Mechanical design of superconducting accelerator magnets. Fernando Toral Accelerator Technology Group CIEMAT, Madrid, Spain

Transcription

1 Mechicl desig o supecoductig cceleto mgets Fedo Tol Acceleto Techology Goup CIEMAT, Mdid, Spi

2 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice,

3 Reeeces BOOKS [] S. Timosheko, Stegth o mteils, New Yok, D. V Nostd Compy, 9. [] M. Wilso, Supecoductig mgets, Oxod, Cledo Pess, 98. [] Y. Iws, Cse studies i supecoductig mgets, New Yok, Pleum Pess, 99. PAPERS [] R. Meuse, Mgetic ield d stesses o thi d thick cos- widigs, Egieeig Notes M55, M55 d M566 SCHOOLS [5] H. Felice, P. Feci, S. Pestmo, E. Todesco, Supecoductig mgets o pticle cceletos, USPAS,. Uits, d 9. [6] Supecoductivity i pticle cceletos, CERN-96- Repot. [7] C.L. Goodzeit, Supecoductig Acceleto Mgets, USPAS, uy Mechicl desig o SC mgets CAS, Eice,

4 Why is this topic impott? Supecoductig cceleto mgets e chcteized by lge ields d lge cuet desities. As esult, coils expeimet lge stesses. Those oces hve thee impott eects:. Quech tiggeig: the most likely cuse is the elese o stoed elstic eegy whe pt o the coil moves o cck suddely ppes. Due to the low het cpcity o mteils t low tempetues, tht eegy is ble to icese the tempetue o the supecoducto bove its citicl vlue.. Mechicl degdtio, both the coil o the suppot stuctue: i the pplied oces/pessues e bove give theshold (yield stegth), plstic deomtio o the mteils tke plce.. Field qulity: the widig deomtio my ect the ield qulity. Mechicl desig o SC mgets CAS, Eice,

5 Objectives o the mechicl desig The mget pts e poduced d ssembled t oom tempetue, but wokig tempetue is bout -7ºC: dieetil theml cotctios. Tkig ito ccout the oemetioed isks, the mechicl desig will im: To void tesile stesses o the supecoducto. To void mechicl degdtio o the mteils. To study the mget lie cycle: ssembly -> cooligdow -> poweig -> quech. Mechicl desig o SC mgets CAS, Eice, 5

6 Mechicl desig sttegy Clculte electomgetic oces Desig suppot stuctue (i ecessy) to void tesile stesses i the coductos No Is it comptible with the ssembly pocess coolig-dow d quech? Yes Ed Mechicl desig o SC mgets CAS, Eice, 6

7 Outlie Motivtio Bsic cocepts: Electomgetic oce, mgetic eegy d pessue. Stess, sti, Hooke s lw, Poisso s tio, she modulus. Mteil popeties: Youg s modulus, theml cotctio, ilue citei. Soleoids Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 7

8 Electomgetic oce A chged pticle q movig with speed v i the pesece o electic ield E d mgetic ield B expeieces the Loetz oce: F N q( E v B) A coducto elemet cyig cuet desity j i the pesece o mgetic ield B will expeiece the oce desity: N m j L The Loetz oce is body oce, tht is, it cts o ll the pts o the coducto, like the gvittiol oce. F N B L dv L q vxb v j + F qe E B L B Mechicl desig o SC mgets CAS, Eice, 8

9 Mgetic eegy d pessue The mgetic eegy desity u stoed i egio without mgetic mteils ( =) i pesece o mgetic ield B is: The totl eegy U c be obtied by itegtio ove ll the spce, by itegtio ove the coil volume o by kowig the soclled sel-iductce L o the mget: B H U dv A jdv LI ll coil Mechicl desig o SC mgets CAS, Eice, u m B H B The stoed eegy desity my be see s mgetic pessue p m. I cuet loop, the mgetic ield lie desity is highe iside: the ield lies ty to expd the loop, like gs i cotie. B p m N m 9

10 Stess I cotiuum mechics, stess is physicl qutity tht expesses the itel pessue tht eighboig pticles o cotiuous mteil exet o ech othe. Whe the oces e pepedicul to the ple, the stess is clled oml stess () ; whe the oces e pllel to the ple, the stess is clled she stess (). Stesses c be see s wy o body to esist the ctio (compessio, tesio, slidig) o extel oce. x z y A F z F y xy F A N m z P F N m y P A Mechicl desig o SC mgets CAS, Eice,

11 Sti d Hooke s lw A sti is omlized mesue o deomtio epesetig the displcemet δ betwee pticles i the body eltive to eeece legth l. Hooke s lw (678): withi ceti limits, the sti o b is popotiol to the exeted stess σ. The costt o popotiolity is the elstic costt o the mteil, so-clled modulus o elsticity E o Youg s modulus. F F z l E AE δ l A l Questio: wht is the sti o st. steel sque bem o mm side ude to oce? ststeel.8-9 Tesile (pullig) stess (+): elogtio Compessive (pushig) stess (-): cotctio Mechicl desig o SC mgets CAS, Eice,

12 Poisso s tio & she modulus The Poisso s tio is the tio betwee tsvesl to xil sti. Whe body is compessed i oe diectio, it teds to elogte i the othe diectio. Vice ves, whe body is elogted i oe diectio, it teds to get thie i the othe diectio. Typicl vlue is oud.. δ l F z tsvesl xil A she modulus G c lso be deied s the tio betwee the she stess to the she sti. G xy xy E Mechicl desig o SC mgets CAS, Eice,

