Experimental Validation of a Filament Transport Model in Turbulent Magnetized Plasmas

Expe imen al Valida ion o a Filamen T anspo Model in Tu bulen Magne ized Plasmas D. Ca ale o,1P. Manz,2L. Aho-Man ila,3G. Bi kenmeie ,1,2 M. B ix,4M. G o h,5H. W. Mülle ,1,6 U. S o h,1,2 N. Vianello,7,8 E. Wol um,1ASDEX Upg ade eam,1JET Con ibu o s,*and EURO usion MST1 Team† 1Max-Planck-Ins i u e o Plasma Physics, Bol zmanns aße 2, Ga ching, Ge many 2Physik-Depa men E28, Technische Uni e si ä München, James-F anck-S aße 1, Ga ching, Ge many 3VTT Technical Resea ch Cen e o Finland, Helsinki, Finland 4EURO usion Conso ium, JET, Culham Science Cen e, Abingdon, OX14 3DB, Uni ed Kingdom 5Aal o Uni e si y, Espoo, Finland 6Ins i u e o Ma e ials Chemis y and Resea ch, Uni e si y o Vienna, Wh inge s asse 42, A-1090 Vienna, Aus ia 7Conso zio RFX, C.so S a i Uni i 4,I-35127 Pado a, I aly 8Ecole Poly echnique Fédé ale de Lausanne (EPFL), Swiss Plasma Cen e (SPC), CH-1015 Lausanne, Swi ze land (Recei ed 28 May 2015; published 17 No embe 2015) In a wide a ie y o na u al and labo a o y magne ized plasmas, ilamen s appea as a esul o in e change ins abili y. These con ec i e s uc u es subs an ially enhance anspo in he di ec ion pe pendicula o he magne ic ield. Acco ding o ilamen models, hei p opaga ion may ollow di e en egimes depending on he pa allel closu e o cha ge conse a ion. This is o pa amoun impo ance in magne ic usion plasmas, as high collisionali y in he sc ape-o laye may igge a egime ansi ion leading o s ongly enhanced pe pendicula pa icle luxes. This wo k epo s o he i s ime on an expe imen al e i ica ion o his p ocess, linking enhanced anspo wi h a egime ansi ion as p edic ed by models. Based on hese esul s, a no el scaling o global pe pendicula pa icle anspo in eac o ele an okamaks such as ASDEX-Upg ade and JET is ound, leading o impo an implica ions o nex gene a ion usion de ices. DOI: 10.1103/PhysRe Le .115.215002 PACS numbe s: 52.35.Ra, 52.35.Py, 52.55.Fa, 94.30.cq In e change ins abili ies a e a ubiqui ous phenomenon in magne ized plasmas whe e a densi y g adien coexis s wi h a pa allel o ce densi y o he same sign [1]. This ins abili y leads o he o ma ion o elonga ed s uc u es known as ilamen s, lux ubes o p ominences ea u ing a dipole elec ic pola iza ion in he pe pendicula plane. The esul ing E×Bd i p opels he ilamen , g ea ly enhancing con ec- i e pe pendicula anspo . Examples can be ound in dispa a e con ex s, including as ophysical plasmas such as acc e ion discs [2] and plane a y magne osphe es [3], whe e he des abilizing o ce is ypically o he cen i ugal ype, and labo a o y plasmas [4,5], whe e he o ce densi y ypically comes om magne ic p essu e g adien s. This issue is pa icula ly ele an o magne ically con ined usion plasmas, as i de e mines he p opaga ion o ilamen a y s uc u es, which ha e become ecognized as he dominan adial anspo mechanism in he egion be ween he closed magne ic ield lines and he wall, known as he sc ape-o laye (SOL) [6–9]. The e o e, ilamen a y anspo s ongly in luences he pa allel o pe pendicula a io o he pa icle and hea luxes on o plasma acing componen s, hus de e mining hei du abili y and he spu e ing o impu i ies om he main wall. Basic models o ilamen s in usion li e a u e (see, e.g., K asheninniko [5]) desc ibe how elonga ed s uc u es p opaga e as he esul o equilib a ion o plasma pola i- za ion caused by an e ec i e g a i y o ce: aking a educed MHD app oach on a magne ized s a iona y plasma unde some a bi a y o ce densi y F, he cha ge conse a ion equa ion can be exp essed as ∇·d d nmi B2∇⊥ϕ¼1 Bb·∇×Fþ∇∥J∥;ð1Þ whe e n,ϕ,B,J, and mis and o densi y, po en ial, magne ic ield, cu en densi y, and ion mass, d=d ¼ ∂=∂ þðb∇ϕÞ=B ·∇and b¼B=B. Pola iza ion [le - hand side o Eq. (1)] is hus he esul o an equilib ium be ween he d i e ( i s e m