Macroscopic Fields in Accelerators

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1 48 E hs simil effect s v. d q E v Fo eltivistic ticles T hs simil effect s dt E c 3 8 V/m such Electic field is beod techicl limits. Electic fields e ol used fo ve lo eegies o Fo setig to coute ottig bems ith diffeet chge. Mcoscoic Fields i Acceletos E Electosttic setos t CESR Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

2 USPAS Advced Acceleto Phsics -3 Jue 6 49 Sttic mgetic fileds: Chge fee sce: is the bem s desig cuve ; E t j E j t ε Fo fiite fields o the desig cuve c be oe eded i d : m m m b Mgetic Fields i Acceletos

3 5 H llelout H llelout A X A X d s Sufces of Equl Potetil out i A X d s d s X llel llel A d s i i d s A d s d s X Fo lge emebilit Hout is eedicul to the sufce. X d s A d s A Fo highl emeble mteils like io sufces hve costt otetil. Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6 X

4 USPAS Advced Acceleto Phsics -3 Jue 6 5 Koledge of the field d the scl mgetic otetil o closed sufce iside mget detemies the mgetic field fo the comlete volume hich is eclosed. G δ [ ] [ ] [ ] [ ] d G G d G G d G G d G G d V V V V V δ Gee fuctio: Gee s Theoem

5 USPAS Advced Acceleto Phsics -3 Jue 6 5 If field dt i le fo emle the midle of ccloto o of bem lie mget is ko the comlete filed is detemied: Dt of the mgetic field i the le is used to detemie b d b. b b b b [ ] b b b b b b Potetil Esio

6 53 Comle Potetils i i i i i 4 Im{ Im{ Im{ λ λ Itetio equtio: λ λ 4 λ } λ λ [4 λ λ λ λ λ λ λ ] } The fuctios log lie detemie the comlete field iside mget. λ λ λ 4 λ λ Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6 λ λ }

7 USPAS Advced Acceleto Phsics -3 Jue 6 54 e clled the -deedet multiole coefficiets The ide descibes C Smmet oud the -is due to sig chge fte } Im{!!! } 4!!! Im{ ] [ ] [ ϕ λ λ λ λ λ λ λ λ λ λ ϕ λ λ i e π ϕ e 3 S S S N N N Multiole Coefficiets

8 55 Fige Fields d Mi Fields Mi field Fige field Ol the fige field egio hs tems ith λ d Mi fields i cceleto hsics: ϑ e i i fo fo λ i ϕ ϑ ϕ Im{ e } Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

9 56 Mi Field Potetil Mi field otetil: si[ ϕ ϑ ] The isolted multiole: siϕ ϑ Whee the ottio of the coodite sstem is set to The otetils oduced b diffeet multiole comoets hve Diffeet ottio smmet C b Diffeet dil deedece Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

10 USPAS Advced Acceleto Phsics -3 Jue ' '' '' '' ± j m q i m q i m q m q q m γ γ γ γ γ ' ' ' t g dt i e m q g γ g g g e g ig g i t g dt i Focusig i ottig coodite sstem Multioles i Acceletos : Soleoids

11 USPAS Advced Acceleto Phsics -3 Jue 6 58 Soleoid focusig is ek comed to the deflectios ceted b tsvese mgetic field. Tsvese fields: Stog focusig m qv m q ρ γ γ 4 e e m qv q m γ γ q ρ If the soleoids field s eedicul to the ticle s motio its bedig dius ould be Wek focusig < Stog focusig b bout ρ Soleoid vs. Stog Focusig

12 59 Soleoid Focusig Soleoid mgets e used i detectos fo ticle idetifictio vi ϕ q mγ The soleoid s ottio of the bem is ofte comested b evesed soleoid clled comesto. ρ q Soleoid o Wek Focusig: Soleoids e lso used to focus lo γ bems: Wek focusig fom tul ig focusig: R ϕ R [ R cosϕ ϕ Lieitio i : ] Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6 q mγ v ϕ ρ [ R siϕ cosϕ siϕ ] R q mγ

13 6 Im{ i } C Smmet Multioles i Acceletos : Dioles - - i e SN i - Equiotetil cost. d dt q v Diole mgets e used fo steeig the bems diectio dϕ edig dius: d dt ρ ρ qv q d dϕ dl dϕ vdt d / ρ q Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

14 6 Diffeet Dioles C-she mget: H-she mget: Wido fme mget: H I out i out H i I H d s H H l H Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6 Fe Diole stegth: Fe l Fe H H q ρ I