13 Mteil popeties: Youg s modulus MATERIAL K ) YOUNG MODULUS (GP) POISSON RATIO SHEAR MODULUS (GP) Souces (theml pop: NbTi e- Cse Studies u Supecoductig Mgets, Y.Iws NbTi+Cu e- Hdbook o Acceletos Physics d Egieeig, M.Wu Coppe e- Cyogeic egieeig, T.M. Fly Isultio e- Fomv Epoxy e- Composites Hdbook, INTA AISI * (*popeties t K) 6L e- Hdbook o Applied Supecoductivity, B.Seebe WINDING SMEARED-OUT PROPERTIES (. K) z Mechicl desig o SC mgets CAS, Eice, YOUNG MODULUS (GP) POISSON RATIO SHEAR MODULUS (GP) 9.99E- 5.9E- z 5.9E-.8 z.8 z.5

14 Mteil popeties: theml cotctio The mget ssembly is lwys mde t oom tempetue. Oe eeds to lyze the iduced stesses due to dieet cotctio o joied pts duig coolig dow d t cold wokig tempetue. Oe must be vey ceul whe lyzig degdtio o isultig mteils: polyimide (Kpto) oil, vish, esi M. Wilso [] Mechicl desig o SC mgets CAS, Eice,

15 Filue citei The popotiolity betwee stess d sti is moe complicted th the Hooke s lw: A: limit o popotiolity (Hooke s lw) B: yield poit Mechicl desig o SC mgets CAS, Eice, Pemet deomtio o. % C: ultimte stegth D: ctue poit Sevel ilue citei e deied to estimte the ilue/yield o stuctul compoets, s Equivlet (Vo Mises) stess v yield, whee v S. Timosheko [] 5

16 Mteil popeties: NbTi d Nb S NbTi Nb S M. Wilso [] Mechicl desig o SC mgets CAS, Eice, 6

17 Outlie Motivtio Bsic cocepts Soleoids: Thi wll Thick wll Rel cse Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 7

18 Soleoid: thi wll (I) I iiitely log soleoid cyig cuet desity j, the ield iside is uiom d outside is zeo. Loetz oces e pushig the coil outwds i pue dil diectio, cetig hoop stess o the wies. Usig Ampee s lw: B dl I B z jwz B w z Assumig tht the vege coil ield is B /, the mgetic pessue is give by the distibuted Loetz oce: B F L u L zw u j zw u p m z u p m L B p m So, i T soleoid, the widigs udego pessue o 98 tm. Mechicl desig o SC mgets CAS, Eice, 8

19 Soleoid: thi wll (II) The simplest stess clcultio is bsed o the ssumptio tht ech tu cts idepedetly o its eighbos: F L F L coswd L w p m F L p m w B B w I geel, ssumig tht B is the ield t the iemost tu, t dius : p m w F mx B I ou exmple, ssumig dius o cm d thickess o mm, stess is bout MP. It is too high o Nb S (5 MP) d likely o NbTi (5 MP), i oe tkes illig cto o 7% i the widig Wht is the solutio? To it extel cylide with iteeece, which mkes pe-stess o the widig, decesig the tesile zimuthl stess. Mechicl desig o SC mgets CAS, Eice, 9

20 Soleoid: thick wll Thi coil: Rout/Ri=. Shot soleoid: ield mp (let) d Loetz oces (ight) Thick coil: Rout/Ri= The Loetz oces i soleoid ted to push the coil: Outwds i the dil-diectio (F > ) Towds the mid ple i the xil diectio (F y < ) Rdil stesses e ot eglected (lbel ). Whe dil stesses become tesile (positive), thee is isk o esi cckig, which my iduce quech. I summy, log d thi soleoids e mechiclly moe stble. Mechicl desig o SC mgets CAS, Eice, M. Wilso []

21 Itesidd (A) Soleoid: el cse (I) Tiig test Etemieto imá CRISA Theml shield SC soleoid G bobbi Spce SC switch Cyostt Cuet (A) Quech umbe Nº de quech etiig Legth.75 mm Ie dimete 88.7 mm Oute dimete 5 mm Numbe o tus 78 Nomil cuet 5 A Pek ield 5.89 T Boe ield.5 T Cuet desity 9 A/mm Wokig poit 75% Sel iductce.5 H Mechicl desig o SC mgets CAS, Eice, A shot soleoid ws tied with poo esults, below 5% o the lod lie: mechicl desig mistke limits the peomce. S. Sz, Developmet o supecoductig soleoid to test AMS powe supply, CIEMAT, 6

22 Itesidd (A) Soleoid: el cse (II) Etemieto imá CRISA Tiig test 5 Cuet (A) etiig Quech Nº de quech umbe Mechicl desig o SC mgets CAS, Eice, Post-motem lysis: the theml cotctio o G bobbi is smlle th tht o the widig. The bobbi coe ws tued out: the xil stess distibutio is ow completely dieet, o tesile stess o the widig.

23 Numeicl methods ( bit o philosophy) Alyticl expessios e geelly vlid oly o simpliied models. Numeicl methods e ble to model vey pecisely the el lie: Aisotopic mteil popeties. Complicted geomety. Sophisticted boudy coditios: slidig/cotct suces, joits. Lod steps: ssembly, coolig dow, eegizig. Tsiet poblems. Thee is commo mistke: to oget bout lyticl ppoch d come diectly to the umeicl simultio. Howeve, lyticl methods e COMPLETELY ecessy: To udestd the poblem. To mke ist estimte o the solutio. To simpliy the umeicl simultio. To check d UNDERSTAND the esults o the umeicl simultio. Mechicl desig o SC mgets CAS, Eice,

