Influence of the resonant magnetic perturbations on particle transport in LHD

Transcription

1 1 EX/P4-13 Influnc of th rsonant magntic prturbations on particl transport in LHD M.W. Jakubowski 1, P. Drwlow 1, S. Masuzaki 2, K. Tanaka 2, T. Akiyama 2, S. Bozhnkov, A. Dinklag 1, M. Kobayashi 2, T. Morisaki 2, Y. Narushima 2, S. Sakakibara 2, Y. Suzuki 2, R. Wolf 1, H. Yamada 2 1 Max-Planck-Institüt für Plasmaphysik, Wndlstinstr. 1, Grifswald, Grmany 2 National Institut for Fusion Scinc, Orochi-cho, Toki, Japan contact of main author: marcin.jakubowski@ipp.mpg.d Abstract. Purpos of ths studis is invstigations of non-linar plasma rspons on transport du to stochastic ffcts. At LHD, prturbation coils crat Rsonant Magntic Prturbation () with th m/n = 1/1 and 2/1 Fourir componnts. Dpnding on plasma conditions, th prturbation ithr nhancs or hals th natural m/n = 1/1 magntic island. In th cas of an amplifid island th nhancd hat and particl transport across th island causs a rathr significant rduction of th confinmnt. For a hald island thr is a rathr small dcras of of bta with incrasing prturbation currnt. Ths changs coincid with an incrasing width of th opn stochastic volum at th plasma dg nar th X-point. Additionally systmatic xprimnts wr prformd, changing th amplitud of th prturbation linarly with I in th rang of ka. Two scnarios wr ralizd: first, th discharg was rampd up with an xtrnal prturbation alrady suprimposd to th main magntic fild. Scond, th xtrnal prturbation was applid to th plasma alrady ignitd (typical cas of tokamaks with s). As it is shown, thr is a clar diffrnc in th siz of th 1/1 island and th dpndnc of n and T on th prturbation whn comparing thos two scnarios. To crtain amplitud of th xtrnal prturbation th hystrsis ffct is obsrvd and th particl transport and confinmnt ar affctd much strongr in th dischargs with pr-xisting magntic prturbation. Intrstingly abov crtain valu of prturbation currnt a global rduction of T and n profils was obsrvd indpndnt on th chosn scnario. 1. Introduction Mitigation and control of Typ-I Edg Localizd Mods (ELMs) is an important task for nxt stp fusion dvics lik ITER to cop with high plasma facing componnts powr loads. Thrfor, following th rsults obtaind on DIII-D [1], th Rsonant Magntic Prturbations (s) rcntly bcam a vry popular tool to control plasma xhaust in tokamaks lik JET or ASDEX-Upgrad and probably ITER. According to th prsnt undrstanding s rduc prssur gradints in th pdstal rgion by introducing a stochastic boundary allowing supprssing or mitigating ELMs whil kping th outward impurity transport nhancd. Th so calld pump-out [2] rsults from a pitch rsonant coupling of th xtrnal fild to th intrnal magntic fild. It is, howvr, unclar, what th plasma rspons is whn th fild pntrats from th outsid. In hlical dvics th 3D topology of magntic fild lins is an inhrnt fatur, which must b considrd in ordr to undrstand dg transport and xhaust. In stllarators and hliotrons dgr of stochastization is xtrnally controllabl by.g. adjusting th magntic quilibrium. Morovr, additionally on can apply xtrnal prturbation with th coils. In spit of diffrnt origins th stochastic boundary has similar faturs in tokamaks and hlical dvics, which rsults from htrognous opn fild lins rgion [3], [4] at th plasma boundary, whr magntic fild lins intrsct plasma facing componnts. This papr studis changs in transport at th Larg Hlical Dvic (LHD) du to rsonant magntic prturbations. A uniqu (in comparison to tokamaks, which nd plasma currnt to crat th poloidal fild) fatur of hlical dvics is possibility of

