> 1.2 x m -3. A reduced q 95 limit is found for. hydrogen discharges. # Univ. New Mexico, Albuquerque, NM Columbia Univ.

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2 Pdstal profils and fluctuations in C-Mod nhancd D-alpha H-mods A.E. Hubbard, R. L. Boivin, B. A. Carrras*, R.S. Grantz, M. Grnwald, J. W. Hughs, I.H. Hutchinson, J. Irby, V. Klin #, B. LaBombard, Y. Lin, E.S. Marmar, A. Mazurnko, D. Mossssian, E. Nlson-Mlby, T. Sunn M. Porkolab, J. A. Snips, J. Trry, S. Wolf, S. Wukitch Plasma Scinc and Fusion Cntr, MIT, Cambridg MA, *Oak Ridg National Laboratory, Oak Ridg, TN, # Univ. Nw Mxico, Albuqurqu, NM Columbia Univ., Nw York, NY ABSTRACT High rsolution masurmnts on th Alcator C-Mod tokamak [I.H. Hutchinson t al, Phys. Plasmas 1, 1551 (1994)] of th transport barrir in th Enhancd D α (EDA) rgim, which has incrasd particl transport without larg dg localizd mods, show stp dnsity and tmpratur gradints ovr a rgion of 2-5 mm, with pak prssur gradints up to 12 MPa/m. Evolution of th pdstal at th LH transition is consistnt with a larg, rapid drop in thrmal conductivity across th barrir. A quasi-cohrnt fluctuation in dnsity, potntial and B pol, with f o ~ khz and k θ ~ 4 cm -1, always appars in th barrir during EDA, and drivs a larg particl flux. Conditions to accss th stady-stat EDA rgim in dutrium includ δ=> 0.35, q 95 > 3.5 and L-mod targt dnsity n > 1.2 x m -3. A rducd q 95 limit is found for hydrogn dischargs. 1

3 I. Introduction This papr rports on rcnt dg masurmnts on th Alcator C-Mod tokamak (C- Mod), primarily in th Enhancd D α, or EDA, H-mod rgim. Th high confinmnt, or H-mod rgim, first discovrd on th Axisymmtric Divrtor Exprimnt (ASDEX) in , is charactrizd by a dcras in particl and nrgy transport, and consqunt stpning of dnsity and tmpratur gradints, in a narrow rgion just insid th last closd flux surfac (LCFS). In rcnt yars it has bcom apparnt that th plasma paramtrs at th top of th transport barrir, or pdstal, can strongly affct global confinmnt, not only incrasing th stord nrgy, W, by th hight of th pdstal but also modifying th boundary conditions of cor transport. Svral xprimnts, notably C-Mod and ASDEX-Upgrad 2,3,4, hav shown corrlations btwn dg T and cor confinmnt and cor T, or btwn dg prssur and W. Such snsitivity has ld to xprimntal and thortical fforts to undrstand th physics and scaling of th dg pdstal 5, and to incras pdstal tmpratur and prssur. Unfortunatly, thr is a srious ngativ consqunc to incrasing pdstal nrgy. In most high powr xprimnts, th dg prssur is rgulatd by Typ I Edg Localizd Mods (ELMs) 6. Th dg gradints collaps priodically du to a magntohydrodynamic (MHD) instability, xplling much of th nrgy in th pdstal to th scrap-off-layr (SOL). This nrgy, which can b 5-10% prcnt of th total W, is rapidly transportd to th divrtor plats. Extrapolations to a ractor-grad plasma such as th Intrnational Tokamak Exprimntal Ractor (ITER) show that th rsulting hat puls would caus unaccptably high rosion of divrtor plats 7. From a divrtor standpoint, smallr, mor frqunt ELMs such as Typ III ELMs ar prfrabl. Howvr, ths sm to occur whn dg T, and thus confinmnt, ar only modratly abov L-mod. Th Enhancd D α rgim found on C-Mod may satisfy th conflicting rquirmnts of high confinmnt and divrtor hat loads. In this rgim th pdstal is rgulatd by a continuous transport procss, rathr than by priodic MHD vnts. First obsrvd in , it is charactrizd by much lowr particl confinmnt than ELM-fr H-mod, lading to stadystat conditions and lowr radiatd powr 9. Enrgy confinmnt is only modratly rducd, and is comparabl to that with Typ I ELMs on othr dvics. Rgular Typ I ELMs hav not yt bn obsrvd on C-Mod. Sinc th EDA rgim is vry attractiv for a ractor, undrstanding its caus and th conditions undr which it occurs and charactrizing th dg and global 2