24 Wht hve we let? The mechicl desig o supecoductig mget ims to void tesile stesses o the coil d mechicl degdtio o mteils. Electomgetic (Loetz) oce is body oce. We hve eviewed bsic cocepts o stegth o mteils, such s stess, sti, modulus o elsticity, ilue citei Mteil popeties e stogly depedet o tempetue. Coils e composite o isultig mteils d supecoductos. Mgetic pessue iduces hoop stesses i the soleoid coductos. Log d thi soleoids e mechiclly moe stble th thick oes. Dieetil theml coeiciets my iduce pemtue queches i supecoductig mgets. Mechicl desig o SC mgets CAS, Eice,

25 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets: Cos-thet type: Widig ppoximtios: thi shell, thick shell, secto. Ed oces. Pe-stess: low, high d vey high ield mgets. Supeeic type. Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 5

26 Acceleto supecoductig mget types Cosie- type Field qulity domited by the coils (io is optiol). Cuved coils oud cylidicl petue. Supeeic type Field qulity domited by the io yoke. Flt coils (sometimes with o-ple bedig t coil eds). Mechicl desig o SC mgets CAS, Eice, 6

27 Cos- type mgets: Loetz oces (I) The Loetz oces i -pole mget ted to push the coil: Tevto dipole Towds the mid ple i the veticl-zimuthl diectio (F y, F < ) Outwds i the dil-hoizotl diectio (F x, F > ) TQ Mechicl desig o SC mgets CAS, Eice, P. Feci [5] 7

28 Cos- type mgets: Loetz oces (II) I the coil eds, the Loetz oces ted to mke the coil loge: outwds i the logitudil diectio (F z > ). I shot, the ield lies ty to expd the coil, like i cuet loop. Howeve, the coil is uble to suppot the mgetic oces i tesio. These oces must be hold by extel suppot stuctue. Mechicl desig o SC mgets CAS, Eice, 8

29 Appoximtios o widig coss-sectios I ode to estimte the oce, let s coside thee dieet ppoximtios o -ode mget: Thi shell (see Appedix I) Cuet desity = cos (A pe uit cicumeece) o iiitely thi shell Odes o mgitude d popotiolities Thick shell (see Appedix II) Cuet desity = cos (A pe uit e) o shell with iite thickess Fist ode estimte o oces d stess Secto (see Appedix III) Cuet desity = costt (A pe uit e) o secto with mximum gle = 6º/º o dipole/qudupole Fist ode estimte o oces d stess Mechicl desig o SC mgets CAS, Eice, P. Feci [5] 9

30 Thi shell (cuet sheet) (I) Beth s theoem: the complex oce o cuet elemet (pe uit legth i the logitudil diectio z) is equl to the lie itegl o mgetic pessue oud the boudy o tht elemet i the complex ple: F F y if x B dz Fo cylidicl cuet sheet, the totl oce [N/m] o hl coil is: i F Bi Bout ie d I cuet desity is give by = cos [A/m], d ssumig io with = t dius R, the desity oce [N/m ] is: R io x i y i i e e 8 R R e i Mechicl desig o SC mgets CAS, Eice,

31 Mechicl desig o SC mgets CAS, Eice, Thi shell (cuet sheet) (II) Oe c get the tgetil d oml compoets by dot poduct with the tget d oml uit vectos: Fo dipole, the oce o hl the coil is: It is popotiol to the sque o the cuet desity (d ield) d the boe dius. See Appedix o expessios o dipole d qudupole without io. R e t i si R e i cos R io t R d m N F x si cos d m N F y cos si

32 Thi shell (cuet sheet) (III) Oe c coside el widig like sum o cuet sheets d solve the poblem by supepositio. It woks ie o the ield, the stoed mgetic eegy d the oces. Applictio to coecto qudupole pototype mget developed o LHC, MQTL. Mgitude SHEET ROXIE FEM Uits B T/m b uits b uits b uits B mx T L mh/m F x N F y N F. Tol et l., Futhe Developmets o Beth s Cuet-Sheet Theoem: Computtio o Mgetic Field, Eegy d Mechicl Stesses i the Coss-Sectio o Pticle Acceleto Mgets, MT-8, Mechicl desig o SC mgets CAS, Eice,

33 Mechicl desig o SC mgets CAS, Eice, Thick shell (I) We ssume = cos whee [A/m ] is to the coss-sectio ple Ie (oute) dius o the coils = ( ) No io The ield iside the petue is The ield i the coil is The Loetz oce ctig o the coil [N/m ] is B i si B i cos B si B cos B cos B cos si si cos x cos si y R. Meuse []

34 Mechicl desig o SC mgets CAS, Eice, Thick shell (II) I dipole, the ield iside the coil is: The totl oce ctig o the coil [N/m] is: A simple ppoximtio o the mximum stess t the midple is: B y l F x l 9 7 F y b F MP y y

35 Mechicl desig o SC mgets CAS, Eice, 5 Secto: dipole (I) We ssume Uiom = is the coss-sectio ple Ie (oute) dius o the coils = ( ) Agle = 6º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is si si si si B cos si cos si B si si si si B cos si cos si B R. Meuse []

36 Mechicl desig o SC mgets CAS, Eice, 6 Secto: dipole (II) The Loetz oce ctig o the coil [N/m ], cosideig the bsic tem, is The totl oce ctig o the coil [N/m] is cos si B si si B si cos x cos si y 6 6 l 6 F x l F y

37 Ed oces Vitul displcemet piciple: the vitio o stoed mgetic eegy U with the mget legth equls the xil oce pullig om the eds, keepig costt the othe dimesios. Tht is, the stoed mgetic eegy pe uit legth equls the xil oce: i LHC mi dipole, it is 5 kn pe coil ed. I the cse o thi shell, it c be witte s: Fz N R Fo the sme cuet desity, the ed oces o qudupole coil e hl th i dipole. Plese id expessios o thick shell d secto ppoximtios i the Appedices. Clcultios e mde witig the stoed eegy U s uctio o the mgetic vecto potetil A, obtied om the ield: Mechicl desig o SC mgets CAS, Eice, B F z A N U z z, B Az, 7

