Characterization of off-axis fishbones

Plasma Physics and Con olled Fusion Cha ac e iza ion o o -axis ishbones To ci e his a icle: W W Heidb ink e al 2011 Plasma Phys. Con ol. Fusion 53 085028 View he a icle online o upda es and enhancemen s. Rela ed con en ‘Beam-emission spec oscopy’ diagnos ics also measu e edge as -ion ligh - Beam-ion con inemen o di e en injec ion geome ies - Cen al la ening o he as -ion p o ile in e e sed-shea DIII-D discha ges - Recen ci a ions Mechanisms o ene ge ic-pa icle anspo in magne ically con ined plasmas W. W. Heidb ink and R. B. Whi e - O igin o ion cyclo on emission a he p o on cyclo on equency om he co e o deu e ium plasmas in he ASDEX- Upg ade okamak B Chapman e al - Compa ing heo y and simula ion o ion cyclo on emission om ene ge ic ion popula ions wi h sphe ical shell and ing- beam dis ibu ions in eloci y-space B Chapman e al - This con en was downloaded om IP add ess 87.218.223.151 on 18/08/2020 a 11:42 IOP PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION Plasma Phys. Con ol. Fusion 53 (2011) 085028 (23pp) doi:10.1088/0741-3335/53/8/085028 Cha ac e iza ion o o -axis ishbones W W Heidb ink1,MEAus in2, R K Fishe 3, M Ga c´ ıa-Mu˜ noz4, G Ma sunaga5, G R McKee6, R A Moye 7, C M Musca ello1, M Okabayashi8,DCPace 9, K Shinoha a5, W M Solomon8, E J S ai 3, M A Van Zeeland3and Y B Zhu1 1Depa men o Physics and As onomy, Uni e si y o Cali o nia, I ine, CA, USA 2Ins i u e o Fusion S udies, Uni e si y o Texas a Aus in, Aus in, TX, USA 3Gene al A omics, San Diego, CA, USA 4Max-Planck-Ins i u ¨ u Plasmaphysik, Ga ching, Ge many 5Japan A omic Ene gy Agency, Naka Ci y, Iba aki, Japan 6Depa men o Enginee ing Physics, Uni e si y o Wisconsin a Madison, Madison, WI, USA 7Cen e o Ene gy Resea ch, Uni e si y o Cali o nia, San Diego, La Jolla, CA, USA 8P ince on Plasma Physics Labo a o y, P ince on, NJ, USA 9Oak Ridge Ins i u e o Science and Educa ion, Oak Ridge, TN, USA Recei ed 28 Feb ua y 2011, in inal o m 13 June 2011 Published 7 July 2011 Online a s acks.iop.o g/PPCF/53/085028 Abs ac Repe i i e bu s ing ins abili ies wi h s ong equency chi ping occu in high- be a, beam-hea ed plasmas wi h sa e y ac o q>1 in he DIII-D okamak. Al hough he mode s uc u es di e , in many ways, he o -axis ishbones a e simila o he q=1 ishbones i s obse ed on he Poloidal Di e o Expe imen (PDX). The modes a e d i en by ene ge ic apped ions a he as - ion p ecession equency. Du ing a bu s , he equency changes mos apidly as he mode eaches i s maximum ampli ude. La ge ampli ude bu s s ha e la ge g ow h a es and equency chi ps. Unlike PDX ishbones, he decay phase is highly a iable and is usually sho e han he g ow h phase. Also, he wa e o m is highly dis o ed by highe ha monics du ing he la e po ion o a bu s . The adial mode s uc u e al e s i s shape du ing he bu s . Like PDX ishbones, he modes expel apped ions in a ‘beacon’ wi h a de ini e phase ela ionship ela i e o he mode. Se en ypes o loss de ec o s measu e he beacon. The losses scale linea ly wi h mode ampli ude. The neu on a e changes mos apidly a maximum mode ampli ude bu , depending on he loss diagnos ic, he losses o en peak a ew cycles la e . The non-ambipola as -ion losses cause a sudden change in o oidal o a ion equency ac oss he en i e plasma. In addi ion o an o e all d op, he neu on signal oscilla es in esponse o he wa e. Unlike he beacon o los pa icles, which main ains a ixed phase ela i e o he mode, he phase o he neu on oscilla ions s eadily inc eases h oughou he bu s , wi h he g ea es phase slippage occu ing in he highly nonlinea phase nea maximum mode ampli ude. (Some igu es in his a icle a e in colou only in he elec onic e sion) 0741-3335/11/085028+23$33.00 © 2011 IOP Publishing L d P in ed in he UK & he USA 1 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 1. In oduc ion The ishbone ins abili y was i s obse ed [1] du ing deu e ium nea -pe pendicula neu al beam injec ion in o he Poloidal Di e o Expe imen (PDX). The mode had an (m, n) =(1,1) s uc u e in he plasma, as expec ed o an in e nal kink. (He e mand ndeno e he poloidal and o oidal mode numbe s, espec i ely.) The ishbones occu ed in pe iodic bu s s. Du ing each bu s , he mode equency chi ped down in equency om ( ypically) 20 o 12 kHz. The neu on emission d opped a each bu s , wi h he a e o change peaking nea he ime o peak mode ampli ude [2]. Neu al pa icle analyze s (NPAs) de ec ed a ‘beacon’ o expelled apped as ions, a bu s o signal wi h a ixed phase ela i e o he magne ic luc ua ion on each mode cycle [3,4]. The anspo o as ions was explained as con ec i e adial anspo caused by esonance be ween he as -ion p ecession mo ion and he kink mode [5]. The ins abili y was iden i ied as a new b anch o he in e nal kink associa ed wi h he la ge ene ge ic ion popula ion [6]. Subsequen ly, q=1 ishbone ins abili ies we e obse ed on many o he de ices. (A comp ehensi e e iew o bo h he PDX ishbones and subsequen measu emen s on o he okamaks, including DIII-D, appea s in [7].) Bo h an MHD b anch [8] and an ene ge ic- pa icle b anch a e heo e ically p edic ed [9] and obse ed [7]. A comp ehensi e pic u e eme ged: a modes as -ion densi y, he apped ions help s abilize he luid b anch bu , a la ge as -ion densi y, hey des abilize he ene ge ic-pa icle b anch [10]. Fishbone-like modes in plasmas wi h cen al sa e y ac o well abo e uni y we e i s obse ed on JET [11]. Mo e ecen ly, ishbone-like modes we e s udied in JT-60U [12,13] and DIII-D [14,15] plasmas wi h simila qp o iles as he JET plasmas bu highe be a. While q=1 ishbones ha e eigen unc ions whose maximum is inside he q=1 su ace, he mode s uc u e o he o -axis ishbones peaks nea he q=2 su ace [11,15]. Some au ho s ha e sugges ed ha he o -axis ishbones a e in e nal kinks [11], while o he s sugges ha hey a e ela ed o an ex e nal kink [15]. In ei he case, i is likely ha he o -axis ishbone is an ene ge ic-pa icle b anch o he luid in e nal o ex e nal kink mode. A heo e ical s udy showed ha a modes as -ion popula ion can s abilize an in e nal double kink mode bu a la ge popula ion des abilizes a new ishbone b anch [16], jus as i does o he 1/1 in e nal kink. On he o he hand, he obse a ion ha he ins abili ies occu in plasmas ha a e suscep ible o esis i e wall modes sugges s ha he o -axis ishbones may be an ene ge ic-pa icle b anch o he MHD ex e nal kink [15]. (Resis i e wall modes occu in plasmas ha would be uns able o ex e nal kinks in he absence o a conduc ing wall [17].) A ecen pape [15] shows ha he JT-60U and DIII-D modes ha e he same phenomenology and discusses hei ela ionship o he esis i e wall mode. The goal o his pape is o p o ide a de ailed desc ip ion o he o -axis ishbone in DIII-D. The da a a e compa ed and con as ed o PDX ishbones h oughou he pape . The nonlinea e olu ion o he o -axis ishbone bu s s displays no el ea u es no p e iously epo ed o any as -ion d i en ins abili y. The pape begins wi h a desc ip ion o he plasma condi ions and diagnos ics (sec ion 2). Nex , he mode is cha ac e ized (sec ion 3.1) and he loss (sec ion 3.2) and con ined (sec ion 3.3) as -ion da a a e desc ibed. Specula ion abou he easons o he di e ences be ween PDX ishbones and o -axis ishbones appea s in sec ion 4, oge he wi h he conclusion. 2. Appa a us All o he da a in his pape a e om DIII-D. Mos o he discha ges desc ibed in his pape we e discussed in he DIII-D po ion o he pape by Okabayashi e al [15]. A da abase o 513 bu s s 2 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 R (m) -1.0 -0.5 0.0 0.5 1.0 z (m) BILD BES #141089 2315 ms q=2 1.7 2.5 3.0 3.5 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 150o BILD 210o 330o30o BES BES (b) (a) FILD FILD NPA NPA FIDA FIDA FIDA NEUTRONS NEUTRONS ICE ICE ISAT ISAT MIRNOV MIRNOV CER CER ECE ECE Figu e 1. (a) Ele a ion o he DIII-D acuum essel, showing he loca ions o he a ious measu emen s. (The BES, NPA and FIDA signals depend on he edge neu al densi y p o ile, so he indica ed posi ions a e es ima es.) The lux su aces o a ypical equilib ium a e labeled by hei q alue; q0=1.5 on axis and q95 =4.4. (b) Plan iew. The lines ep esen he cen e o he beamlines. The o oidal ield (plasma cu en ) is in he clockwise (coun e -clockwise) di ec ion. was compiled ha con ains all o he n=1 o -axis ishbone bu s s obse ed du ing wo days o ope a ion. The plasma condi ions a e simila o nea ly all o he bu s s: plasma cu en Ip=0.95–1.14 MA; o oidal ield BT=1.72; mino adius a=0.60 m; no malized be a βN=βT/(Ip/aBT)=2.1–2.7; line-a e age plasma densi y ¯ne=(3.4–4.2)×1019 m−3. The beam powe was he ac ua o o eedback con ol o βN, so i a ies be ween 5.7 and 14.9 MW o he bu s s in he da abase, wi h a ypical a e age powe o 10 MW . The beams injec bo h in he co-Ipdi ec ion (⩽15 MW ) and in he coun e -Ipdi ec ion (⩽5 MW ); bo h nea - angen ial ( angency adius R an =1.15 m) and nea -pe pendicula (R an =0.76 m) angles a e employed. The a e age injec ion ene gies o he co- angen ial, co-pe pendicula , coun e - angen ial, and coun e -pe pendicula beams a e 66–80 keV, 60–73 keV, 80–81 keV and 60– 75 keV, espec i ely. Typically, he beam be a is ∼1/6 o he o al be a. In many discha ges, ∼2.7 MW o elec on cyclo on cu en d i e powe is injec ed o a oid neoclassical ea ing modes [14]. The plasma is deu e ium, he neu al beams injec deu e ium a oms, and he p ima y impu i y is ca bon om he g aphi e walls (Ze ≃2). All o he discha ges ha e he shape shown in igu e 1, a lowe single null di e o con igu a ion. The ∇Bd i is downwa d owa d he di e o and all o he plasmas a e in H-mode. The equilib ium is based on EFIT [18] solu ions o he G ad–Sha ano equa ion ha use mo ional S a k e ec [19] measu emen s o he in e nal magne ic ield. The cen al sa e y ac o is q0=1.15–1.78, he magne ic shea is ela i ely weak nea he magne ic axis, c osses he q=2 su ace nea a majo adius o R=2.1 m and ises apidly o a alue o q95 =4.3–4.7 a he edge. (q95 is he sa e y ac o a he su ace ha encloses 95% o he poloidal lux.) Typical cen al elec on and ion empe a u es a e Te=5 and Ti=6 keV. 3 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al Figu e 1shows he loca ions o he p incipal diagnos ics. To oidal and poloidal a ays o Mi no coils [20] a e he p ima y luc ua ion diagnos ic. In his pape , all o he Mi no coil aces a e om a coil ha is loca ed a a o oidal angle