on he igh -hand side) and he pa allel closu e e m (second e m on he igh -hand side) accoun ing o he cu en pa allel o B. Figu e 1shows his o a SOL con ex , whe e F¼2nmic2 s=Re s ands o he e ec o cu a u e and ∇B(csis he sound speed and e indica es he adial di ec ion). This can be easily gene al- ized o many o he o cing mechanisms such as he cen i ugal o ce in Keple ian sys ems, g a i y, e c. [3,10]. Equa ion (1) yields di e en solu ions depending on he pa allel closu e used o J∥: he usual hypo hesis in Published by he Ame ican Physical Socie y unde he e ms o he C ea i e Commons A ibu ion 3.0 License. Fu he dis i- bu ion o his wo k mus main ain a ibu ion o he au ho (s) and he published a icle’s i le, jou nal ci a ion, and DOI. PRL 115, 215002 (2015) PHYSICAL REVIEW LETTERS week ending 20 NOVEMBER 2015 0031-9007=15=115(21)=215002(5) 215002-1 Published by he Ame ican Physical Socie y he SOL is ha he ilamen ex ends along he ield line o he a ge pla es, and J∥is hus limi ed by he shea h [7]. In his egime, known as “shea h limi ed”(SL), he pola iza ion e m is neglec ed and ∇∥J∥¼ð2=L∥Þncseð1− exp ½−eðϕ−ϕ Þ=TeÞ is canceled by he d i e e m. He e, ϕ ,e,Te, and L∥a e he loa ing po en ial, elec on cha ge, elec on empe a u e, and pa allel connec ion leng h. By sol ing Eq. (1), he pe pendicula eloci y o he ilamen , b, is hen ound o scale as b¼2cs L∥ Rρs δb2 ∝ 1 δ2 b ;ð2Þ whe e ρsand Ra e he ion gy o adius and okamak majo adius, and δbis he ilamen pe pendicula size. Howe e , se e al phenomena, such as high SOL collisionali y, la ge X-poin magne ic shea , elec omagne ic e ec s, e c., may in alida e he wall connec ion hypo hesis, e ec i ely discon- nec ing he ilamen om he wall [7].In hiscase,∇∥J∥→0 and pola iza ion cancels he d i e e m, leading o a di e en egime, known as he “ine ial egime”(IN), in which b¼csffiffiffiffiffiffiffiffiffiffi ~ pe δb R ∝δ1=2 b;ð3Þ whe e ~ peis he p essu e in he ilamen no malized o he backg ound alue [11].These basic models ha e been e ined by he inclusion o ealis ic SOL elemen s such as ho ions [12]andla ge luc ua ionampli udes(“ ull- ”app oxima ion) [13], leading o imp o ed e sions o Eqs. (2) and (3): SL b¼csð1þτiÞL∥ R ~ n ¯ nþ~ nρs δb2 ; IN b¼csffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1þτiÞ~ n ¯ nþ~ n δb R ;ð4Þ whe e τi¼Ti=Te,and¯ nis he backg ound densi y. No e ha he iso he mal limi has been assumed o app oxima e ~ p≃T~ n. These scaling laws should be conside ed as uppe bounda ies, as any de ia ion om he pu e in e change c oss phase be ween elec ic ield and p essu e luc ua ions educes he eloci y o he blob wi h espec o p edic ions [14,15]. Al hough hese models ha e been success ully compa ed wi h expe imen in basic plasmas [16] and ex ensi e cha ac e iza ion wo k has been made in okamaks [17–19], a di ec measu emen o he ansi ion be ween he wo egimes emains o be achie ed in a usion ele an plasma. Ne e heless, such ansi ion has been in oked o explain he o ma ion o he SOL densi y shoulde , i.e., a subs an ial inc ease o he a SOL densi y adial e- olding leng h, λn≃½∇ log n−1, obse ed in many okamaks when a ce ain densi y is exceeded du ing low con inemen (Lmode) ope a ion [20–22]. Recen expe imen s in ASDEX Upg ade (AUG) [23] linked he inc ease in λn o an inc ease o he ilamen size and associa ed pe pendicula pa icle anspo in he ou e midplane Γ⊥; il, which can be up o 40% o he o al anspo a e he ansi ion acco ding o compa ison o EMC3-EIRENE simula ions [24]. This ansi ion akes place as he collisionali y inc eases in he SOL a he onse o di e o de achmen , when s ong ecycling begins o cool down he plasma in on o he a ge pla es [25], sugges ing ha he a o emen ioned dis- connec ion migh play a key ole. My a e al. [26] p edic ed his p ocess in a wo egion model o he SOL using he e ec i e collisionali y Λ, Λ¼L∥=cs 1=νei Ωi Ωe ∝nT−3=2 