct of sawtooth oscllaton s also ncludd, whr a Porcll sawtooth modl [1] s usd to dtrmn a sawtooth crash and a modfd Kadomtsv magntc rconncton modl [13] s usd to dscrb th ffcts of sawtooth crash..1 I modl In ths work, th I s formd by th supprsson of cor anomalous transport du to Ex flow shar and magntc shar. hs ffct s ncludd n th anomalous cor transport calld th Mxd ohm/gyroohm (Mxd /g) modl [14]. hs cor transport modl s an mprcal modl. It was orgnally a local transport modl wth ohm scalng. A transport modl s sad to hav ohm scalng whn th transport dffusvts ar proportonal to th gyro-radus tms thrmal vlocty ovr a plasma lnar dmnson such as major radus. ransport dffusvts n modls wth ohm scalng ar also functons of th profl shaps (charactrzd by normalzd gradnts) and othr plasma paramtrs such as magntc q, whch ar all assumd to b hld fxd n systmatc scans n whch only th gyro-radus s changd rlatv to plasma dmnsons. h orgnal JE modl was subsquntly xtndd to dscrb on transport, and a gyroohm trm was addd n ordr for smulatons to b abl to match data from smallr tokamaks as wll as data from largr machns. A transport modl s sad to hav gyroohm scalng whn th transport dffusvts ar proportonal to th squar of th gyroradus tms thrmal vlocty ovr th squar of th plasma lnar dmnson. h ohm contrbuton to th JE modl usually domnats ovr most of th plasma. h gyroohm contrbuton usually maks ts largst contrbuton n th dp cor of th plasma and plays a sgnfcant rol only n smallr tokamaks wth rlatvly low powr and low magntc fld. o nclud th I ffct, th ohm contrbuton s modfd. h ohm/gyroohm transport modl wth I ffct ncludd [15] can b wrttn n th followng way: 1.. (1) g whr.5 g 4. no () D H D Z.3. 7 (3) 6 g 5 1 (4) 41 5 n R n q,.8,1., E.14 s. (5) IG h Ex s th flow sharng rat and th valu of IG, th IG growth rat, s stmatd as v t /qr, n whch t s th on thrmal vlocty. In, ALDUR cod, th Ex sharng rat s calculatd as follows: Ex R Er R, (6) whr R s th major radus, and ar th polodal and torodal magntc flds, rspctvly, s th polodal flux, and E r s th radal lctrc fld for th man plasma ons, whch s calculatd as follows: whr E r p 1 v v, (7) Zn r p r s th prssur gradnt, v and v ar th polodal and torodal vlocts and, n s th on dnsty, Z s th on charg numbr and th lmntary charg. Not that n ths work, th torodal vlocty s takn drctly from xprmnt.. E modls In th ALDUR cod, a boundary condton s st at th top of th pdstal. As a rsult, th cod rqurs both tmpratur and dnsty at th top of th pdstal. A smpl modl for stmatng pdstal tmpratur can b dvlopd by usng th valus of pdstal wdth and pdstal prssur gradnt [16]. In ths work, th pdstal wdth s stmatd usng a magntc and flow shar stablzaton concpt ( C w s ) [17] and th pdstal gradnt s stmatd usng frst balloonng mod prssur gradnt lmt. h ffct of bootstrap currnt and gomtry ar also consdrd. h pdstal tmpratur taks th followng form: c 4 kv. C s pd 33 W q M R n pd,19, (8) 348

3 . Onjun, IER Prformanc Study wth th Prsnc of Intrnal ransport arrr whr n pd,19 s th lctron dnsty at th top of th pdstal n unts of 1 19 m -3. In gnral, th pdstal dnsty (n pd ) n H-mod plasmas s a larg fracton of ln avrag dnsty (n l ). In th rport by G. atman t al. [4], th pdstal dnsty s takn to b n. 71 pd. (9) 3. Smulatons of IER h ALDUR ntgratd prdctv transport modlng cod s usd to carry out th smulatons of IER wth th dsgnd paramtrs (R = 6. m, a =. m, I p = 15 MA, = 5.3, 95 = 1.7, 95 =.33 and n l = 1.x1 m -3 ). In ths work, th plasma currnt and dnsty ar gradually rampd up to th targt valus wthn 1 sc. h plasma currnt at th start up phas s 3 MA and s slowly ncrasd to th targt. It s found that th plasma rachs th H-mod phas at th tm of sc. It s worth notng that thr ar svral physcs that hav not bn ncludd n ths smulatons, such as ELM crashs and noclasscal tarng mods. As a rsult, th smulaton rsults ar not approprat to rprsnt th dynamc of plasma n IER. Howvr, ths smulatons nclud nough physcs to dscrb plasma whn t rachs th stady stat. h smulatons stll yld complx and ntrstng ntractons wthn th plasma tslf such as th slf plasma hatng by th alpha partcl and rdstrbuton of hatng powr aftr sawtooth crash stll