38 Wht hve we let? Thee e two mi types o supecoductig cceleto mgets: supeeic d cos-. I cos- mgets, the widig coss-sectio my be ppoximted i dieet wys: thi shell, thick shell o sectos. Axil oces o coil eds equl the stoed mgetic eegy pe uit legth. Mechicl desig o SC mgets CAS, Eice, 8

39 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets: Cos-thet type: Widig ppoximtios: thi shell, thick shell, secto. Ed oces. Pe-stess: low, high d vey high ield mgets. Supeeic type. Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 9

40 Pe-stess (I) Oe o the mi coces o the mechicl desige is to void tesile stesses o the supecoductig coductos whe they e poweed. The clssicl solutio is to pply pe-compessio: ch bidge. Fo cos- widig coigutios, the extel stuctue usully pplies dil iwd compessio which is tsomed ito zimuthl compessio iside the coil which coutects the omtio o tesile stesses tht would othewise ppe ude the ctio o the electomgetic oces. Mechicl desig o SC mgets CAS, Eice,

41 Pe-stess (II) The oute shell must be sti eough. F A simple ppoch is to ssume the dil Loetz oce s uiom pessue o tke the hoizotl compoet: p The mximum stess i the shell t cool-dow is usully bout - MP. Fo -pole mgets, oe c compute the mximum bedig momet i thi cylide ude dil oces septed by gle o : F cosx Mechicl desig o SC mgets CAS, Eice, MP F N / m M P 6M si MP Rok s omuls o stess d sti, McGw-Hill F Lx F F x

42 Pe-stess: low ield mgets (I) Let s ssume s low ield mgets i coil pek ield is below T. Coductos e usully moolithic wies (ully impegted coils). The coils o most o LHC coecto mgets wee pe-compessed by scissos io lmitios: The pe-compessio is povided by oute lumium shikig cylide. The io cot be hollow cylide becuse it cotcts less th the coils. Usig eccetic pied lmitios with dieet oiettios, the iwds pessue is mde ltetively o eighbou coils. The io is plced vey close to the coils o ield ehcemet. It is simple system o seies poductio: ie blkig. A. Ijspeet,. Slmie, Supecoductig coil compessio by scisso lmitios, LHC Repot 7, 996 Mechicl desig o SC mgets CAS, Eice,

43 Cuet level t Quech I [Amps] Pe-stess: low ield mgets (II) Lessos tht c be extcted om oe o the qudupole LHC coecto pototypes, MQTL, which ws. m log: Holes i the io to impove the ield qulity e elliptic to decese the stesses t the hole ie edge. Slow tiig test, with o impovemet om to.9 K: mechicl poblem. It is ot solved with icesed iteeece (ModA). Detiig suggests slip-stick movemets betwee the io lmitios d the coils due to xil oces. 65 Retiig/Tiig Queches o MQTL K Quech Numbe Mechicl desig o SC mgets CAS, Eice, F. Tol, PhD Thesis, Mdid,

44 Pe-stess: low ield mgets (III) I the coils o qudupole pototype o TESLA5/ILC poject wee eegized without y suppot stuctue, they would expeiece tesile (positive) stesses. Nomil cuet is A, t 5% o the lod lie. Deomtios (mm) i zimuthl diectio Stesses (MP) i zimuthl diectio F. Tol et l., Fbictio d Testig o Combied Supecoductig Mget o the TESLA Test Fcility, MT-9, 5 Mechicl desig o SC mgets CAS, Eice,

45 Pe-stess: low ield mgets (IV) The coil ssembly ws potected by wpped glss-ibe bdge. The pe-compessio ws povided by oute lumium cylide. The io ws split i ou sectos. Ech secto hd dii which itted with the coils d the shikig cylide t cold coditios. Mechicl desig o SC mgets CAS, Eice, Deomtios (mm) i zimuthl diectio Stesses (MP) i zimuthl diectio 5

46 CURRENT (A) Pe-stess: low ield mgets (V) The ist tiig test ws quite poo. Two o the io sectos wee shimmed to blce the pe-compessio: secod tiig impoved lot. Tiig did ot impove coolig dow to.9k: mechicl poblem limits peomce, likely the ed oces o the ested dipole coils h=85 mm h=5 mm h=5 mm Alumium oute dimete beoe e-ssembly Mechicl desig o SC mgets CAS, Eice, QUENCH NUMBER tiig K qud tiig K combied tiig K qud tiig K qud etiig K qud ist cmpig K h=85 mm h=5 mm h=5 mm Alumium oute dimete te e-ssembly 6

47 Pe-stess: high ield mgets (I) Let s coside s high ield mgets those with coil ields i the ge om to T. Coductos e usully cbles with polyimide tpe isultio. I the cse o the Tevto mi dipole (B om =. T), ssumig iiitely igid stuctue without pe-stess, the pole would move o bout - m, with stess o the mid-ple o -5 MP t omil cuet. Mechicl desig o SC mgets CAS, Eice, Azimuthl displcemets P. Feci [5] Azimuthl stess distibutio 7

48 Pe-stess: high ield mgets (II) We ocus ow o the stess d displcemet o the pole tu (high ield egio) i dieet pe-stess coditios. The totl displcemet o the pole tu is popotiol to the pe-stess. A ull pe-stess coditio (- MP) miimizes the displcemets. Alumium oute dimete beoe e-ssembly P. Feci [5] Mechicl desig o SC mgets CAS, Eice, Alumium oute dimete te e-ssembly 8