o 307◦. A his magne ic ield and densi y, he elec on cyclo on emission (ECE) diagnos ic [21] measu es op ically hick, hi d ha monic ECE emission o he spa ial posi ions shown in he igu e. The cha ge-exchange ecombina ion (CER) diagnos ic [22] measu es he empe a u e, o oidal o a ion, and densi y o ca bon ions; on some discha ges, he CCD came a acqui ed da a in 0.5 ms ime bins o de ec apid changes in o oidal o a ion. The p ima y diagnos ic o he con ined as ions is a neu on scin illa o ha measu es 2.5 MeV neu ons p oduced in deu e ium–deu e ium usion eac ions. Two complemen a y scin illa o s wi h iden ical elec onics a e moun ed beside a acuum lange jus ou side he acuum essel: a plas ic scin illa o and a ZnS(6Li) scin illa o . The plas ic scin illa o can esol e oscilla ions in neu on lux wi h equencies 10 kHz, while he ZnS scin illa o has an e ec i e bandwid h o ∼3 kHz [23]. Consis en wi h he expec ed ins umen al esponse, he luc ua ions in neu on lux discussed in sec ion 3.3 a e much weake on he ZnS signal han on he plas ic signal. All neu on da a in his pape a e om he plas ic scin illa o . Se en di e en diagnos ics de ec escaping as ions. The beam-ion loss de ec o (BILD) is a Fa aday cup ha is moun ed on he edge o a acuum po 12 cm below he midplane [24]; in his pape , he signals a e om he oil ha de ec s co-ci cula ing o bi s. The as -ion loss de ec o (FILD) is a scin illa o -based diagnos ic ha esol es he gy o adius and pi ch o he escaping as ions in an image ha is eco ded on a CCD came a [25]. Fo highe bandwid h measu emen s, a pho omul iplie de ec s ligh om a po ion o he scin illa o . A ecip oca ing Langmui p obe wi h obus g aphi e ips [26] measu es luc ua ions in ion sa u a ion cu en (ISAT); a he ime o he measu emen s, he p obe was in he sc ape-o egion 6.1 cm om he las -closed lux su ace and 5.6 cm om he ou e wall. A solid-s a e NPA ope a ed in cu en mode measu es luc ua ions in cha ge-exchange eac ions when as ions escape o he high neu al densi y egion a he plasma edge. The as -ion D-alpha (FIDA) diagnos ic [27,28] measu es Dopple -shi ed ligh emi ed by as ions a e hey unde go a cha ge-exchange eac ion. Fo he apidly changing backg ound condi ions associa ed wi h hese ishbone bu s s, he empo al esolu ion o he spec oscopic FIDA diagnos ics p o ed inadequa e o de ec changes in co e as -ion densi y; howe e , bu s s o edge FIDA emission a e obse ed by he il e -based -FIDA diagnos ic [28] on bo h ‘ac i e’ sigh lines ha iew an injec ed beam and ‘passi e’ sigh lines ha do no in e sec an injec ed beam. The beam-emission spec oscopy (BES) diagnos ic [29] su e s om con amina ion by edge FIDA ligh o hese ishbone bu s s [30], complica ing use o he da a o in e nal eigen unc ion measu emen s o densi y luc ua ions. Howe e , o one discha ge whe e he neu al beams iewed by he BES diagnos ic we e o , he signals a e en i ely om passi e FIDA ligh p oduced when as ions a e expelled o he high neu al densi y egion a he plasma edge [30]. The se en h edge loss diagnos ic is indi ec . When as ions a e expelled in o he sc ape-o egion, hey usually des abilize ion cyclo on emission (ICE) [7]. These wa es a e hough o be magne oacous ic wa es exci ed by he aniso opic ‘bump-on- ail’ dis ibu ion unc ion caused by he losses [31]. Fo hese expe imen s, he signal om a high-bandwid h o oidal coil [32] was il e ed by wo bandpass il e s, ec i ied and digi ized. The ‘lowe pass’ il e includes he i s deu e ium cyclo on ha monic a he plasma edge, while he ‘highe pass’ il e spans he second and hi d ha monics. All ishbone bu s s ha mee ce ain c i e ia a e included in he da abase. Figu e 2shows examples o included and excluded bu s s. Like he i s bu s in igu e 2(a), all o he included bu s s a e n=1 modes ha o a e in he di ec ion o he plasma cu en . Roughly 3% o he 4 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al -150 -100 -50 0 50 100 150 2313 2314 2315 2316 2317 0 1 2 3 4 5 6 TIME (ms) #141092 -200 -100 0 100 200 1950 1952 1954 1956 1958 0 1 2 3 4 5 6 n=4 n=1 TIME (ms) MIRNOV (T/s) BILD (V) #141086 (a) (c) (b) (d) Figu e 2. Sample Mi no coil (a), (b) and BILD (c), (d) signals o bu s s ha a e excluded om he da abase. (a), (c) The n=1 bu s a 1951 ms in (a) is included bu he n=4 bu s a 1957 ms is excluded. (b), (d) Bu s s wi h app eciable bea ing due o a s eady ea ing mode (in his case, an n=3 mode) a e also excluded. No e ha he BILD signals sa u a e a 5 V. obse ed bu s s ha e highe o oidal mode numbe s (usually n=3o n=4). Like he n=1 modes, hese highe equency modes chi p down in equency and cause losses ha ha e a de ini e phase ela i e o he wa e; howe e , hese highe equency modes a e no discussed u he he e. The e a e also many examples o ishbone bu s s ha occu in plasmas wi h s eady ea ing modes ( igu e 2(b)). Phenomenologically, hese bu s s appea iden ical o he e ained bu s s bu , because o di icul ies in accu a ely analyzing he Mi no coil signal in he p esence o s ong bea ing, hey a e excluded om ou da abase. 