2 2 EX/P4-13 applying th magntic prturbation bfor plasma build-up with th main magntic fild componnts alrady prsnt. In this work w study th ffcts on non-linar plasma rspons on particl transport by studying: Effct of amplification/haling of th m/ n = 1/1 magntic island Comparing rsults of dischargs with xtrnal prturbation applid bfor plasma build-up to a typical tokamak cas with th s applid during th discharg. 2. Exprimntal st-up magntic flux [V s] 1.5 x cancl 0 ka a) b) toroidal angl ϕ [dg] FIG. 1 a) Top viw of LHD vssl with contours (thick black lins) of th prturbation coils. b) Shap of magntic prturbation as masurd by th magntic flux loops st at th outr ports of LHD. For mor dtails on orintation of magntic prturbation in rlation to 1/1 island s [7]. Th LHD is th largst oprating hliotron-typ plasma confinmnt dvic with poloidal/toroidal priod numbrs of 2/10 and is quippd with suprconducting hlical and poloidal coils. Typical plasma major and avrag minor radii ar R = 3.6 m and a = 0.6 m, rspctivly. Th hat and particl xhaust is ralizd with th hlical divrtor with a rathr complicatd dg magntic structur of an opn stochastic rgion btwn LCFS and rsidual X-point [5]. As th stochastic layr hr dos not rsult from an xtrnal prturbation, thr is no problm of nonlinar suprposition of th prturbation and a magntic quilibrium. This maks LHD an xcllnt tool to study xprimntally th stochastic boundary. In ordr to corrct rror filds or altr th 3D magntic topology, LHD is quippd with a st of 10 pairs of coils localizd at th top and bottom of th machin (s FIG. 1a). Th rsulting magntic 5 prturbation has a strngth of δb/ B ϕ 10 with th main mods bing m/ n= 1/1 and m/ n= 2/1. Evn if th amplitud of th magntic prturbation is rlativly small, it can hav a significant ffct on th magntic topology at th plasma dg. Ths changs can b prsntd with so calld Poincaré and laminar plots [6]. Exampls of such plots can b sn in FIG. 2. Thy ar calculatd with th fild lin tracing cod KMAG assuming a linar suprposition of an xtrnal prturbation and a magntic quilibrium. On of th most significant consquncs of nrgizing th prturbation coils can b th sding of a 1/1 island (locatd at R 2.9 m in th lft graph of FIG. 2), which can significantly dgrad th confinmnt. Actually, dpnding on th plasma conditions,.g. bta or collisionality and phas of th magntic prturbation on can ithr nhanc or hal th at LHD naturally xisting 1/1 magntic island [7]. Th othr ffct of applying a magntic prturbation is th cration of a stochastic boundary. Typically it is a combination of magntic fild lins of diffrnt connction lngth with complicatd 3D topology [3]. With rspct to th intraction of th fild lins with th plasma facing componnts, two kinds of fild lins with rathr

3 3 EX/P4-13 diffrnt transport proprtis ar xpctd: laminar fild lins - du to a short connction lngth thy ar assumd to guid th dg plasma through paralll transport radially outwards and dposit hat and particls onto th plasma facing componnts. Th adjacnt longr fild lins show a stochastic spatial distribution which causs nhancd radial fild lin displacmnts and thus an incrasd radial transport of particls and nrgy vn from th mor cntral rgions clos to th last closd flux surfac (LCFS). Th aras of diffrnt fild lin connction lngth ar rflctd in th htrognous structur of th plasma dnsity and tmpratur. FIG. 2 lft) Poincaré plots for LHD dischargs with β = 0% and currnt of 0 and 1.9 ka. right) Laminar plots of th ara nar th X-point for th sam conditions as Poincaré plots. Colours dnot connction lngth in mtrs. 3. Changs in transport du to magntic prturbation. Th ffcts of on transport in LHD plasmas is shown in FIG. 3, whr svral cass of diffrnt phas and amplitud of rsonant magntic prturbation ar dpictd. In top lft graph of FIG. 3 th changs in th plasma dnsity ar prsntd. Th dark gry lin shows a rfrnc cas without prturbation, i.. B ϕ = 2.75T, R ax = 3.6 m, β 0.7 % and lin 19 avragd dnsity n = 7 10 m -3. Adding th prturbation in both cass lads to global dnsity rduction causd by th rsonant magntic prturbations. Th phas of th s sms to hav an ffct on th plasma raction. For th ( +) phasing (rd curv in FIG. 1 b)) th 1/1 island grows at ρ 0.8 [7], which rsults in a global rduction of th plasma dnsity (s FIG. 3 top lft). As will b shown latr it is causd by th nhancd transport across th 1/1 island. At th sam tim also th lctron tmpratur profil is lowrd (top right graph of FIG. 3). Also rd (1.2 ka) and grn (1.9 ka) solid curvs show incras of th island width with th amplitud of th magntic prturbation. Thos changs rsult in a global chang of th confinmnt as shown in FIG. 3(d). Opn points show masurd plasma bta as a function of applid Prturbation currnt for th cas of ( + ) phas. Alrady at I LID 600 A th volum avragd β drops by 30% and dos not chang significantly whn incrasing Prturbation currnt to almost 2 ka. Th small dcras of confinmnt btwn 600 A and 2 ka is causd by chang in both: plasma dnsity and tmpratur. Changs in th dnsity and tmpratur (dashd lins in FIG. 3) du to magntic prturbation with th ( + ) phas (blu curv in FIG. 1b) ar not as dramatic as in th cas of th ( + ) phas. In th tmpratur profil on can rcogniz that th natural 1/1 island is hald and ithr dos not xist or its width is blow th diagnostic rsolution. Nvrthlss th plasma dnsity is globally dcrasing whn applying prturbation currnt as compard to a rfrnc cas of 0