occurs and lads to ntrstng obsrvaton. Not that th sawtooth oscllaton s consdrd durng th tm of 1 sc to 995 sc. For ach smulaton, an anomalous transport s calculatd usng th Mxd /g transport modl, whl th noclasscal transport s computd usng th NCLASS modul [18]. h boundary condtons ar provdd at th top of th pdstal by th pdstal modl dscrbd abov, whch wll b vard latr to obsrv ts snstvty. It s assumd that th lctron and on pdstal tmpraturs ar of th sam valus. In ths smulatons, th auxlary hatng powr of 4 MW, whch s a combnaton of 33 MW NI hatng powr wth 7 MW of RF hatng powr, s usd. A slow currnt ramp (rachng th targt valu n 1 sc) s usd durng th frst stag of ach smulaton of th burnng plasma xprmnts. h plasma dnsty s also rampd up to th fnal plasma dnsty durng ths stag; whl th full hatng s appld snc th bgnnng. Not that th plasma dnsty s rampng up and controlld at th targt valus by usng gas puffng mthod. Durng ths ramp, th plasma maks a transton from L-mod to H-mod. Snc thr s a strong hatng at th bgnnng, all smulatons ntr th H-mod phas approxmatly n l wthn sc. In fgur 1, th torodal vlocty and Ex usd n ths work ar shown. h torodal vlocty s takn from an optmzd magntc shar (OS) dscharg n JE xprmnt, dscharg 454. h Ex profl s calculatd by Eqs. (6) and (7) by usng th torodal vlocty from th top panl of fgur 1. orodal vlocty (x1 5 m/s) Ex (x1 5 s -1 ) Fg Normalzd mnor radus h torodal vlocty (top) and Ex (bottom) profls usd n ths work ar plottd as a functon of a normalzd mnor radus. orodal vlocty profl s takn from JE xprmnt (dscharg 454), whl th Ex s calculatd usng Eqs. 6 and

4 . Onjun, IER Prformanc Study wth th Prsnc of Intrnal ransport arrr Ion tmpratur (kv) Elctron tmpratur (kv) Elctron dnsty (x1 19 m -3 ) Fg I xcludd I ncludd Normalzd mnor radus h profls for on (top) and lctron (mddl) tmpraturs and lctron dnsty (bottom) ar plottd as a functon of a normalzd mnor radus at tm of 1 sc. h smulatons ar carrd out wth and wthout th ffct of I. Fgur shows profls for on tmpratur (top), lctron tmpratur (mddl) and lctron dnsty (bottom) as a functon of normalzd mnor radus at a tm of 1 sc. h smulatons ar carrd out usng Mxd /g modl wth th ffcts of I xcludd and ncludd. It can b sn that all on and lctron tmpratur profls ar pak. Whn th ffcts of I ar ncludd, th cntral tmpratur ncrass sgnfcantly, whr th dg rmans th sam. It s found that th pdstal s almost constant aftr th dnsty rachs a targt valu. It s worth notng that th on pdstal tmpratur s assumd to b th sam wth th lctron tmpratur. Also, th ffct of ELMs s not ncludd n ths smulatons. For th lctron dnsty, th profl shap s a rlatvly small pak. It s also found that n both smulatons, th lctron dnsty profl s almost th sam, whch mans that th formaton of I dos not hav an mpact of dnsty profl. In addton, t s found that th I ffctv rgon s up to =.6. hs I rgon rsults from th rducton of th transport n th rgon clos to th plasma cor, whch can b sn n fgur 3. It s worth mntonng that th safty factor profl n ths IER smulaton s a monotonc profl wth a flat profl nar th plasma cntr, whch s dffrnt from what obsrvd n JE dscharg 454. hs subjct s byond th scop ths papr. It rathr lavs ths ssu for futur work. (m /s) Fg I xcludd I ncludd Normalzd mnor radus h profl of total on dffusvty s plottd as a functon of normalzd mnor radus from th cntr up to a normalzd radus of.8 at tm of 1 sc. h smulatons ar carrd out wth and wthout I ffcts. h summary of cntral tmpratur and dnsty s shown n abl 1. It can b sn that th cntral on tmpratur ncrass sgnfcantly whn th I ffcts ar ncludd. h cntral on tmpratur n th smulaton whn I s ncludd s about 36.7 kv, whch s n ffctv rang for fuson producton. h cntral on and lctron tmpraturs ncras 198% and 13%, rspctvly. hs ncras of cntral tmpratur wll hav a strong mpact on th plasma stord nrgy and th nuclar fuson powr producton. Fgur 4 shows th plasma stord nrgy as a functon of tm btwn 9 sc to 1 sc. It can b sn that th valu of plasma stord nrgy s n th rang 35