3. Da a 3.1. Mode p ope ies The o -axis ishbone bu s s ypically las o 2–3 ms and occu abou e e y 20 ms. Figu e 3 shows a ypical Mi no coil signal. Ini ially, he signal is nea ly sinusoidal du ing he g ow h phase. The ampli ude g ows app oxima ely exponen ially. A maximum ampli ude, he wa e o m becomes s ongly dis o ed om a sine wa e. Da a om he o oidal a ay show ha his dis o ion is associa ed wi h he appea ance o highe nha monics: in o he wo ds, he en i e s uc u e becomes dis o ed. The mode pe iod isibly leng hens as he bu s passes h ough i s maximum ampli ude. Figu e 3also illus a es analysis o he signal o inclusion in he da abase. Fi s , he maxima and minima a e iden i ied ( igu e 3(a)). Then he ec i ied ampli ude o he maxima and minima a e plo ed ( igu e 3(b)). No e ha , du ing he ise phase, he ampli udes o he maxima and minima ha e nea ly he same alue bu , du ing he decay phase, he maxima a e la ge han he minima. The ampli ude da a a e i o exponen ials o ob ain he g ow h and decay a es. In he hi d s ep, he ime di e ence be ween he maxima and minima is g aphed ( igu e 3(c)). The ini ial mode equency is ob ained om a i o he i s se e al cycles, while he inal mode equency is ob ained om he las wo cycles. The equency chi ping a e is ob ained om a linea i o he change in pe iod nea peak mode ampli ude. The mode dis o ion is de i ed om he di e ence in pe iod be ween hal -cycles, T1/2/¯ T1/2. 5 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al -400 -200 0 200 400 0.00 0.10 0.20 1837.5 1838.0 1838.5 1839.0 1839.5 1840.0 0 100 200 300 400 (a) Mi no (T/s) Rise TIME (ms) #141076 (b) Ampli ude (T/s) Fall Ini ial Final Chi p (c) Hal -pe iod (ms) Dis o ion 0 5 10 15 20 25 30 Hal -c y cle # Figu e 3. (a) Mi no coil signal o a ypical ishbone bu s . The symbols indica e he maxima and minima used o calcula ion o he hal -pe iod. (b) Ampli ude o he maxima and minima o he same bu s , oge he wi h exponen ial i s o he g ow h and decay phases. (c) Hal -pe iod in milliseconds o each hal -cycle h oughou he bu s . The ini ial equency is de i ed om a ho izon al i a low ampli ude. The equency chi ping a e is ob ained om a linea i nea maximum ampli ude. (The dashed e ical line indica es he ime o maximum ampli ude.) The inal equency is an a e age o e he las wo cycles. Linea i s o he long hal -pe iods and he sho hal -pe iods a e used o measu e he wa e o m dis o ion. (This quan i y is ze o o a sine wa e.) This de ini ion o dis o ion gi es simila esul s o al e na i e de ini ions [15] based on he ampli ude o he de ia ion om a sine wa e. The a e o change o he dis o ion is also eco ded in he da abase. The obse ed ise ime inc eases wi h he maximum ampli ude o he mode ( igu e 4(a)). The co ela ion coe icien is 0.72 o hese da a. (Figu e 4(a) shows he co ela ion wi h d˜ B/d ; he co ela ion wi h he peak ampli ude ˜ Bis sligh ly highe ( =0.76).) PDX ishbones had a simila ise ime and dependence on mode ampli ude [33]. In con as , as shown in igu e 4(b), he decay a e is unco ela ed wi h mode ampli ude ( =0.05). Unlike PDX ishbones, he decay a e is gene ally as e han he g ow h a e. An example o he wide a ia ion in beha io du ing he decay phase o a pai o o he wise simila bu s s is shown in igu e 5. This example illus a es he ollowing gene al ea u es: (1) he e olu ion o he bu s s is qui e ep oducible du ing he g ow h phase; (2) equency chi ping and mode dis o ion always occu nea maximum ampli ude; (3) he decay phase is highly a iable. Some imes he bu s decays in a ew cycles, while o he imes i pe sis s o many. O en he mode dis o ion emains la ge bu some imes nea ly sinusoidal successo oscilla ions pe sis a small ampli ude ollowing he p ima y, highly dis o ed, c ash. The magni ude o he equency chi ping scales wi h mode ampli ude ( igu e 4(c)) ( =0.77). The a e o change o he chi ping a e also scales wi h mode ampli ude ( =0.55). The equency chi ping also inc eased wi h mode ampli ude o PDX ishbones [2]. Wi hin a gi en bu s , he chi ping a e is la ges in he pe iod jus a e maximum ampli ude. Simila ly, 6 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 0 2 4 6 8 0 5 10 15 0 50 100 150 200 250 PDX Peak Mi no Ampli ude (T/s) 0 1 2 3 4 5 RISE γ / ω (%)DROP γ / ω (%) (a) (b) (c) FREQ. CHIRP (kHz) Figu e 4. (a) G ow h a e, (b) decay a e and (c) change in equency i− inal e sus peak mode ampli ude o all o he bu s s in he da abase. The g ow h and decay a es a e no malized o he mode equency in he plasma ame, ω=2π( i− o ), whe e o is om he R=212 cm CER channel. The lines a e linea i s o he da a. The e o ba s a e he alues obse ed o ypical cases in PDX [33]. -1 0 1 2 -300 -200 -100 0 100 200 300 400 RELATIVE TIME (ms) MIRNOV (T/s) #141092 1801 ms 1981 ms Figu e 5. Example o wo simila bu s s wi h s ikingly di e en beha io in he decay phase. 