4 paramtrs in EDA H-mod ar important aims of th C-Mod xprimntal program. Du to th compact siz (a=0.21 m, R=0.68 m) and high fild and dnsity (B T < 8 T, n < m 3 ) of C- Mod, th dvic occupis a uniqu paramtr spac and has vry narrow pdstals, with widths < 1 cm 10. Much of th rcnt progrss in undrstanding th EDA rgim has com from improvd masurmnts of th profils and fluctuations in th pdstal rgion. In th nxt sction, th stady-stat profils and tim volution of pdstal paramtrs, primarily n and T, ar prsntd. Sinc th rsults turn out to b similar in ELM-fr and EDA H-mods, both rgims ar covrd. Sction III givs dtaild obsrvations in th EDA rgim, in particular of quasi-cohrnt fluctuations which ar found to caus th nhancd particl transport. Th conditions to accss th rgim ar xamind. Possibl physical xplanations for th fluctuations ar discussd in Sction IV. II Pdstal charactristics and volution A. Diagnostics Svral high rsolution diagnostics hav bn addd to masur both pdstal profils and fluctuations. Of particular importanc is a nw high rsolution dg Thomson scattring (TS) diagnostic 11, which sampls th plasma vrtically at up to 22 spatial points, giving radial rsolution δr of 1.5 mm whn mappd to th midplan, and masurs T and n vry 33 ms. T profils ar also masurd with two lctron cyclotron mission (ECE) polychromators at th midplan, which hav lowr spatial rsolution but sub-ms tim rsolution 10. Th dnsity pdstal can also b infrrd from a CCD (charg coupld dvic) array masuring visibl brmsstrahlung 12, proportional to n 2 Z ff /f(t ), which has δt=1 ms and δr = 1 mm. Two soft x- ray arrays, with δr =1.5 mm, ar mainly snsitiv to pdstals in th dnsity of mdium Z impuritis, primarily fluorin. 13 High rsolution diagnostics of XUV and dutrium Lyman α mission nabl th photon radiation and local nutral dnsity and ionization rats to b masurd 14,15. Edg fluctuation diagnostics includ a rflctomtr masuring dnsity fluctuations at 5 critical dnsity layrs btwn 0.3 and 1.5 x m -3, which ar typically all in or nar th pdstal rgion 16. Phas contrast imaging (PCI), viwing vrtically and intgrating along vrtical chords, is abl to rsolv fluctuation wavnumbrs along th major radius using 12 channls with 3 mm radial spacing. Two scanning Langmuir probs masur fluctuations in dnsity and 3

5 potntial, as wll as dg n and T profils. For som dischargs a magntic fluctuation prob was addd to th midplan prob had. B. Pdstal paramtrs Figur 1: Pdstal profils of (a) lctron tmpratur from ECE (solid lin), TS (circls), and horizontal scanning Langmuir prob (triangls) (b) lctron dnsity from TS (circls), prob, (triangls) and brmsstrahlung (lin), (c) lctron prssur, from TS, and (d) missivity of soft x-rays (midplan viw, +) and XUV photon radiation (dashd lin, amplitud dividd by 10) for a 5.4 T, 1 MA EDA H-mod with 3 MW of RF powr. n is drivd from brmsstrahlung using n z ff / z av, whr th avrag z ff for this discharg is 1.4. An xampl of pdstal profils in T, n, p and soft x-ray and XUV missivity, obtaind in an RF hatd EDA H-mod discharg, is shown in Fig.1. In ordr to compar data from various diagnostics, all paramtrs ar mappd to th outr midplan. Uncrtaintis in flux rconstruction using EFIT 17, and in diagnostic positions, giv ris to rlativ rrors ~ 5 mm. It can b sn that all plasma paramtrs vary sharply ovr only a fw mm, with n and impurity dnsitis having th narrowst widths. Th stpst prssur and T gradints, xcding 10 MPa/m and 60 kv/m rspctivly, occur in th outr part of th pdstal, whr n also drops sharply. At this point T is lss than 200 V, so that th collisionality ν* is typically Insid this rgion T continus to incras for svral mm with a lowr gradint of ~25 kv/m, but still abov th cor T of ~ 10 kv/m. Th transition btwn dg and cor gradints, which sts th boundary condition for cor confinmnt, typically occurs btwn ψ== 0.90 and 0.95, whr 4