eð5Þ as he con ol pa ame e , whe e νei is he elec on-ion collision a e and Ωi=e s ands o he gy o equency o ions o elec ons. The disconnec ion akes place o Λ>1, when he cha ac e is ic pa allel anspo ime is longe han he in e se o ion-elec on collision equency. Subsequen wo k indica es ha his esul s in enhanced pe pendicula anspo as he consequence o inc eased ilamen eloci ies and c ea ion a es [27]. Resul s om Re . [23] showed ha he ansi ion in AUG coincides wi h Λ≃1. The ela ion be ween ilamen egime ansi ion and he shoulde o ma ion has also been shown in JET [28], whe e independen measu emen s o collisionali y in he di e o and midplane egions sugges ed ha only he collisionali y in he di e o egion could accoun o he disconnec ion p ocess. The ques ion o whe he he collisionali y in he di e o Λdi is de e mining he shoulde o ma ion is o g ea p ac ical impo ance, as nex gene a ion okamaks a e o eseen o ope a e wi h pa ially de ached, locally colli- sional di e o s, while emaining ho and collisionless a he midplane. I shoulde o ma ion is domina ed by a ilamen ansi ion induced by di e o collisionali y, his phenomenon will no be educed by a la ge machine size, as i would acco ding o o he p oposed mechanisms such as ioniza ion o neu als o igina ed om main wall ecycling [29]. In such a case, a shoulde will p obably be o med [28], which would impac subs an ially he main FIG. 1 (colo online). Tokamak geome y. A SOL ilamen has been ep esen ed along wi h he ield line connec ing i o he a ge pla e (in ed). PRL 115, 215002 (2015) PHYSICAL REVIEW LETTERS week ending 20 NOVEMBER 2015 215002-2 wall pa icle luxes and e osion. In o de o de e mine he ole o Λdi in shoulde o ma ion, an expe imen was ca ied ou in AUG: in L-mode discha ges, di e o de ach- men depends s ongly on inpu powe PIN occu ing a lowe midplane densi ies o lowe hea ing powe . He e, Λdi is de ined as in Eq. (5), using nand TeLangmui p obe measu emen s om he a ge pla es. Also, L∥has been es ima ed as he connec ion leng h be ween he a ge and he X-poin heigh a he lux su ace o he measu emen s L∥≃1 5πRq95,whe eR≃1.65 m is he okamak majo adius and q95 ≃5is he sa e y ac o [25]. This assump ion is based on ecip oca ing p obe and spec oscopic mea- su emen s o he cold egion ex ension in on o he di e o a he ime o he ansi ion [23,30]. The e o e, by ealizing a se ies o densi y amps wi h di e en hea ing powe s (0, 300, and 600 kW o ECH powe , plus 500 kW o Ohmic hea ing in all cases), Λdi co e s a ange o mo e han 2 o de s o magni ude, c ossing he Λdi ¼1 c i ical poin a di e en alues o edge densi y, ¯ ne.Thisis shown in he inse o Fig 2, whe e he e olu ion o he di e o collisionali y is displayed o h ee PIN cases. Di e en exponen ial g ow h o Λdi can be obse ed, depending on he PIN (highligh ed by colo ed dashed lines). The onse o de achmen is highligh ed by colo ed e ical lines. De ails on he diagnos ic se up and da a analysis a e analogous o hose desc ibed in Re . [23]. Typical plasma pa ame e s a he SOL o AUG a e lis ed in Table I. Two di e en egimes appea app oxima ely a each side o Λdi ¼1, as can be seen in Fig. 2. Fo low collisionali y, he size o ilamen s emains a ound 1 cm, and inc eases loga i mically wi h Λdi . Howe e , o dominan collision- ali y (Λdi >1), he size o ilamen s inc eases by up o an o de o magni ude. The da a se shows no dependence on PIN; hence, he ansi ion is no de e mined by a¯ ne h eshold, as can be deduced om he di e en Λdi ðPIN;¯ neÞpa hs seen in Fig. 2.Fu he mo e, he eloci y o small ilamen s ollows he SL scaling 1=δ2 b and la ge ones he IN scaling ffiffiffiffiffi δb p. This is shown in Fig. 3, whe e he measu ed a e age ilamen eloci y ⊥and size δba e no malized wi h csand ρs, espec i ely, as in Re . [12]. Also, he uppe bounds in he wo egimes a e ep esen ed by plo ing he espec i e exp essions