7 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 50 100 150 200 250 0.0 0.2 0.4 0.6 0.8 1.0 Dis o ion Peak Mi no Ampli ude (T/s) Figu e 6. Dis o ion o he wa e o m T1/2/¯ T1/2nea maximum mode ampli ude e sus peak Mi no ampli ude o all o he bu s s in he da abase. Illus a i e examples o wa e o ms wi h dis o ions o 0.32 and 0.76 a e included. PDX ishbones [33] and high equency chi ping ins abili ies in DIII-D [34] chi p he as es nea maximum mode ampli ude. All o he ishbones exhibi mode dis o ion ( igu e 6). Mos bu s s exhibi e y s ong dis o ion bu e en he mos weakly dis o ed wa e o ms de ia e signi ican ly om a sine wa e. Analysis o he poloidal Mi no coil da a [15] shows ha he sinusoidal po ion o he wa e o m has an m=3 s uc u e bu he dis o ed po ion has an m≃2 s uc u e. S ong mode dis o ion was no obse ed o PDX ishbones [33]. Figu e 7shows he adial mode s uc u e du ing he ea ly phase as measu ed by he ECE diagnos ic. The δTe luc ua ions a e la ges nea he q=2 adius (R≃2.1 m). The e is a ∼60◦phase a ia ion be ween he weak luc ua ions obse ed nea he magne ic axis and he s onge luc ua ions obse ed nea he q=2 su ace. In he heo y o ene ge ic-pa icle ins abili ies, i is impo an o de e mine i he eigen unc ion changes shape o emains cons an du ing a bu s . (I he eigen unc ion changes shape, p ope ea men o nonlinea e ec s equi es a ‘non-pe u ba i e’ model.) To in es iga e he empo al cons ancy o he mode s uc u e, we compa e he ela i e ampli ude o he a ious ECE channels o he Mi no coil as he bu s e ol es. Fo he example in igu e 8(a), he a io o wo ECE signals emains nea ly cons an du ing he g ow h phase bu de ia es nea maximum ampli ude. Du ing he g ow h phase, he ECE signals g ow mo e slowly han he in eg a ed Mi no signal; a e he maximum he ECE signals decay mo e slowly han δB. Figu e 8(b) shows he a e age beha io o a se o simila bu s s. Al hough he unce ain ies associa ed wi h incohe en Te luc ua ions and wi h condi ional a e aging o an ensemble o bu s s a e subs an ial, he da a appea o ollow he same end as he example in igu e 8(a): δTeg adually dec eases ela i e o δB du ing he g ow h phase, hen ises in he decay phase. Due o he la ge a iabili y o beha io in he decay phase, he s anda d de ia ions a e la ge bu examina ion o indi idual bu s s shows ha he e a e subs an ial di e ences in he e olu ion o he a ious channels du ing his phase. We conclude ha he mode s uc u e a ies, as expec ed o a s ongly d i en non-pe u ba i e ene ge ic-pa icle mode. The ini ial mode equency is de e mined by he as -ion p ecession equency. Figu e 9 shows calcula ions by an o bi - ollowing Mon e Ca lo (OFMC) code [35] o he p ecession equencies p e,0o as ions deposi ed by he ou di e en angles o beam injec ion in a ypical discha ge. These calcula ions neglec he adial elec ic ield bu analy ical heo y [36] and sepa a e calcula ions show ha inclusion o he elec ic ield inc eases he ac ual p ecession 8 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 0 50 100 150 200 250 Peak Mi no Ampli ude (T/s) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0123456 F equency Chi p (kHz) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Peak beam-ion loss a e (ms-1)Peak beam-ion loss a e (ms-1) (a) (b) Figu e 14. Maximum neu on loss a e e sus (a) maximum Mi no ampli ude and (b) change in mode equency, i− inal o all o he bu s s in he da abase wi h cons an beam powe du ing he bu s . Linea (solid lines) and quad a ic (dashed line) i s o he da a a e included. las -closed lux su ace and 5.6 cm om he essel wall. This loca ion minimizes con ibu ions o he ion sa u a ion cu en om he mal ions, while s ill allowing as ions o s ike he collec o ip. High-bandwid h FILD measu emen s became a ailable a he end o he expe imen al campaign. Fo his measu emen , he pho omul iplie imaged a po ion o he scin illa o cen e ed on a lowe pi ch angle (∼50◦) han he p ima y ishbone loss peak a ∼70◦. Ne e heless, e idence o a cohe en beacon is also obse ed by his diagnos ic ( igu e 15(c)). Two NPA channels made high-bandwid h measu emen s h oughou he campaign. The NPA sigh lines o igina e om a lowe po , ise up o in e sec he coun e beams nea he midplane, hen s ike he inne wall abo e he midplane; o oidally, he sigh lines a e no mal o he plasma. Whe he he iewed coun e beams a e o o on, ishbone modes cause beacon- like bu s s on he NPA de ec o s ( igu e 15(c)). P esumably, hese bu s s a e caused by as ions ha a e expelled o he high neu al densi y egion a la ge majo adius. On PDX, he signal on he e ically iewing NPA ha iewed he ou e edge o he plasma was wo o de s o magni ude la ge han he NPA ha iewed he inne edge o he plasma [3,40]. The e also a e some indica ions o educ ions in ac i e signal caused by he ishbone bu s . No mally, he signal o he BES diagnos ic is domina ed by beam emission om he ac i e injec ed beam bu , in he case o la ge losses o as ions, FIDA ligh om he edge plasma can also be app eciable [30]. In DIII-D, he BES il e s accep Dopple -shi ed D-alpha ligh p oduced by as ions on escaping apped o bi s. To a oid he complica ion o concu en beam emission, he da a in igu e 15(d) a e om a discha ge whe e he ac i e beams we e bo h o . Bu s s o ligh a e obse ed. In he case o he BES diagnos ic, wo bu s s pe cycle a e o en obse ed because he BES sigh line in e cep s he plasma edge a wo di e en o oidal 15 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.40.0-0.4 120-1-2 4 2 -4 -2 0 #141089 2319 ms -0.8 -4 -2 0 2 4 6 -0.5 0.0 0.5 1.0 -0.4 -0.2 0.0 0.2 0.4 #142124 1618 ms -400 -200 0 200 400 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 -400 -200 0 200 400 600 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 