49 Pe-stess: high ield mgets (III) The pctice o pe-stessig the coil hs bee pplied to ll the cceleto lge dipole mgets: Tevto (K. Koepke, et l., IEEE Ts. Mg., Vol. MAG-5, No. l,. 979) HERA (S. Wol, AIP Co. Poc. 9, 99, pp. 6-97) SSC (A. Deved, AIP Co. Poc. 9, 99, pp. 9-7 d T. Ogitsu, et l., IEEE Ts. Appl. Supecod., Vol., No. l, Mch 99, pp ) RHIC (. Mutoe, BNL, pivte commuictios) LHC (CERN---v-, ) The pe-stess is chose i such wy tht the coil emis i cotct with the pole t omil ield, sometime with mechicl mgi o moe th MP. Mechicl desig o SC mgets CAS, Eice, 9

50 Pe-stess: high ield mgets (IV) Colls wee implemeted o the ist time i the Tevto dipoles. Sice the, they hve bee used i ll but oe (RHIC) the high ield cos- cceleto mgets d i most o the R&D mgets. They e composed by stiless-steel o lumium lmitios ew mm thick. The colls tke ce o the Loetz oces d povide high ccucy o coil positioig. Its shpe tolece is bout +/- mico. A good kowledge o the coil popeties (iitil dimesios d E) is mdtoy to pedict il coil sttus. I dditio, coll deomtio must be tke ito ccout. LHC mi dipole colls Mechicl desig o SC mgets CAS, Eice, L. Rossi, Supecoductig Mgets, CERN Acdemic Tiig, 5-8 My. 5

51 Pe-stess: high ield mgets (V) Sice the ucompessed coil is ovesized with espect to the coll cvity dimesio, t the begiig o the collig pocedue the colls e ot locked (ope). The coil/coll pck is the itoduced ito collig pess. The pessue o the pess is icesed util omil vlue. Colls e locked with keys, ods o welded, the the pess is elesed. Oce the collig pess is elesed, the coll expeiece spig bck due to the clece o the lockig etue d deomtio. The pe-stess my chge duig cool-dow due to the dieet theml cotctio o the colls d coils. Mechicl desig o SC mgets CAS, Eice, LHC dipole collig L. Rossi, The LHC om costuctio to commisioig, FNAL semi, 9 Apil 7. 5

52 Pe-stess: high ield mgets (VI) Fo ields bove 6T, it is usully ecessy tht the est o the stuctue cotibutes to suppot the Loetz oces. At omil ield, LHC dipole expeieces F x =.7 MN/m d F y =-.75 MN/m pe qudt. I tht cse, the stiless steel oute shell is split i two hlves welded oud the yoke with high tesio (bout 5 MP). The shell thickess is such tht the mximum stess t cool-dow is bout - MP. Whe the yoke is put oud the colled coil, gp (veticl o hoizotl) emis betwee the two hlves. This gp is due to the coll deomtio iduced by coil pestess. I ecessy, duig the weldig pocess, the weldig pess c impose the desied cuvtue o the cold mss. I the LHC dipole the omil sg is o 9. mm. Mechicl desig o SC mgets CAS, Eice, L. Rossi, The LHC om costuctio to commisioig, FNAL semi, 9 Apil 7. 5

53 Pe-stess: high ield mgets (VII) Ed pltes, pplied te shell weldig, povide xil suppot to the coil ude the ctio o the logitudil Loetz oces. Toque my be pplied to ed bolts. The oute shell c ct s liquid helium cotie. TQ qudupole (P. Feci) LHC mi dipole (L. Rossi) Mechicl desig o SC mgets CAS, Eice, SSC dipole (A. Deved) 5

54 Pe-stess: vey high ield mgets (I) Let s cll vey high ield mgets those beyod T. These e R+D objects. All the colled mgets peseted so e chcteized by sigiict coil pe-stess losses: The coil eches the mximum compessio (bout MP) duig the collig opetio. Ate cool-dow the esidul pestess is o bout - MP. Wht i the equied coil pe-stess te cool-dow is gete th MP? P. Feci [5] Mechicl desig o SC mgets CAS, Eice, 5

55 Pe-stess: vey high ield mgets (II) Oe solutio cosists o usig blddes to ssemble the mget. The TQ qudupole coil is suouded by ou pds d ou yokes, which emi ope duig ll the mget opetios. A lumium shell cotis the cold mss. Iitil pe-compessio is povided by wtepessuized blddes d locked by keys. Ate cool-dow the coil pe-stess iceses due to the high theml cotctio o the lumium shell. Mechicl desig o SC mgets CAS, Eice, P. Feci [5] 55

56 Pe-stess: vey high ield mgets (III) I the cse o TQS pototype qudupole (LBL+FNAL), the collig pess opetio is substituted by the bldde opetio. A spig bck occus whe bldde pessue is educed, sice some clece is eeded o key isetio. The coil pe-stess sigiictly iceses duig cool-dow. R+D wok is ogoig to pove tht these mgets: Ae ble to povide cceleto ield qulity. My be bicted with legths o sevel metes. Oe o the mgets o LHC upgde is beig desiged ollowig this ppoch: MQXF (T/m gdiet i 5 mm petue). Mechicl desig o SC mgets CAS, Eice, P. Feci [5] 56

57 Pe-stess: vey high ield mgets (IV) Othe ovel stess mgemet system (TAMU, Texs A&M) is bsed o itemedite coil suppots. Ech coil block is isolted i its ow comptmet d suppoted septely. Loetz oce exeted o multiple coil blocks does ot ccumulte, but it is tsmitted to the mget me by the Icoel ibs to Icoel pltes. A lmi spig is used to pelod ech block. Mechicl desig o SC mgets CAS, Eice, C. Goodzeit [7] 57