6 ψ=is th normalizd poloidal magntic flux. ECE masurmnts hav shown that this rgion of improvd T xpands inward with incrasing nt powr P in -P 4 rad ; th outr rgion of stpst T dos not xpand. In contrast, th dnsity pdstal is indpndnt of powr. In ordr to charactriz th hight and width of th pdstals in a systmatic way and compar with othr xprimnts, profils ar fit with a tanh function 18. Howvr, such functions cannot captur all of th structur rvald by TS profils; fittd widths tnd to dpnd on th xact rgion of th plasma fittd as wll as diagnostic rsolution. This may wll account for som of th data scattr and discrpancis notd in scalings using diffrnt diagnostics, and btwn diffrnt xprimnts 5. Scalings of pdstal paramtrs in RF-hatd H-mods hav bn xamind in a rang of plasma conditions, B T = T, I p = MA, P RF = 1-5 MW and lin avragd dnsity n= 1-6 x m -3. Th hights of th T and n pdstals show fairly clar dpndncs. As might b xpctd, n,pd is proportional to n. Th dg tmpratur at ψ=0.9 scals as ( P /n ) in 0.5± 0.1 at fixd currnt, and also incrass with I p. Thr is a strong corrlation btwn I p and both n,pd and n in H-mod. Th pdstal prssur thus also incrass with currnt. Th dpndnc is mainly in th prssur gradint p, rathr than pdstal width. Th bst mpirical scaling found for this is p I ν. Intrstingly, non of th lctron pdstal widths shows a 1.24± ± 0.03 p * pd clar dpndnc on I p. Widths do not gt systmatically narrowr, in contrast to scalings with ρ pol, β 0.4 pol or ρ 0.6 pol which hav bn rportd on th Japan Tokamak-60 Upgrad (JT-60U) and DIII-D xprimnts 19,20, but consistnt with masurmnts on ASDEX Upgrad 21. As has bn rportd prviously, th width of th x-ray pdstals dos dcras with I 22 p. Our prsnt undrstanding is that this rflcts th width of th impurity barrir, formd nar th top of th dnsity pdstal as a rsult of noclassical pinchs, and that it dpnds on th particl diffusivity 13. Th outboard x-ray width is also th only on to show a systmatic diffrnc btwn ELM-fr and EDA plasmas. It is widr in EDA, consistnt with th highr obsrvd impurity particl transport 22. T and n pdstal profils in ELM-fr and EDA H-mods with similar global paramtrs ar indistinguishabl. Th stability of idal infinit-n ballooning mods in th pdstal has bn analysd using TS profils, assuming T i is qual to T to driv th total prssur. For a discharg similar to 5