0.0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) T/s T/s Vol s Vol s (a) (b) (d) ( ) (e) (c) #141069 1497 ms #142125 1614 ms #141069 1339 ms #142126 1662 ms BILD ISAT BES FILD NPA Lowe Band Re e ence Ac i e Highe Band ICE FIDA Figu e 15. Loss-de ec o da a du ing a ishbone bu s om (a) he BILD oil, (b) he Langmui p obe Isa ip, (c) he FILD scin illa o and SSNPA de ec o , (d) a cen al BES channel on a discha ge wi hou any beam emission, (e) ac i e and passi e -FIDA channels and ( ) ICE passband signals ha include he undamen al cyclo on esonance (lowe band) o he i s ew ha monics (highe band). The diamonds ep esen peaks used o measu e he phase ela i e o he Mi no signal. loca ions. The sigh line is angled sligh ly downwa d. The i s peak co esponds o a poloidal posi ion below he midplane, while he second peak co esponds o a poloidal posi ion abo e he midplane. Gene ally, he i s peak (lowe poloidal posi ion—in he di ec ion o he ∇B d i ) appea s ea lie in he e olu ion o he mode and is la ge in ampli ude han he second peak, al hough o en he wo peaks a e compa able du ing he decay phase. Like he o he edge diagnos ics, bo h peaks ha e a ixed phase ela i e o he mode. 16 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 0 50 100 150 200 250 300 0 50 100 150 200 250 PHASE LAG (º) ISAT ICE SSNPA FILD BILD BES BES FIDA FIDA TOROIDAL ANGLE (º) Figu e 16. Measu ed phase lag ela i e o he Mi no signal e sus o oidal angle o he diagnos ic. The e ical e o ba ep esen s he s anda d de ia ion o e se e al cycles and he ho izon al e o ba is an es ima e o he unce ain y in angle. The solid lines show he expec ed a ia ion o an n=1 mode. Bu s s o edge FIDA ligh a e also obse ed by a dedica ed FIDA diagnos ic ( igu e 15(e)). The sigh lines o his diagnos ic look down a a can ed o oidal angle om an uppe po owa d he essel loo [28]. One channel iews one o oidal di ec ion o in e sec a hea ing beam ( o ac i e FIDA measu emen s), while he o he channel iews in he opposi e o oidal di ec ion o p o ide a e e ence signal. The bandpass il e o hese measu emen s accep s Dopple -shi ed ligh om co-going ions in he case o he ac i e iew and om coun e -going ions o he e e ence iew. Bo h sigh lines in e sec he edge egion nea he op and bo om o he essel. Bo h channels obse e beacon-like bu s s o signal ha p esumably a e caused by expulsion o as ions by he ishbones. Because he ∇Bd i is downwa d, he bu s s a e p obably caused by as ions ha cha ge exchange wi h neu als nea he bo om o he essel. Beacon-like bu s s o signal a e also measu ed by he ICE diagnos ic ( igu e 15( )). Bo h he highe band and lowe band il e ed signals measu e bu s s wi h a de ini e phase ela i e o he mode, al hough he a ia ion o he phase is somewha la ge han o he o he loss diagnos ics. The highe band signal co ela es mo e eliably wi h he Mi no signal han he lowe band signal. Fo he highe band, like he maximum neu on loss a e, he signal peaks a he same ime as he maximum Mi no ampli ude (wi hin s a is ical e o ). The magni ude o he ICE signal summed o e he bu s also co ela es s ongly wi h he maximum mode ampli ude ( =0.52). Gi en ha he ICE adia ion is p oduced h ough a wo-s age p ocess ( he ishbones expel as ions, which hen exci e magne oacous ic wa es), i is a he su p ising ha he ICE signal p o ides such a eliable measu emen o he beacon and o he iming and magni ude o he losses. The phase o all o he beacon measu emen s is summa ized in igu e 16. Fo diagnos ics ha measu e he same quan i y, such as he wo FIDA measu emen s and he wo BES peaks, he phase di e ence be ween he measu emen s ag ees wi h he o oidal sepa a ion o he de ec ion poin s, as expec ed o an n=1 mode. Fo he la ge da ase , al hough each diagnos ic measu es a well-de ined phase ela i e o he mode, he e is no clea pa e n o he en i e se o measu emen s. Upon e lec ion, his is no su p ising. The ishbone mode o a es a he ela i ely slow p ecession equency. On he o he hand, he phase o any pa icula diagnos ic signal depends on he inal leg o he o bi o he as ions ha p oduce ha signal; his inal leg occu s a he much highe bounce equency. On his inal leg, a loss o bi such as he one shown in igu e 12(b) mo es o e 90◦ o oidally. Since he di e en diagnos ics 17 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al -0.01 0 0.01 0.02 0.03 0.04 0.05 125 130 135 140 110 115 120 125 130 76 78 80 82 84 86 88 90 -4 -2 0 2 4 36 38 40 42 44 46 48 50 -4 -2 0 2 4 28 30 32 34 36 38 40 42 -4 -2 0 2 4 14 16 18 20 22 24 26 -4 -2 0 2 4 6 8 10 12 14 16 18 20 RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) RELATIVE TIME (ms) TOROIDAL ROTATION (km/s) NEUTRON LOSS RATE (ms-1) (a) (b) 177 cm (c) 187 cm (d) 193 cm (h) 219 cm (g) 212 cm( ) 204 cm(e) 199 cm Figu e 17. Time e olu ion o (a) he as -ion loss a e in e ed om he d op in neu on signal and (b)–(h) he o oidal o a ion o 7 CER channels. The da a a e condi ionally a e aged o e an ensemble o ela i ely la ge (130 <B max <180 T s−1) ishbone bu s s. The e o ba in (a) ep esen s he s anda d de ia ion o he peak loss a e. The e o ba s in (b)–(h) ep esen he s anda d de ia ion o he ela i e change be ween −0.75 and −0.25 ms. measu e di e en