58 Pe-stess: cotovesy (I) As we hve see, the pe-stess voids the ppece o tesile stesses d limits the movemet o the coductos. Cotovesy: which is the ight vlue o the pe-stess? I Tevto dipoles, it ws let tht thee ws ot good coeltio betwee smll coil movemets (<. mm) d mget leig cuve. I LHC shot dipole pogm, the coils wee uloded t 75% o omil cuet, without degdtio i the peomce. I LARP TQ qudupoles: With low pe-stess, ulodig but still good quech peomce With high pe-stess, stble plteu but smll degdtio TQS low pestess TQS low pestess TQSb high pestess TQSb high pestess P. Feci [5] Mechicl desig o SC mgets CAS, Eice, 58

59 CURRENT(A) Pe-stess: cotovesy (II) I LHC coecto sextupoles (MCS), speciic test pogm ws u to id the optiml vlue o pe-stess. Coils wee poweed ude dieet pe-compessios immesed i the sme ield mp th the mget: Leig cuve ws poo i ee coditios. Tiig ws optiml with low pe-stess d oud MP. Degdtio ws obseved o high pe-stess (bove MP). Filly, omil pe-stess o seies poductio ws MP MP AZIMUTHAL PRE-STRESS 5MP AZIMUTHAL PRE-STRESS MP AZIMUTHAL PRE-STRESS MP AZIMUTHAL PRE-STRESS MP AZIMUTHAL PRE-STRESS N.OF QUENCHES Mechicl desig o SC mgets CAS, Eice, M. Bjko et l., Tiig Study o Supecoductig Coils o the LHC Sextupole Coecto Mget, LHC Repot 6,

60 Wht hve we let? Pe-compessio is the clssicl wy to void tesile stesses o the coils whe eegizig supecoductig mget. Dieet costuctio/desig methods, depedig o the electomgetic oce/ield vlues: Low ield: shikig oute shell High ield: colls + oute shell Vey high ield: blddes, itemedite coil suppots. I mget tiig does ot impove om. to.9k, thee is mechicl limittio. Cotovesy: which is the ight vlue o pe-compessio? Mechicl desig o SC mgets CAS, Eice, 6

61 Supeeic cceleto mgets (I) The stess distibutio i the coil is dieet om tht i the cos- mgets: whe poweed, the coil expeieces i-ple expsio oces, d it is usully ttcted by the io. I smll mgets, simple suppot stuctues (like wedges) e suiciet to hold the coils. wedge F. Tol et l. Developmet o Rditio Resistt Supecoductig Coecto Mgets o LHC Upgde, ASC Mechicl desig o SC mgets CAS, Eice, coil io pole 6

62 Supeeic cceleto mgets (II) Lge supeeic mgets e vey commo i gmet septos (NSCL-MSU, RIKEN, FAIR) d pticle detectos (SAMURAI, CBM). Usully, the io is wm. The, the Loetz oces o the coil e hold by stiless steel csig which is lso the helium vessel. I some cses, pt o these oces my be tseed to the extel stuctue by mes o low-het-loss suppots. Cyostt (SUS) SUS cylide yoke GFRP cylide Suppot lik 8K shield (Al) K shield (Al) coil 6x8 pole H. Sto, Supecoductig Dipole Mget o SAMURAI Spectomete, ASC- Mechicl desig o SC mgets CAS, Eice, Coil vessel (SUS6L) GFRP Hete (Cu wie) Coss-sectiol view 6

63 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 6

64 Tooids (I) As the mgetic pessue vies log the coil, it is subjected to stog bedig oces. I oe wts to simpliy the suppot stuctue: Ech coil expeieces et oce towds the cete becuse the ield is stogest thee: it is wise to ltte the ie edge o the coil, to le o suppot stuctue. The est o the cicumeece will distot to shpe wokig ude pue tesio, whee o bedig oces e peset. This tesio must be costt oud the coil. Assumig R s the distce to the cete d the locl dius o cuvtue o the coil, the coditio o locl equilibium would be: T B R B(R) B dr dz TR KR d I costt R R R dz Thee is o lyticl solutio. Figue o the ight shows mily o solutios. B R I Mechicl desig o SC mgets CAS, Eice, M. Wilso [] 6

65 Tooids (II) Tooids e usul i usio ectos. Nomil cuets e lge. Coils e used to be woud with cble-i-coduit coductos (CICC). EDIPO poject: supeeic dipole to chcteize coductos o ITER coils. Boe ield is.5 T. Mget legth is. m. Loetz oces e huge: F x = tos F y =-5 tos F z = tos. Lucs, EFDA dipole, 5 Mechicl desig o SC mgets CAS, Eice, 65

66 Tooids (III) Thee e two dieet FEM models o mechicl lysis: A geel model, with less detils, to study the suppot stuctue deomtio. A sub-model o the coil to lyze the stesses o the coductos, mily i the isultio: Loetz oces e tseed s pessues the cotct with the suppot stuctue is modeled s boudy coditio. Lucs, EFDA dipole, 5 Mechicl desig o SC mgets CAS, Eice, 66

67 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 67

68 F (N) Fil exmple: AMIT cycloto (I) AMIT poject (Sedecl-CIEMAT): compct, T supecoductig cycloto. Io pole dius is 75 mm. Wm io cocept. Electomgetic oces betwee the coils c be ttctive o epulsive, depedig o the eltive positio d the cuet. Desig choice is epulsive, bout kn pe coil. COILS SUPPORT IRON HELIUM VESSEL CRYOSTAT WARM IRON SOLUTION COIL FORCE VS CURRENT I (A) Mechicl desig o SC mgets CAS, Eice, 68