7 that shown in Fig. 1 which had P up to 12 MPa/m, nar th maximum obsrvd to dat, th gradint is found to xcd th first stability limit calculatd using only ohmic currnts, by about 40%. Howvr, whn th collisional dg bootstrap currnt is includd in EFIT rconstructions, th limit incrass and a narrow rgion of apparnt scond stabl accss appars. Th pdstal is thn found to b stabl to idal ballooning. C. Tim volution Sinc C-Mod uss ion cyclotron rsonanc hating (ICRH), which has continuously variabl powr, and th dg paramtrs ar masurd with milliscond tim rsolution, th tim volution of th H-mod pdstal can b followd both at th L-H and H-L transitions and as a function of powr. Figur 2 illustrats th bhaviour of T and n, both at r/a=0.86 which is inboard of th dg transport barrir, for an EDA H-mod discharg in which P RF was slowly rampd from MW and thn down to 0. Th top trac shows a jump in T dg btwn L- mod and H-mod, on a fw ms tim scal, as wll as a modrat dpndnc on powr in ach rgim. This clarly shows th bifurcation in thrmal transport. Strong hystrsis btwn th L- H and H-L powr thrsholds can b sn. As prviously found on C-Mod, data ar consistnt with a thrshold in dg tmpratur, or a closly rlatd quantity, to ntr and rmain in H- mod 23. Th dnsity, in contrast, also shows a bifurcation at th L-H and H-L transitions but dos not vary with powr in ach rgim. Sinc th fulling coms only from dg ionization, which dpnds on dg profils, both particl transport and sourcs ar diffrnt in L and H- mod 15. 6

8 Figur 2: Variation of T (top) and n (bottom) at r/a=0.86 vs nt powr P in -P rad, at 0.5 ms intrvals during a singl 5.4 T, 0.8 MA discharg with slowly varid RF powr. Arrows indicat th dirction of tim volution. Points abov th dashd lin ar in H-mod, which is EDA aftr th first fw ms. Th fast volution at th L-H transition of a similar discharg with a powr ramp is shown in Figur 3(a). Both dg T and n ris sharply, with initial rats of ~20 kv/s and 2.3 x10 21 m -3 /s rspctivly. All ECE channls in th dg rgion show a simultanous brak in slop, within th xprimntal dtrmination of 0.5 ms; th rat of incras is largst nar th top of th pdstal. Variation of dp/dt from 0.6 MW/s to 11 MW/s did not giv a systmatic variation of dt /dt, indicating that th dg T is not a uniqu function of th incrmntal powr P-P thrsh. Rathr, th rat of incras in nrgy is consistnt with a suddn drop of χ across th transport barrir, so that th whol input powr P thrsh is ffctivly blockd and contributs to th rapid pdstal formation. 7

9 Figur 3: (a) Evolution of T (top trac), n (middl trac) and w =kn T, masurd at r/a= 0.88, at th L-H transition for a 5.4 T, 0.8 MA EDA H-mod discharg with n = 1.8 x m -3 in L-mod. Th dashd lin in th bottom panl shows th prdiction of Eq. 1, taking χ A = 0.5 m 2 /s and χ b = 0.02 m 2 /s. (b) Sam paramtrs, for a discharg idntical xcpt that L-mod Th volution of th nrgy pdstal which would rsult from a dcras in transport from an anomalous diffusion cofficint χ A to a rducd lvl χ b in th barrir (g χ no ) has bn modlld both numrically and analytically. For constant powr flux q in, th gratst chang occurs at th tim of th transition and at th insid of th rgion of dcrasd transport, whr ( χ χ ) dw / dt = q q = 1 / q and w pd is th total pd in out b A in n = 1.18 x m -3, which rmains ELM-fr. Not th highr T scal. Th sam χs ar usd to prdict w (t). plasma nrgy at th pdstal top. Its volution aftr th transition (t=0) is givn by 8