ypes o loss o bi s, he inal o bi leg e ec i ely sc ambles he o oidal phase o he a ious measu emen s. A simila esul was ob ained o PDX ishbones. Bo h he NPA [3] and a silicon de ec o ha di ec ly measu ed los as ions [41] obse ed a beacon bu he wo diagnos ics did no obse e he same phase ela i e o he mode [33]. Since he as -ion losses a e non-ambipola , hey should ansien ly al e he adial elec ic ield E . Because he plasma mus p ese e adial o ce balance, a changing elec ic ield al e s he o oidal o a ion. To de ec his e ec , CER measu emen s o o oidal o a ion a e acqui ed in 0.5 ms ime bins. To ob ain adequa e s a is ics, da a om 16 simila ishbone bu s s a e condi ionally a e aged. The esul s appea in igu e 17. All CER channels measu e an ab up d op in o oidal o a ion o ∼−10 km s−1(1 kHz) when he neu on loss a e is g ea es . This sugges s ha as -ion losses occu h oughou he plasma. Compa ing channels, he d op pe sis s longe a la ge majo adius han i does in he co e. The magni ude o he d op is compa able o he ∼+10 km s−1jump in o oidal o a ion ha is obse ed when a single neu al beam sou ce injec s o 10 ms [42]. E iden ly, he ishbone bu s ac s like a ‘nega i e beam blip.’ A 10 ms beam blip injec s abou +0.5 C o cha ge. F om he ∼10% d op in neu on a e o hese bu s s, he es ima ed cha ge o expelled as ions is ∼−0.3 C, so he ‘nega i e beam blip’ associa ed wi h he ishbone should educe he o oidal o a ion abou as much as a posi i e beam blip inc eases i , jus as is obse ed. 3.3. Con ined as ions In addi ion o he d op in signal associa ed wi h as -ion losses, he neu on signal also con ains oscilla ions ( igu e 18). A e il e ing ou high- equency noise, hese oscilla ions a e isible 18 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al -400 -200 0 200 400 1837 1838 1839 1840 0.80 0.85 0.90 0.95 1.00 1.05 1838.0 1838.5 1839.0 1839.5 1840.0 (a) Mi no (T/s) (b) Neu ons (a.u.) TIME (ms) (c) #141076 0 5 10 15 20 25 30 (d) Hal -cycle # 0 0.4 0.8 Dis o ion Neu on Phase 0 400 800 Figu e 18. Time e olu ion o (a) he Mi no coil signal and (b) he neu on signal du ing a ishbone bu s . (c) O e lay o he oscilla ions in he Mi no signal and he neu on signal. An e o unc ion i o he d op in he neu on a e is used o de end he neu on signal. (d) E olu ion o he mode dis o ion and neu on phase (deg ees) e sus hal -pe iod numbe . The dashed e ical line indica es he ime o maximum ampli ude. in he o al signal ( igu e 18(b)) bu hey become pa icula ly e iden a e de ending he signal o emo e he o e all d op ( igu e 18(c)). In con as o all o he los -ion measu emen s, he phase o hese neu on oscilla ions does no emain cons an h oughou he ishbone bu s . Ins ead, he phase s eadily slips ela i e o he Mi no ace as he bu s e ol es ( igu e 18(c)). The phase slippage is la ges nea maximum ampli ude, which is also when he mode dis o ion 19 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 0.0 0.5 1.0 1.5 2.0 -8-6-4-20246 -100 0 100 200 300 400 4 5 6 7 8 9 PERIOD # ( ela i e o Mi no peak) 0 200 200 150 150 100 100 50 50 MIRNOV AMP. (T/s) MIRNOV FREQ(kHz) (c) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 Peak Mi no Ampli ude (T/s) 0 100 200 300 400 NEUT. AMP. (%) NEUT. AMP. (%) NEUT. PHASE (º) PHASE SLIP (º) (a) (b) (d) Figu e 19. A e age neu on luc ua ion (a) ampli ude and (c) phase e sus pe iod numbe o 40 ela i ely la ge (140 <B max <162 T s−1) ishbone bu s s. The e olu ion o he mode (a) ampli ude and (c) equency o he same bu s s is also shown. The e o ba s ep esen he s anda d de ia ion o his ensemble. (b) Neu on luc ua ion ampli ude and (d) phase slippage e sus maximum Mi no ampli ude o all bu s s wi h cons an beam powe du ing he bu s . The lines a e linea i s o he da a. The ampli ude is an a e age o e cycles −3–0; he phase slippage is he a e age o e cycles −5—3 sub ac ed om he a e age o e cycles 1–3; he u ilized cycles a e highligh ed by boxes in (a) and (c), espec i ely. and equency chi ping apidly inc ease ( igu e 18(d)). Fo his pa icula case, in he cou se o he bu s , he phase slips o e 360◦. Because i measu es (p edomina ely) i gin neu ons, he plas ic scin illa o signal is sensi i e o he geome ical posi ion o he con ined as ions ha p oduce he neu on eac ions. Neu on oscilla ions o simila ampli ude we e measu ed o PDX ishbones [2]. S achan e al [2] showed ha hese oscilla ions we e caused by he helical dis o ion o he neu on- emi ing co e. Using he expec ed geome ical e iciency o he plas ic scin illa o and he measu ed displacemen o he in e nal kink mode, hey showed ha he p edic ed oscilla ions ag ee in bo h ampli ude and phase wi h he obse a ions. No phase slippage was epo ed. S achan’s model canno accoun o he phase slippage associa ed wi h o -axis ishbones. P esumably, as o PDX ishbones, he oscilla ions a e associa ed wi h mo ion o con ined as ions owa d and away om he de ec o . (Mo ion ela i e o he he mal deu e ium densi y g adien may also con ibu e.) Bu he phase slippage indica es ha he oscilla ions o he majo i y o con ined as ions decouples om he mode i sel , e en while he expelled ions e ain hei phase. This decoupling accele a es when he mode is la ge, dis o ing and changing