69 Fil exmple: AMIT cycloto (II) Suppot stuctue must hold: Rdil oces will iduce pessue i the widig. Sice the coil is thick, it is vey likely tht POSITIVE dil stesses will ppe i the cete o the coil. I y cse, they will iduce high HOOP stesses i the supecoducto. Axil oces will pull both coils towds the io, thus iducig POSITIVE xil stesses i the widigs. Axil oces will iduce BENDING MOMENTS t the coes o the suppot stuctue (hollows e ecessy to itoduce the vcuum chmbe). F z F. Muill, CIEMAT, Mechicl desig o SC mgets CAS, Eice, 69

70 Fil exmple: AMIT cycloto (III) Pth deiitio o stess evlutios: FROM INTERNAL Fce o COIL TO EXTERNAL FACE o Shikge Y Axis (MP) Stesses i the coil d lumium cylide hve bee clculted t wm, cold d eegized coditios. Figues show dil distibutio o dil d hoop stesses i those coditios. Rdil stesses i the coil e lwys egtive while hoop stesses e positive d limited to 5 MP i the coil d 5 MP i the cylide. COIL AL. COIL AL. COIL AL. Rdil (Let Axis) Rdil (Let Axis) Rdil (Let Axis) Hoop (Right Axis) Hoop (Right Axis) Hoop (Right Axis) X Axis (mm) Mechicl desig o SC mgets CAS, Eice, Stesses t Wm Stesses t,k Stesses t,k d Mget ON. Muill, CIEMAT, 7

71 Fil exmple: AMIT cycloto (IV) Stess distibutio i the stiless steel suppot stuctue hs bee clculted om the mgetic oces d the theml dieetil cotctios usig FEM. Mximum vlues e locted i the coes (see igue) due to the bedig momets iduced by the xil mgetic oces. Thei vlue is i the ode o 8 MP. Mx 8 MP Mgetic Foces t Coil Stess distibutio i the Stuctue Mechicl desig o SC mgets CAS, Eice,. Muill, CIEMAT, 7

72 Foce (N) Fil exmple: AMIT cycloto (V) 6 Mgetic Foce om No-Peect Aligmet o Coils Cse 5 X Y Z O-Axis Distce (mm) Whe the coils e ot ceted with the io poles, some oces will ise. These oces hve bee clculted i thee xes (X & Y xes e dieet due to the pesece o the vcuum chmbe hole i the io). The oces e i the diectio o the misligmet with positive slope (tyig to icese the o-xis eo). Mechicl desig o SC mgets CAS, Eice,. Muill, CIEMAT, 7

73 Fil exmple: AMIT cycloto (VI) Stesses i the suppots hve bee clculted t both, ceted d o-xis coditios. Uppe ods will develop lge stesses sice the coils hg om them o the oe hd d they e used to lig the mget, developig theml cotctios o the othe hd, while the lowe ods e ee util the mget is cold d i positio d the the uts e closed exetig to them ceti tesio to povide ssembly stiess. Stesses i the G Rods. CONDITIONS: Cold, djusted, mget ON Mximum vlue: 6 MP Stesses i the G Rods. CONDITIONS: Cold,.5 mm o-y xis, mget ON Mximum vlue: 59 MP Mechicl desig o SC mgets CAS, Eice,. Muill, CIEMAT, 7

74 Outlie Motivtio Bsic cocepts Soleoids Acceleto mgets Tooids Fil exmple Mesuemet techiques Mechicl desig o SC mgets CAS, Eice, 7

75 Mesuemet techiques: stess Cpcitive guge: the bsic piciple is to mesue the vitio o cpcity iduced by pessue i cpcito. Beig S the e o the two pllel electodes, the thickess o the dielectic, d the electic pemittivity, the cpcity C is give by C S / Whe pessue is pplied, the cpcity will chge C S / E Clibtio: the cpcity c be mesued s uctio o pessue d tempetue. Mechicl desig o SC mgets CAS, Eice, N. Siegel, et l., Desig d use o cpcitive oce tsduces o supecoductig mget models o the LHC, LHC Poject Repot 7. 75

76 Mesuemet techiques: sti The bsic piciple is to mesue the vitio o esistce iduced by sti i esisto. The guge cosists o wie ged i gid ptte boded o the suce o the specime The sti expeieced by the test specime is tseed diectly to the sti guge. The guge espods with lie chge i electicl esistce. The guge sesitivity to sti is expessed by the guge cto R / R GF l / l The GF is usully ~. Guges e clibted by pplyig kow pessue to stck o coductos o bem. C.L. Goodzeit, et l., IEEE Ts. Mg., Vol. 5, No., Mch 989, p Mechicl desig o SC mgets CAS, Eice, 76

77 Mesuemet techiques: coil popeties The elstic modulus E is mesued by compessig stck o coductos, usully clled te-stck, d mesuig the iduced deomtio. The theml cotctio is give by lwo l l whee l w d l c e the uloded height o the specime espectively t oom d cold tempetue. It c be lso evluted usig the stess loss i ixed cvity. wo co M. Reytie, et l., IEEE Ts. Supecod., Vol., Issue, Mch, p K.P. Chow d G.A. Millos, IEEE Ts. Supecod., Vol. 9, Issue, ue 999, p. 5. D.R. Chichili, et l., IEEE Ts. Supecod., Vol., Issue, Mch, p. 7. Mechicl desig o SC mgets CAS, Eice, 77

78 Shot summy The mechicl desige o supecoductig mgets should void tesile stesses o the coils d the mechicl degdtio o mteils. Pe-compessio is the clssicl wy to void tesile stesses o the coils whe eegizig supecoductig mget. Numeicl methods povide bette modelig, but lyticl ppoch is vey vluble. Filly, oe should lwys eview the pevious expeiece, it is ot ecessy to eivet the wheel. Mechicl desig o SC mgets CAS, Eice, 78