10 ( χ χ ) q A b wpd () t = wpd ( 0) + t (1) π χ χ χ 1/2 1/2 ( + ) b A A Th prdictd rats of chang at othr positions ar slowr, and hav a mor complicatd tim dpndnc. Th thick solid lin in th lowr trac of Fig. 3(a) shows th prdiction of Eq. 1, taking χ A = 0.5 m 2 /s, dtrmind from an L-mod powr balanc analysis, and χ b = 0.02 m 2 /s. This simpl modl agrs quit wll with th masurd w pd, which dos hav an approximatly t 1/2 dpndnc. Th volution of a lowr dnsity, ELM-fr discharg is shown in Fig. 3(b) and is again fairly wll dscribd by Eq. 1, taking th sam conductivitis; th xprimntal w pd is slightly highr. Howvr, th rlativ contributions of T and n ar vry diffrnt. At low dnsity th T transint clarly dominats and th dnsity ris is 8 tims wakr, 3 x10 20 m -3 /s. This rflcts variation in th particl sourc availabl to ful th H-mod at low dnsity. Th total ionization rat drivd from Lyman=α=masurmnts is also about an ordr of magnitud lowr, ~5 x10 20 /s. At highr dnsity, with a sourc rat of ~6 x10 21 /s, th two trms in th prssur incras ar comparabl. A mor complt transport analysis of th transint bhaviour at othr radii and plasma conditions will b prsntd in a sparat publication. III. EDA H-mod A. Global Charactristics Th dfining global fatur of EDA H-mods is that thy hav much lowr particl confinmnt, both of th main spcis and of impuritis, than ELM-fr H-mods. Th lowr τ p in EDA has bn shown most clarly by impurity ablation xprimnts 24, and is also rflctd by a dcras in th rats of ris of both dnsity and radiatd powr. n and P rad usually rach a stady stat, as shown in Fig. 4. Stady phass of up to ~8 τ E hav bn achivd, limitd only by th duration of th plasma discharg and th RF powr. Th chang in τ p is usually accompanid by an incras in th D α mission to a lvl comparabl to L-mod, lading to th nam of th rgim. Enrgy confinmnt in EDA H-mod is also lowr than in ELM-fr H- mods, but by a much smallr fraction than th particl confinmnt. Th H-factor, dfind as th ratio of τ E to th H-mod scaling τ 25 ITER89-P, can b up to 2, with ~1.8 bing mor typical. τ E is consistnt with th ELMy H-mod scaling, ITER98y2 26. Th major advantag of th EDA 9

11 rgim ovr Typ I ELMy H-mod is that th incrasd particl transport occurs by a continuous, rathr than an intrmittnt, procss. Figur 4: High powr, stady EDA H- mod with B T =5.4 T, Ip=1 MA. Paramtrs shown, from top, ar n (10 20 m -3 ), cntral T (kv), stord nrgy (kj), τ E /τ ITER89P, midplan D α (mw/cm 2 /Sr), launchd RF powr and P rad (dashd lin) (MW). B. Fluctuation Masurmnts Coincidnt with th obsrvd incrass in particl transport in th EDA rgim, quasicohrnt (QC) dg fluctuations ar always obsrvd on svral diagnostics. Th tim volution of dnsity fluctuation spctra on PCI and rflctomtr signals for thr short H-mods is shown in Fig. 5. Th first H-mod is ELM-fr, and shows no fatur. In th two EDA H-mods, a pak in th spctra appars, with f initially abov 200 khz and subsquntly dcrasing to 120 khz as th pdstals volv. Th pak frquncy in stady EDA is usually in th rang of khz. Th frquncy spctrum, which has f/f ~ (full width half maximum), and th wavnumbr spctrum, cntrd at k R ~6 cm -1, ar masurd by PCI. Th wavnumbr k R, masurd along a major radius at th top and bottom of th plasma, corrsponds to a poloidal wavnumbr of k θ ~ 4 cm -1. Th lin intgratd amplitud of th dnsity fluctuations is up to 5 x m -2. Whil th PCI cannot provid spatial localization, this information is obtaind from th 10