o Eq. (4). In o de o do his, he local magne ic ield (BSOL ¼1.4T), cu a u e adius (RSOL ¼2.15 m), ne and Te alues a he p obe posi ion ha e been conside ed. To es ima e ~ n, he iso he mal hypo hesis has been ex ended o p obe measu emen s, and he ion sa u a ion luc ua ion le el ~ ji;sa has been used as a p oxy. Compa ison o Fig. 3 wi h Fig. 2 e eals how bo h g oups o da a poin s co espond o hose ea u ing Λdi <1and Λdi >1: The ho izon al do ed line c ossing he elbow in Fig. 2, is ep esen ed e ically in Fig. 3, whe e i sepa a es he wo scalings. Again, he same beha io is seen o di e en PIN alues, indica ing he scaling is independen o his pa ame e (and hus also o ¯ ne). Fo bo h egimes, cold and ho ions ha e been conside ed (τi¼3,as p oposed in Re . [12]). Filamen s in he IN egime a e be e ep esen ed by he cold model. This is consis en wi h bo h heo e ical analysis [19] and a SOL measu e- men s ca ied ou wi h ield analyze s [31], which sugges FIG. 2 (colo online). Size o ilamen s s collisionali y pa ame e , Λdi . Colo s indica e di e en hea ing powe s. Thin solid lines p o ided as a guide o he eye o ma k he wo egimes. In he inse , e olu ion o collisionali y wi h edge densi y. TABLE I. Typical plasma pa ame e s a AUG SOL. Bn eTeTiρscsνei 1.5 T 1–10 1018 m−315 eV 50 eV 10−4m25 km=s107s−1 0 50 100 150 200 250 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 δb/ρs Vpe p/cs SL (τi = 0) SL (τi = 3) IN (τi = 0) IN (τi = 3) EM FIG. 3 (colo online). Filamen scaling. Colo code as in Fig. 2. Black do ed line indica es he egime sepa a ion, as obse ed in Fig. 2. Red and black lines indica e IN and SL egimes,asexp essedinEq.(4). Solid o dashed line indica es τi¼0=τi¼3. Blue solid line indica es he elec omagne ic egime desc ibed in Re . [12]. PRL 115, 215002 (2015) PHYSICAL REVIEW LETTERS week ending 20 NOVEMBER 2015 215002-3 ha ilamen s cool down a e he ansi ion. Da a poin s in he lowe le co ne o Fig. 3, co esponding o he smalles alues o δb, ollow he IN scaling a he han he SL. This e ec has been p edic ed [32] o SL ilamen s wi h δb≪δ≃15ρs,whichwould e e oanIN-like scaling. Las ly, he elec omagne ic scaling p oposed in Re . [12], in which elec omagne ic e ec s domina e collisionali y in he ∇∥J∥ e m, ep esen s a wo se i ing o he da a han he SL and IN ones. Finally, global pe pendicula pa icle anspo is ound o be linked o di e o collisionali y. In Fig. 4, he densi y p o iles emain almos cons an un il Λdi ≃1is su passed. Fo Λdi >1, he SOL wid h apidly inc eases by a ac o o 3, indica ing a subs an ial inc ease in Γ⊥.As be o e, all pa ame e scans in AUG ma ch on o one cu e when Λdi is used as he o de ing pa ame e . He e, as an indica ion o he SOL wid h, λnis de i ed om Li-beam spec oscopy in he i s 25 mm ou side he sepa a ix, as explained in Re . [23]. These esul s a e independen on how de achmen is achie ed: I ni ogen is pu ed in he di e o , local adia ion cools down he egion inducing de achmen a a lowe ange o densi ies o a gi en PIN. In he inse in Fig. 2, seeding would cause a shi o he dashed line o he le compa ed o he unseeded dis- cha ge a he same PIN. Howe e , he λn alues om hese discha ges [emp y(solid) pu ple do s indica ing be o e (a e ) he pu ing] scale exac ly as he unseeded ones, despi e he di e en ¯ neand PIN ange (see Fig. 4). Measu emen s in JET yield e y simila esul s: λnand Λdi a e calcula ed o he discha ges p esen ed in Re . [28], using equi alen li hium beam and a ge p obes da a. The esul ing da a, displayed in Fig. 4as ligh blue s a s, display a ema kable simila i y o he ones measu ed a AUG. Beyond magne ic usion, hese esul s can be ega ded as he alida ion o a gene ic model o he p opaga ion o s uc u es esul ing om in e change ins abili ies in mag- ne ized plasmas. In his sense, no only SOL ilamen s and ilamen a y s uc u es obse ed in he Jo ian and