4 4 EX/P4-13 ka. Th dcras, howvr, is not as profound as in th ( +) cas. Additionally, th lctron tmpratur is actually incrasing all ovr th plasma radius to such a lvl, that th plasma prssur profil (s FIG. 3, bottom lft) rmains unchangd as compard to th cas without prturbation. Th confinmnt loss is minor and happns only whn th prturbation currnt xcds 1 ka. In ( + ) cas, th rduction of p compard to th rfrnc cas is quit significant and is causd by nhancd transport du to th nlargd 1/1 island. In tokamaks similar changs in th dnsity ar causd by stochastic boundary [8]. Exprimntal vidnc showd that th combind ffct of th nhancd lctron outflow du to th stochastic boundary and rsulting chang in ExB shar is rsponsibl for nhancmnt of th radial particl transport and thus lading to th pump-out ffct in TEXTOR [9]. It would b intrsting to s if also at LHD similar mchanism is rsponsibl for altring th particl transport in invstigatd dischargs. Unfortunatly, during th xprimnts th diagnostics, which would allow to masur changs in ExB shar at th plasma boundary wr not prsnt at LHD, thrfor w cannot compar rsults of TEXTOR and LHD dirctly. Howvr, th indication for th nhancd transport du to th opn stochastic volum nar th plasma dg can b found in dnsity profils as masurd by th Thomson scattring. FIG. 4 shows a ratio of th lctron dnsity with and without magntic prturbation at two lvls of Currnt. A rathr significant drop of th rlativ dnsity (compard to a cas without xtrnal prturbation) happns nar th X-point locatd at R 4.65 m. With incrasing Prturbation currnt this ffct is strongr. It is consistnt with changs in magntic fild topology as shown in FIG. 4b). With incrasing amplitud of th magntic prturbation on a) b) nhancd hald c) d) LID currnt [A] FIG. 3. Elctron dnsity (a), lctron tmpratur (b) and lctron prssur (c) for cass without (solid gray), hald 1/1 island (dashd) and nhancd 1/1 island (solid). Data obtaind from Thomson scattring diagnostic. d) Plasma bta as a function of th prturbation currnt. β [%]

5 5 EX/P4-13 FIG. 4 lft) Changs in dnsity profils as masurd by Thomson scattring with producd by prturbation coils ( + ) cas in FIG.1. right) Changs in topology of stochastic boundary at th location of Thomson scattring. Colors dnot diffrnt connction lngth ( L c ) of magntic fild lins. Dark rd ara indicat rgions with L > 350m obsrvs chang in th structur of th stochastic rgion nar th X-point. Fild lins with vry long connction lngth (> 400 m) ar rplacd by laminar flux tubs with rlativly short connction lngth (~100 m). Th changs in th dnsity ar compatibl with th typical pictur of th nhancd convctiv losss du to opn flux tubs conncting th rgion nar th X-point with th plasma facing componnts. Ths ffcts hav bn first masurd in tokamaks,.g. TEXTOR [4], whr th rgion of highr gradint is pushd into th smallr plasma radii by introducing a laminar zon at th plasma dg, as wll as in hlical dvics [10]. 4. Transport inducd by th magntic island c In ordr to prform mor systmatic studis on changs in th particl transport with th amplitud of s a sris of dischargs with varying prturbation coil currnts wr prformd. Two cass wr ralizd: A discharg is ignitd with th xtrnal prturbation alrady suprimposd to a confining vacuum magntic fild (rd curvs in FIG. 5). During th cours of th discharg th amplitud of th magntic prturbation is rducd by ramping I LID down to 0 ka. On should not, that this scnario is not possibl in tokamaks, sinc on nds plasma currnt to crat main componnts of th magntic filds. Th prturbation coils ar nrgizd aftr th plasma build-up (blu curvs in FIG. 5) and I is rampd up to a maximum valu within 7s. This is a rathr typical xampl of th invstigations in tokamak plasmas. For both typs of dischargs th amplitud of th s was changd by scanning th prturbation coil currnt in th rang of ka. To facilitat masurmnts with long stabl plasma conditions ECRH with 1 MW injctd powr instad of NBI hating was usd.