apidly in equency. This phenomenon occu s o all o -axis ishbone bu s s. Figu es 19(a) and (c) show he a e age beha io o a se o simila bu s s. The neu on luc ua ion ampli ude usually peaks sligh ly be o e maximum Mi no ampli ude. (Fo an a e age o all o he bu s s in he da abase, he peak occu s wo cycles p io o he Mi no maximum.) The phase changes mos apidly when he equency changes. No e ha a ixed empo al delay ela i e o he mode would p oduce phase changes o he opposi e sign. Fo he en i e da abase, he neu on luc ua ion ampli ude scales linea ly wi h maximum Mi no ampli ude ( igu e 19(b)) ( =0.80). The phase slippage also ends o inc ease wi h maximum Mi no ampli ude ( igu e 19(d)) ( =0.55). In his la e case, he ela i ely la ge unce ain y in de e mina ion o he phase slip may accoun o some o he sca e . 20 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al 4. Discussion and conclusion Many ea u es o DIII-D o -axis ishbones a e simila o PDX q=1 ishbones. •The modes occu in high-be a plasmas nea an MHD s abili y limi . •They a e n=1 modes d i en by neu al beam ions. •The ini ial mode equency ma ches he p ecession equency o ull-ene gy apped ions; also, he adial p o ile o he p ecession equency is ai ly la , so as ions can s ay in esonance while being anspo ed adially. •The equency chi p is la ge ( / i≃0.4) and inc eases wi h inc easing mode ampli ude. Also, du ing a bu s , he equency chi p a e is la ges nea maximum mode ampli ude. •The g ow h a e is γ/ω ≃5%. •The modes appea in epe i i e bu s s. (The bu s cycle was mo e egula o PDX ishbones bu his di e ence is p obably caused by he s ong beam modula ion in he DIII-D expe imen s.) •The modes cause losses o as ions ha peak nea he ime o maximum mode ampli ude. •The magni ude o he losses scales app oxima ely linea ly wi h mode ampli ude. •Fas ions a e expelled o he ou side o he plasma in a ‘beacon’ (wi h a ixed phase ela i e o he mode). •Highe nmodes wi h simila phenomenology a e occasionally obse ed, as hey we e on PDX [2]. In addi ion, he loss o as ions causes a sudden d op in o oidal o a ion. This e ec was no measu ed on PDX bu p obably occu ed. On he o he hand, se e al ea u es o DIII-D o -axis ishbones di e om PDX ishbones. •On PDX, he decay a e was smalle han he g ow h a e bu he opposi e is ue o o -axis ishbones. Also, he decay phase is highly a iable o o -axis ishbones bu , in PDX, excep when a saw oo h c ash occu ed, he decay a e was egula . •On PDX, he wa e o m emained nea ly sinusoidal h oughou he bu s . In con as , o o -axis ishbones, he wa e o m always becomes highly dis o ed nea maximum mode ampli ude. •On PDX, he luc ua ions in he neu on signal main ained a ixed phase ela i e o he mode. Fo o -axis ishbones, he neu on phase slips con inuously when he ampli ude is la ge and he mode equency and wa e o m shape a e changing apidly. In addi ion, o o -axis ishbones, he adial eigen unc ion changes shape du ing he e olu ion o a bu s . This in o ma ion is no a ailable o PDX ishbones. The many simila i ies be ween PDX ishbones and o -axis ishbones suppo s he no ion ad anced by Okabayashi e al [15] ha o -axis ishbones a e an ene ge ic-pa icle b anch o a kink mode, jus as PDX ishbones a e an ene ge ic-pa icle b anch o he 1/1 in e nal kink. In his pa adigm, he bu s cycle esembles classic p eda o –p ey elaxa ion oscilla ions because he inc ease in as -ion densi y associa ed wi h beam ueling pushes a ma ginally s able mode ac oss he s abili y bounda y, hen he expulsion o he as ions s abilizes he mode [6,43]. In con as o a esis i e wall mode (o o he no mal mode o he backg ound plasma), he mode equency is de e mined by he p ecession equency o he as ions. The la ge equency chi ping and he non-pe u ba i e na u e o he eigen unc ion a e consis en wi h he idea ha he o -axis ishbone is a beam mode ha exis s due o he in ense as -ion popula ion. Wha accoun s o he di e ences in nonlinea beha io o PDX and o -axis ishbones? One possible explana ion is ha he o -axis ishbone is an ex e nal mode ins ead o an in e nal mode. (The esponse o he ins abili y o eedback is s ong e idence o he ex e nal na u e o 21 Plasma Phys. Con ol. Fusion 53 (2011) 085028 W W Heidb ink e al he o -axis ishbones [15].) In his hypo hesis, he mode dis o ion is caused by he dissipa ion associa ed wi h he conduc ing wall. Ano he di e ence be ween PDX ishbones and o -axis ishbones is he beam ueling. In PDX, all o he sou ces injec ed a he same angle, so he as -ion dis ibu ion unc ion was concen a ed a a single pi ch angle. In con as , he DIII-D expe imen s employ many angles o injec ion. (In addi ion, Teis su icien ly high ha he pi ch-angle sca e ing a e is compa able o he slowing-down a e, which u he iso opizes he dis ibu ion unc ion.) Pe haps he esponse o con ined as ions om o he sou ces is esponsible o he phase slippage in he neu on oscilla ions and also con ibu es o he dis o ion o he mode. A key goal o he ene ge ic-pa icle communi y is o de elop a p edic i e capabili y o as -ion d i en ins abili ies. The ascina ing nonlinea e olu ion o o -axis ishbones is a ipe opic o heo e ical s udy. 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