Sa u nian magne osphe es by he Galileo and Cassini spacec a [33,34] can be desc ibed wi h isomo phical cu a u e o cen i ugal o ce-d i en in e change ins abili y models [7,10], bu also hei e ec on densi y adial p o iles is s ikingly simila o such di e en sys ems: The adial densi y p o ile o he equa o ial iogenic plasma o us in he Jo ian magne osphe e is domina ed by he con ec ion o “isola ed in e changing lux ubes”[3]. In his case, he pa allel closu e condi ion is de e mined by he ionosphe ic conduc i i y a high plane a y la i ude ins ead o he plasma-wall in e ac ion in he di e o egion. The adial dis ance a e which connec ion be ween he equa o and he ionosphe e disappea s is es ima ed a ound 20 Jo ian adii [10]. Galileo measu emen s show how he adial densi y g adien is s ongly dec eased when c ossing his disconnec ion h eshold [35]. In pa icula , he cha ac e - is ic g adien wid h ½∇ log n−1—λnin he SOL case—is inc eased by a ac o o 3 be ween 20 and 40 Jo ian adii, which is simila o he inc ease obse ed in Fig. 4 o Λdi >1. Also, he azimu al wa e numbe o he in e - change ins abili y—which would be he magne osphe ic equi alen o 1=δb—is expec ed o dec ease by a ac o o 6 upon disconnec ion [36], which is again consis en wi h he esul s obse ed in Fig. 2. Summa izing, he ole o Λdi as a con ol pa ame e o he ansi ion o bo h ilamen and global pe pendicula anspo egimes has been demons a ed, a e sepa a ing i s e ec om o he plasma pa ame e s such as ¯ neo PIN. The eloci y scaling o ilamen s changes om 1=δ2 b o ffiffiffiffiffi δb pwhen he c i ical alue Λdi ¼1 is su passed. These esul s ep esen s ong e idence o ilamen p opaga ion being go e ned by he mechanism p esen ed in Re . [26], in which he in e up ion o he pa allel ci cui due o collisionali y swi ches ilamen s om he SL o he IN egime. This change in SOL u bulence is accompanied by a subs an ial inc ease o he pe pendicula pa icle lux Γ⊥in he a SOL, measu ed in wo di e en okamaks. The ema kable simila i y o AUG and JET esul s suppo s he p edic ion o a shoulde o ma ion in ITER. This has impo an implica ions o main wall pa icle luxes and e osion in u u e usion de ices. Finally, he simila i y be ween ilamen s d i en by isomo phic ins abili ies in such dispa a e con ex s as he SOL o usion de ices and plane a y magne osphe es poin s owa ds a uni e sal ea u e o anspo in mag- ne ized plasmas. This wo k has been ca ied ou wi hin he amewo k o he EURO usion Conso ium and has ecei ed unding om he Eu a om esea ch and aining p og amme 2014–2018 unde G an Ag eemen No. 633053. The iews 10−2 10−1 100 10 15 20 25 30 35 40 45 50 55 Λdi λn (mm) AUG (ohmic) AUG (300 kW) AUG (600 kW) AUG Seeding ( e ) AUG Seeding (gas) JET FIG. 4 (colo online). Densi y e- olding leng h scaling wi h di e o collisionali y. Black, blue, and ed ci cles ep esen PIN as in Fig. 2. Pu ple ci cles co espond o seeded discha ges [emp y(solid) mean be o e (a e ) N2pu ing]. Ligh blue s a s a e da a poin s om JET. S aigh lines ma k he wo egimes as in Fig. 2. PRL 115, 215002 (2015) PHYSICAL REVIEW LETTERS week ending 20 NOVEMBER 2015 215002-4 and opinions exp essed he ein do no necessa ily e lec hose o he Eu opean Commission. The i s au ho belongs o he “Leyendas U banas”g oup c ea ed by CSIC in 2014. *See he Appendix o F. Romanelli e al., P oceedings o he 25 h IAEA Con e ence 2014, S . Pe e sbu g, Russia. †See h p://www.eu o‑ usionscipub.o g/ms 1 [1] F. F. Chen, Phys. Fluids 8, 912 (1965). [2] M Fu ukawa, Z. Yoshida, M. Hi o a, and V. K ishan, Plasma Fusion Res. 2, 016 (2007). [3] D. J. Sou hwood and M. G. Ki elson, J. Geophys. Res. 94, 299 (1989). [4] M. Endle , H. Niede meye , L. Giannone, E. Kolzhaue , A. Rudyj, G. Theime , and N. Tsois, Nucl. Fusion 35, 1307 (1995). [5] S. I. K asheninniko , Phys. Le . 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