6 6 EX/P4-13 From FIG. 5 it is clar that th dpndnc of th magntic confinmnt (rprsntd by plasma bta in FIG. 5) to th amplitud of th magntic prturbation is diffrnt in both cass. In th cas of th rampd up magntic prturbation β starts to drop at I 1 ka with an almost linar dpndnc on th prturbation currnt. For th lattr on, whr th magntic prturbation is rampd down, th linar drop of β with I LID starts alrady at a fw hundrd Amprs. Howvr, in spit of dissimilaritis at low prturbation coils currnt, both dischargs show intrsting fatur abov 2.3 ka: incrasing I dos not lad to changs in β anymor. Th tim trac of plasma bta saturats at about 0.15%. A diffrnc in th lowr thrshold for confinmnt changs can b most likly xplaind by a wakr pntration of th xtrnal prturbation fild applid to th xisting plasma in comparison to th cas, whr th plasma is ignitd with th magntic fild bing alrady suprimposd with th prturbation (s also [7], [11] for mor dtaild discussion). Indd, th island siz as indicatd by th dashd lins in FIG. 6 (a-b) shows diffrnt island widths for th sam Prturbation currnt. Th top graphs of FIG. 6 show a rlativ chang of lctron tmpratur (masurd by th Thomson scattring diagnostic). Th ordinat thr rprsnts LHD major radius, th abscissa th Prturbation coils currnt and th color map shows a ratio of T masurd during s to a rfrnc discharg. Th 1/1 island with its cntr at R 4320 mm shows a diffrnt volution dpnding on th applid scnario. As xpctd, in cas of ramping down th magntic prturbation (s FIG. 6b) th island disappars at I approaching 0 ka. Whn applying to th xisting discharg (s FIG. 6a) on obsrvs a thrshold (hr roughly 600 A) bfor th 1/1 island is inducd. For mor dtails on th pntration of th magntic prturbation into LHD plasmas s also th work of Sakakibara, t al. [11]. As alrady indicatd by bta masurmnts at I 2.3 ka, indpndnt on th chosn scnario, thr LID rf is a global drop of th lctron tmpratur profil to ratio of T / T 0.6, i.. th profil flattns ovr a larg rang of R. In ordr to invstigat th transport in a mor quantitativ way th so calld charactristic scal lngth for th radial gradints L / n tim [s] FIG. 5. Tim tracs of plasma bta (top) and prturbation coil currnt (bottom) Ris introducd, whr dn Ln = n dr, with dnsity gradints takn from th Thomson scattring masurmnts at diffrnt valus of coil currnt and R = 3.6 m is th plasma major radius. 3 1 Δβ 0.07% β [%] I LID [ka] up rfrnc down Δβ 0.07%