12 rflctomtr and Langmuir probs. Th mod is sn nar th midplan on rflctomtr channls which ar locatd in th stp dnsity rgion of th pdstal, and dos not xtnd abov th barrir. It appars at diffrnt dnsity layrs dpnding on n,pd. Th transition from th ELM-fr to EDA rgim is also typically accompanid by an incras in th broadband rflctomtry fluctuations, up to at last 400 khz. Frquncy (khz) Frquncy (khz) Dα (W/sr/m 2 ) Rflctomtr Phas Contrast Imaging # ELMfr EDA EDA Tim(sc) Figur 5: Contour plots of dnsity fluctuation signals from rflctomtry (top) and PCI (middl) vs frquncy and tim, in a sris of 3 short RF-hatd H- mods, as shown by th D α mission (bottom). Th EDA H-mods hav a quasi-cohrnt fatur dcrasing in f to ~120 khz. Fast scanning probs, which masur abov and blow th midplan and hav bn insrtd past th LCFS only in low powr ohmic H-mods, also s a strong cohrnt mod in dnsity and potntial at th sam frquncy. Th structur and radial location of th mod ar shown in Fig. 6. Th amplitud of th fluctuation in potntial (6a) only incrass onc th prob pntrats to within 1 mm of th sparatrix, th sam location at which th pdstal dnsity gradint (6b) bcoms larg. It rachs a strong lvl, with local fluctuations of ordr 50% in both n and Φ. Th amplitud drops ~1mm insid R sp, so that th mod is apparntly localizd within a rgion of width ~ 2mm. It is possibl, howvr, that th dp pntration of th prob is somhow affcting th fluctuations locally. Dirct vidnc that th obsrvd quasi-cohrnt 11

13 fluctuations ar indd rsponsibl for much of th nhancd particl transport is obtaind by corrlating dnsity and potntial fluctuations. Th flux Γ=calculatd from ne, shown in Fig. 6(c), rachs a high lvl of 1.2 x /m 2 s. In ELM-fr H-mod, in contrast, th transportd flux is an ordr of magnitud lowr. Whil thr ar significant uncrtaintis associatd with such stimats, this strongly suggsts that th physics bhind th incrasd particl transport of th EDA rgim is linkd to th origin of ths quasi-cohrnt fluctuations. In fact, th apparanc and strngth of th fluctuations is now considrd th most rliabl signatur of th transition btwn ELM-fr and EDA H-mods in ithr ohmic or RF hatd dischargs. Figur 6: Langmuir prob masurmnts in an ohmic EDA discharg with I p =0.72 MA and B T = 2.6 T. Th two tracs ar obtaind during inward and outward prob scans. (a) amplitud Φ of cohrrnt fluctuations (V), (b) dnsity profil (10 20 m -3 ), (c) particl flux Γ (10 20 /m 2 s) drivd from ne for all fluctuation frquncis. Prsumably bcaus of th high k of th fluctuations, no magntic signatur corrsponding to th quasi-cohrnt mod has bn dtctd on pick-up coils locatd in th vacuum vssl wall or limitr surfacs. In ordr to dtrmin if th mod has a magntic componnt, a small B p prob was mountd on th fast scanning prob had so that it could b movd clos to th sparatrix. A vry clar magntic signatur, up to 200 T/s, was thn sn in th EDA rgim. This mod has th sam frquncy and tim volution as th lctrostatic 12

14 fluctuations sn by th rflctomtr and Langmuir prob. Th pak obsrvd mod amplitud is ~3x 10-4 T, corrsponding to high local currnt prturbations, of ordr 10 A/cm 2 and ~10% of th dg currnt dnsity. Th QC mod thus has a significant magntic componnt. Th mod amplitud droppd off vry rapidly with radius, typically as xp(-1.6 cm -1 r), consistnt with k θ ~ 1.6 cm -1 and with th lack of signal on limitr coils, which cannot dtct lvls blow10-7 T. In contrast, Typ III ELM prcursors masurd by th scanning magntic prob during th sam discharg sris, which had f~160 khz, wr sn by wall-mountd probs with an amplitud only ~20 tims lowr than nar R sp. This is consistnt with a lowr k θ ~ 0.5 cm -1, as has prviously bn rportd for ELM prcursors 27,28. Th QC mod thus diffrs from such prcursor activity. C. Conditions to accss th EDA rgim EDA H-mods hav now bn obtaind routinly on C-Mod ovr svral run campaigns and a wid rang of plasma conditions. Systmatic studis of th paramtrs which favour accss to th rgim hav bn prformd. As has prviously bn rportd 24, th most consistntly important conditions ar th safty factor, q, and th plasma triangularity, δ. In dutrium plasmas, low q 95 (< 3.5) and low δ (< 0.3) favour ELM-fr dischargs. High q 95 (> 4.0) and highr=δ (> 0.35) favour EDA. Thr may b an uppr limit to δ==for EDA, but this oprational spac has not bn wll xplord. Th dpndnc on longation, if any, appars to b wak. An ion mass dpndnc was rcntly found in xprimnts with hydrogn plasmas. EDA H-mods wr obtaind vn at q 95 =2.5, th lowst stabl valu achivd without disruptions. EDA H-mods hav bn obtaind both with ICRH and with ohmic hating alon 29, showing that fast particls do not play a significant rol and that high powr is not ssntial. For xampl, th discharg shown in Fig.2 transitiond to EDA with powr at th LH thrshold, and n rmaind in stady stat at powrs down to th H-L thrshold. On th othr hand, in som dischargs whr q is marginal for EDA, rducing th RF powr lads to wakr particl transport and to incrasing dnsity and impurity radiation. Ohmic EDA H-mods hav bn obtaind at B T as low as 2.5 T and I p down to 0.54 MA. 13