5 . Onjun, IER Prformanc Study wth th Prsnc of Intrnal ransport arrr of MJ for th smulaton wth I xcludd; whl th plasma stord nrgy ncrass to 45 MJ whn I s ncludd. abl 1: h summary of cntral tmpratur and dnsty at th tm of 1 sc. Paramtrs I xcludd I ncludd, [kv] , [kv] n, [1 19 m -3 ] pd [kv].6.6 n,pd [1 19 m -3 ] W tot (MJ) I xcludd I ncludd m (sc) Fg.4 h plasma stord nrgy s plottd as a functon of tm for th smulaton whn I s xcludd and ncludd. hr ar two typs of auxlary hatng usd n th IER smulaton. h total amount of nutral bam njcton hatng powr, P NI, s 33 MW. Anothr sourc of auxlary hatng s th RF hatng. h total amount of RF hatng powr s 7 MW. For smplcty, th RF hatng profls ar takn to b a parabolc shap, although t s rcognzd that th physcs of RF hatng mght b mor complcatd n th IER plasma. Not that Ohmc hatng s small compard to othr typs of hatng. h alpha hatng powr s also shown n fgur 5. It s found that th alpha hatng powr s th man hatng sourc of th plasma n th smulaton wth I. Howvr, th alpha powr hatng s slghtly hghr than th NI hatng powr n th smulaton wthout I. Fgur 6 shows th alpha powr producton from th smulatons whn I s xcludd and ncludd. It can b sn that th alpha powr from th smulaton whn I s ncludd s much hghr than that wthout I. h avrag of alpha powr durng th tm of 9 sc to 1 sc s summarzd n abl. h fuson prformanc can b valuatd n trm of Fuson Q, whch can b calculatd as Fuson Q 5 P, avg, P AUX whr P,avg s an avrag alpha powr and P AUX s an auxlary hatng powr (qual to 4 MW for ths smulatons). It can b sn n abl that th Fuson Q ncrass by % whn I s ncludd. abl : h summary of avrag alpha powr and corrspondng fuson Q. Paramtrs I xcludd I ncludd P [MW] Fuson Q Powr dposton (MJ/m 3 ) Powr dposton (MJ/m 3 ) Fg NI for lctron NI for on Alpha Powr otal Powr Normalzd mnor radus h powr dposton profls ar shown as a functon of normalzd mnor radus for th smulatons whn I s xcludd (top) and ncludd (bottom). 351

6 . Onjun, IER Prformanc Study wth th Prsnc of Intrnal ransport arrr Alpha Powr (MW) Fg m (sc) I xcludd I ncludd h alpha plasma producton s plottd as a functon of tm for th smulaton whn I s xcludd and ncludd. 4. Concluson Slf-consstnt smulatons of IER hav bn carrd out usng ALDUR cod, whr th ffcts of both E and I ar consdrd. h E condton s provdd by th pdstal modl basd on magntc and flow shar stablzaton wdth scalng togthr wth balloonng mod nstablty prssur gradnt modl; whl th formaton of I rsults from th supprsson of transport by E r x shar and magntc shar. It s found that th formaton of an I has a strong mpact on both tmpratur profls, spcally nar th cntr of th plasma. caus of th ncluson of th I ffct, th cntral on tmpratur ncrass mor than a factor of two. h ncras of cntral tmpratur rsults n a sgnfcant mprovmnt of alpha powr producton and, consquntly, fuson prformanc. In th smulaton wth I, t s obsrvd th rducton of on thrmal transport n most of th plasma cor, whch rsults n strongr gradnts and, consquntly, hghr valus of th cntral tmpratur. [4] G. atman t al., Plasma Phys. Control. Fuson 45, 1939 (3) [5]. Onjun t al., Phys. Plasmas 1, 8513 (5) [6]. Onjun t al., J. of Physcs: Confrnc Srs 13, 134 (8) [7] K. harasrsuth t al., hammasat Intrnatonal Journal of Scnc and chnology 13, 45 (8) [8] R. Pcha t al., Proc. of 35th EPS Confrnc on Plasma Physcs, Hrsonssos 9-13 Jun 8 (8) [9] C. E. Sngr t al., Comput. Phys. Commun. 49, 399 (1988) [1] D. Hannum t al., Phys. Plasmas 8, 964 (1) [11]. Onjun t al., Phys. Plasmas 8, 975 (1) [1] F. Porcll t al., Plasma Phys. Control. Fuson 38, 163 (1996) [13] G. atman t al., Phys. Plasmas 13, 755 (6) [14] M. Erba t al., Plasma Phys. Control. Fuson 39, 61 (1997) [15]. J. J. ala, t al., Phys. Control. Fuson 43, 57 (1) [16]. Onjun t al., Phys. Plasmas 9, 518 () [17] M. Sughara t al., Nucl. Fuson 4, 1743 () [18] W. A. Houlbrg t al., Phys. Plasmas 4, 331 (1997) 5. Acknowldgmnts h author thanks Prof.Dr.A H Krtz, Dr.G atman, Dr.V Paral, Dr.A Pankn, Dr.S Suwanna, Dr.N Poolyarat, and Dr.R Pcha for thr hlpful dscussons and supports. hs work s supportd by Commsson on Hghr Educaton (CHE) and th haland Rsarch Fund (RF) undr Contract No. RMU Rfrncs [1] R. Aymar t al., Plasma Phys. Control. Fuson 44, 519 () [] A. Hubbard, Plasma Phys. Control. Fuson 4, A15 () [3] J.W. Connor t al., Nucl. Fuson 44, R1 (4) 35