79 Appedices All the Appedices e tke om Uit, USPAS couse o Supecoductig Acceleto Mgets, (P. Feci et l.) Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 79

80 Appedix I Thi shell ppoximtio Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 8

81 Appedix I: thi shell ppoximtio Field d oces: geel cse We ssume = cos whee [A/m] is Rdius o the shell/coil = No io The ield iside the petue is Bi si B The vege ield i the coil is B to the coss-sectio ple The Loetz oce ctig o the coil [N/m ] is x B i si B cos si cos B si cos y si cos Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 8

82 Appedix I: thi shell ppoximtio Field d oces: dipole I dipole, the ield iside the coil is B y The totl oce ctig o the coil [N/m] is F x B y F y B y The Loetz oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue liely with the boe dius. I igid stuctue, the oce detemies zimuthl displcemet o the coil d cetes septio t the pole. The stuctue sees F x. Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 8

83 Appedix I: thi shell ppoximtio Field d oces: qudupole I qudupole, the gdiet [T/m] iside the coil is G The totl oce ctig o the coil [N/m] is B c F x B c 5 G 5 F y B c 8 5 G 8 5 The Loetz oce o qudupole coil vies with the sque o the gdiet o coil pek ield with the cube o the petue dius (o ixed gdiet). Keepig the pek ield costt, the oce is popotiol to the petue. Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 8

84 Appedix I: thi shell ppoximtio Stoed eegy d ed oces: dipole d qudupole Fo dipole, the vecto potetil withi the thi shell is d, theeoe, The xil oce o dipole coil vies with the sque o the boe ield liely with the mgetic pessue with the sque o the boe dius. Fo qudupole, the vecto potetil withi the thi shell is d, theeoe, A z A z F z By B cos c Fz Beig the pek ield the sme, qudupole hs hl the F z o dipole. cos G Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 8

85 Appedix I: thi shell ppoximtio Totl oce o the mid-ple: dipole d qudupole I we ssume om ch coditio, whee ll the θ ccumultes o the mid-ple, we c compute totl oce tsmitted o the mid-ple F θ [N/m] Fo dipole, Fo qudupole, F B y d F B c d G Beig the pek ield the sme, qudupole hs hl the F θ o dipole. Keepig the pek ield costt, the oce is popotiol to the petue. Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 85

86 Appedix II Thick shell ppoximtio Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 86

87 Appedix II: thick shell ppoximtio Field d oces: geel cse We ssume = cos whee [A/m ] is to the coss-sectio ple Ie (oute) dius o the coils = () No io The ield iside the petue is The ield i the coil is The Loetz oce ctig o the coil [N/m ] is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 87 B i si B i cos B si B cos B cos B cos si si cos x cos si y

88 Appedix II: thick shell ppoximtio Field d oces: dipole I dipole, the ield iside the coil is The totl oce ctig o the coil [N/m] is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 88 B y l F x l 9 7 F y

89 Appedix II: thick shell ppoximtio Field d oces: qudupole I qudupole, the ield iside the coil is G B y l beig l The totl oce ctig o the coil [N/m] is F x l 5 F y l Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 89

90 Appedix II: thick shell ppoximtio Stoed eegy, ed oces: dipole d qudupole Fo dipole, d, theeoe, Fo qudupole, d, theeoe, Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 9 cos A z 6 F z cos l A z l 8 8 F z

91 Stess o mid-ple (MP) Appedix II: thick shell ppoximtio Stess o the mid-ple: dipole d qudupole Fo dipole, Fo qudupole, 57.8 midd ( ) _ mid ple _ v / d 5 l 6 6 _ mid ple / l d 7 9 v l _ mid ple _ mid ple _ No she Rdius (m) Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 9

92 Appedix III Secto ppoximtio Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 9

93 Appedix III: secto ppoximtio Field d oces: dipole We ssume = is the coss-sectio ple Ie (oute) dius o the coils = () Agle = 6º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 9 si si si si B cos si cos si B si si si si B cos si cos si B

94 Appedix III: secto ppoximtio Field d oces: dipole The Loetz oce ctig o the coil [N/m ], cosideig the bsic tem, is The totl oce ctig o the coil [N/m] is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 9 cos si B si si B si cos x cos si y 6 6 l 6 F x l F y

95 Appedix III: secto ppoximtio Field d oces: qudupole We ssume = is the coss-sectio ple Ie (oute) dius o the coils = () Agle = º (thid hmoic tem is ull) No io The ield iside the petue The ield i the coil is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 95 si si si si l B cos si cos si l B si si si si l B cos si cos si l B

96 Appedix III: secto ppoximtio Field d oces: qudupole The Loetz oce ctig o the coil [N/m ], cosideig the bsic tem, is The totl oce ctig o the coil [N/m] is Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 96 si cos x cos si y cos l si B si l si B l 6 7 F x 9 l F y

97 Appedix III: secto ppoximtio Stoed eegy, ed oces: dipole d qudupole Fo dipole, d, theeoe, Fo qudupole, d, theeoe, Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 97 cos si A z 6 F z cos l si A z l 8 8 F z

98 Stess o mid-ple (MP) Appedix III: secto ppoximtio Stess o the mid-ple: dipole d qudupole Fo dipole, Fo qudupole, d 5 v 6 / _ mid ple _ mid ple _ l 6 l 8 /6 _ mid ple d _ mid ple _ v l No she 7.5 midd ( ) Rdius (m) Supecoductig Acceleto Mgets, uy -7,. Electomgetic oces d stesses i supecoductig cceleto mgets 98