15 A thrshold for EDA in targt dnsity at th L-H transition is obsrvd 30. In a sris of H-mods (two of which ar shown in Fig. 3) with q 95 = 4.7 and=δ = 0.42, wll within th usual EDA rang, ELM-fr H-mods with no fluctuations wr consistntly producd whn th targt n was lss than 1.2 x m -3. As th dnsity was raisd shot to shot, fluctuations appard and particl transport bcam progrssivly strongr. Figur 7 illustrats th gradual transition from ELM-fr to EDA transport. Each point corrsponds to a diffrnt H-mod, with th H-mod tim slic takn at 80 ms (~τ E ) from th L-H transition to avoid th initial transints. Th rat of incras of n (7a) is an indication of dutrium transport. High rats indicat that particls ar accumulating rapidly, as is typical of ELM-fr dischargs, whil low rats show an approach to stady stat. dp rad Figur 7: Fluctuations and indicators of particl transport in a sris of 5.3 T, 0.8 MA H-mods with varying targt dnsity at th L-H transition. H-mod tims ar takn 80 ms aftr th transitions. / dt (not shown) has a vry similar trnd. Anothr masur of impurity transport is th width of th x-ray missivity pdstal (7b, diamonds), which calculations show dpnds on D imp 13. Th D α mission nar th midplan is shown for comparison (opn squars). Th amplitud of th QC dnsity fluctuations on PCI ar intgratd ovr 40 khz about th spctral pak (7c). Th dashd lin rprsnts th minimum broadband lvl of fluctuations; points clos to this hav no visibl cohrnt fatur. All of ths indicators (a) dn / dt, which drops as stady stat is approachd. (b) D α mission (squars, in mw/cm 2 /Sr) and width of th X-ray pdstal (diamonds, in mm), which dpnds on impurity diffusivity. (c) Amplitud of cohrnt fatur in PCI fluctuations. 14