7 7 EX/P4-13 a) b) Charactristic scal lngth, LHD #108487, ramp up 0.1 ka 0.5 ka 1.0 ka 1.5 ka 2.0 ka 2.5 ka Charactristic scal lngth, LHD #108494, ramp down 0.1 ka 0.5 ka 1.0 ka 1.5 ka 2.0 ka 2.5 ka L n /R L n /R major radius - R [mm] c) d) major radius - R [mm] LID rf FIG. 6 (a-b) Ratio of lctron tmpratur masurd with and without prturbation ( T / T ) by th Thomson scattring diagnostic for a cas whr I was (a) rampd down and (b) rampd up. Dashd lins indicat island width. (c-d) Changs in charactristic scal lngths in particl transport. Cas (c) corrsponds to graph (a) and th cas (d) to th graph (b). Th rsults ar prsntd in FIG. 6 (c-d). Du to a lack of spac th charactristic scal lngths ar shown only for th dnsity gradints. Howvr, th sam quantitis calculatd for lctron tmpratur show a rathr similar bhavior. Th most visibl tndncy in FIG. 6 (c-d) is that raising th coil currnts flattns th gradints (indicatd by incrasing L n / R) within th magntic island cntrd at R 4.3 m. It is also clarly visibl in T profils shown in FIG. 3 and in FIG. 6. Although it happns for both scnarios (i.. ramping up - FIG. 6c and down - FIG. 6d), th ffct is strongr for th cas of pr-xisting magntic prturbation. Th hystrsis coms from th bttr coupling of th magntic prturbation with plasma magntic quilibrium and thus largr island width. Intrstingly, for I 2 ka th maximum dos not incras anymor. Instad, th flattning of th gradints xtnds towards largr radii with rathr sharp boundary at R 4.4 m for both cass. This suddn chang of th Ln drivativ points out a sparatrix of th 1/1 magntic island. Plas not, that th position of this sparatrix is indpndnt on th chosn scnario. It sms that th coupling of th magntic prturbation to th main fild abov crtain valu of I is rathr similar. This bhavior coincids with a flattning of

8 8 EX/P4-13 lctron tmpratur profils as sn in FIG. 6 (a-b). Enhancd gradints in dnsity and tmpratur appar at two locations: 4.1 R 4.25 m and R 4.5 m. Th outr ara ( R 4.6 m) was idntifid in Sc. 3 as th stochastic rgion nar th X-point, whr incrasing th prturbation changd th proprtis of magntic flux tubs. Th qustion rmains, what happns at (4.1 R 4.25)? For both scnarios a ris of th gradints is obsrvd, which could com from nhancd transport thr as wll as a raction of th plasma to th flattning of th lctron tmpratur and dnsity insid th magntic island. Nvrthlss it is important to notic, that on th contrary to th changs insid th island hr L / R dos not saturat for n I 2 ka. Again, although at low currnts th transformation is mor rapid for th pr-xisting prturbation, it rachs almost th sam valu of L / R 0.07 at n I = 2.9 ka. 5. Summary W hav invstigatd changs in transport du to 3D magntic topology at LHD. It appars that applying th magntic prturbation with main Fourir componnts of 1/1 and 2/1 can hav rathr significant ffcts on transport, whn sding a big 1/1 magntic island or rathr modrat whn th 1/1 island is hald. Th lattr ffct sms to com from th apparanc of th short connction lngth flux tubs nar th X-point. Dnsity rduction appars in both cass, whn applying rsonant magntic prturbation with high nough amplitud. Dpnding on th pntration of th magntic prturbation, which can b chosn by applying magntic prturbation ithr prior to ignition or during th discharg, changs in transport du to stochastic volum appar at vry low amplitud of LID coil currnts or at a givn thrshold, which dpnds on many factors (s [7], [11]). Howvr, abov 2 ka, th diffrnc disappars and both plasmas show similar lvl of transport across th stochastic boundary. Bibliography [1] T. E. Evans, t al., Natur Physics, vol. 2, no. 6 (2006) [2] O. Schmitz, t al., Physical Rviw Lttrs, vol. 103, no. 16 (2009) [3] M. W. Jakubowski, t al., Physical Rviw Lttrs, vol. 96, no. 3 (2006) [4] O. Schmitz, t al., Nuclar Fusion, vol. 48 (2008) [5] S. Masuzaki, t al., Nuclar Fusion, vol. 42, no. 6 (2002) [6] M. W. Jakubowski, t al., Nuclar Fusion, vol. 44, no. 6 (2004) S1 S11 [7] Y. Narushima, t al., Nuclar Fusion, vol. 48, no. 7 (2008) [8] O. Schmitz, t al., Journal of Nuclar Matrials, vol (2007) [9] J. W. Conn, t al., Nuclar Fusion, vol. 51, no. 6 (2011) [10] T. Morisaki, t al., Journal of Nuclar Matrials, vol (2003) [11] S. Sakakibara, t al., in ths procdings (IAEA San Digo, 2012) EX/P4 30.