16 of EDA vary smoothly as n is incrasd from 1.1 to 2.0 x m -3. In particular, th amplitud of th QC dnsity fluctuation corrlats wll with all masurs of particl transport, giving furthr vidnc that this mod is indd rsponsibl. This soft thrshold for EDA is typical of othr boundaris, such as thos in q or δ, so that som dischargs ar difficult to classify as ELM-fr or EDA. It should b notd that th thrshold dnsity, whil highr than typical dnsitis on othr tokamaks, is quit low for C-Mod, only 15% of th Grnwald dnsity limit and clos to th low dnsity limit for obtaining H-mods. It is thus not clar how to xtrapolat this condition to othr dvics. Th actual thrshold is likly to dpnd on a rlatd quantity, such as th midplan nutral prssur, pdstal dnsity or n, or dg collisionality. All of ths paramtrs ar closly corrlatd; in particular, th low dnsity ELM-fr dischargs had ν* < 1 at th pdstal midpoint, whras mor typical highr dnsity H-mods hav ν* ~5-10. IV. Discussion H-mods with at last som similaritis to th EDA rgim hav bn obsrvd in svral othr xprimnts. Quasi-cohrnt fluctuations which had many similar faturs to thos on C- Mod wr rportd in arly H-mods on th Princton Divrtor Exprimnt (PDX) 31. Ths tndd to occur in short bursts and wr apparntly sn in most H-mods, including thos with ELMs. A Low Particl Confinmnt rgim with global faturs quit similar to EDA was rportd in a fw RF hatd dischargs in th Joint Europan Torus (JET) 32. Howvr, rcnt attmpts to rproduc it hav not bn succssful 33. Probably th most common rgim combining small ELMs and good nrgy confinmnt is H-mod with Typ II or Grassy ELMs. Ths dischargs, which hav bn obsrvd on DIII-D 34, JT-60U 35 and most rcntly on ASDEX Upgrad 36, ar charactrizd by a dcras in th amplitud and incras in th frquncy of (normally Typ I) ELMs, oftn accompanid by a gnral incras in th D α lvl. Th conditions for ntring this rgim, particularly in q and shaping, bar strong similaritis to thos for EDA; th rquirmnts for dnsity ar lss clar. Howvr, pdstal fluctuation diagnostics, which could dtrmin whthr a QC fatur similar to that on EDA was prsnt, wr not availabl for ths othr xprimnts. Such masurmnts would b of grat intrst to dtrmin whthr th Typ II and EDA rgims hav a common physical origin. Th abov tokamaks oprat at lowr fild, and typically at highr β N, than C-Mod. It should b mntiond that that small ELMs do appar in high powr C-Mod dischargs whn β N > 1.2. Most rcntly, 15

17 a quiscnt H-mod rgim has bn rportd on DIII-D 37. It is charactrizd by continuous dnsity and magntic fluctuations localizd in th pdstal. Howvr, this mod apparntly has much longr poloidal wavlngth than that sn on C-Mod, and only appars whn th dg nutrals ar lowrd by cryopumping. Now that dtaild masurmnts of th pdstal profils and fluctuations in EDA H- mods ar availabl, work is in progrss to idntify th physical origin of th mod rsponsibl for th nhancd particl tranport. Sinc this fluctuation is continuous and at high ω and k, it is likly to involv a microinstability rathr than larg-scal MHD instability. Howvr, w now know that it has a substantial lctromagntic as wll as lctrostatic componnt. Sinc pdstal paramtrs and gradints ar, somwhat surprisingly, not markdly diffrnt in EDA and ELMfr H-mods, it appars that th stability conditions for th mod must b changing; th conditions for EDA thus giv som indication of which instability might b involvd. Drift ballooning mods ar bing considrd as on possibility. A cohrnt fatur somwhat similar to th QC mod, which has k 2 π /L θ pd, has bn found in lctromagntic dg turbulnc simulations by Rogrs and Drak 38. Th condition for diamagntic stabilization of such mods scals as m 1/2 /q, so that thy bcom mor unstabl at high q, consistnt with EDA obsrvations. Th substantially lowr q thrshold found for EDA in H vs D dischargs is also consistnt with such a scaling. W plan to study th growth rats of this instability, and its dpndnc on paramtrs such as shaping and ν*, using a gyrokintic stability cod. Whil mor thortical and xprimntal work rmains to undrstand fully th physics of th EDA rgim, th rsults to dat show that stady stat, high confinmnt dischargs can b rliably and rproducibly producd undr a wid rang of plasma conditions. Th rgim appars attractiv for fusion ractor applications, providd sufficint plasma shaping is possibl. Comparison of EDA with similar rgims on othr tokamaks would b vry usful in ordr to build up a databas of rsults undr diffrnt dimnsional conditions and idntify which dimnsionlss paramtrs, in particular thos rlatd to dnsity, might b important. ACKNOWLEDGEMENTS Th authors wish to acknowldg th fforts of th ntir Alcator C-Mod tam, in particular th RF group, in carrying out th xprimnts rportd hr. This work was supportd by U.S. Dpt. of Enrgy Contract No. DE-FC02-99ER

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