15 6 Diole Fields T: Ticl limit sice the field becomes domited b the coils ot the io. Limitig j fo Cu is bout A/mm <.5 T: Ticll used egio < T: Regio i hich I Shims educe the sce tht is oe to the bem but the lso educe the fige field egio. Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

16 63 Whee is the veticl Diole? HERA Tuel USPAS Advced Acceleto Phsics -3 Jue 6

17 64 Multioles i Acceletos : Quduoles Im{ i } - C Smmet I quduole ticles e focused i oe le d defocused i the othe le. Othe modes of stog focusig e ot ossible. Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

18 65 Quduole Fields Equiotetil: cost. I H d s H d k e Quduole stegth: q q I Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

19 66 Rel Quduoles SLAC The coils sho tht this is uight quduole ot otted o ske quduole. PETRA Tuel Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

20 Im{ i } C 3 Smmet S 3 N S 3 S N N Multioles i Acceletos 3: Setuoles 3 3 i Setuole fields hdl ifluece the ticles close to the cete hee oe c lieie i d. ii iii 63 I lie oimtio b shifted setuole hs quduole field. Whe deeds o the eeg oe c build eeg deedet quduole. O Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

21 Setuole Fields Equiotetil: cost I H d s H d 3 3 k Quduole stegth: q q 6I 3 Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

22 69 Rel Setuoles ESRF USPAS Advced Acceleto Phsics -3 Jue 6

23 7 The CESR Tuel USPAS Advced Acceleto Phsics -3 Jue 6

24 7 Highe ode Multioles Highe ode multioles come fom Field eos i mgets Mgetied mteils Fom multiole mgets tht comeste such eoeous fields To comeste olie effects of othe mgets To stbilie the motio of m ticle sstems To stbilie the olie motio of idividul ticles Im{ i } i q q Multiole stegth: k! uits: m /q is lso clled ρ d used to descibe the eeg of multil chge ios Nmes: diole quduole setuole octuole decole duodecole Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

25 USPAS Advced Acceleto Phsics -3 Jue 6 7 The discussed multioles oduce midle smmetic motio. Whe the field is otted b π/ i.e oe seks of ske multiole. v v v v v v v v v v v v ϑ π F F dt d dt d { } { } { } [ ] Re Im Im Im i i i i e i e i e ϑ ϑ ϑ ϑ Midle Smmetic Motio

26 73 Suecoductig Mgets Above T the field fom the be coils domite ove the mgetitio of the io. ut Cu ies cot cete much filed ithout io oles: 5T t 5cm distce fom 3cm ie ould equie cuet desit of j I d d π Cu c ol suot bout A/mm. A 389 mm Suecoductig cbles outiel llo cuet desities of 5A/mm t 4.6 K d 6T. Mteils used e usull Nb los e.g. NbTi Nb 3 Ti o Nb 3 S. Suecoductig mgets e ot ol used fo stog fields but lso he thee is o sce fo io oles like iside ticle hsics detecto. Suecoductig.T mgets fo iside the HERA detectos. Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

27 74 Suecoductig Mgets Poblems: Suecoductivit bkes do fo too lge fields Due to the Meisse-Ochsefeld effect suecoductivit cuet ol flos o thi sufce le. Remed: Suecoductig cble cosists of m ve thi filmets bout m. Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

28 USPAS Advced Acceleto Phsics -3 Jue 6 75 Stight ie t the oigi: I e I j π π ϕ Wie t : { } { } i I I I I I I I e i i i i ϕ π π π π π π π Im l Im l Im l I ] [ π This c be eeseted b comle multiole coefficiets i i Comle Potetil of Wie

29 76 Cetig multiole be ceted b gemet of ies: π π δ Ai-coil Multioles e i ϕ Iˆ di dϕ if dϕ I ϕ Iˆ cos ϕ ϕ dϕ Idel multiole Aoimte multiole Geog.Hoffstette@Coell.edu USPAS Advced Acceleto Phsics -3 Jue 6

30 77 Rel Ai-coil Multioles Quduole coecto RHIC Tuel LHC diole USPAS Advced Acceleto Phsics -3 Jue 6

31 78 LHC double quduole Secil SC Ai-coil Mgets Accuc RHIC Sibei Ske diole USPAS Advced Acceleto Phsics -3 Jue 6

[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2

[5 points] (c) Find the charge enclosed by the cylindrical surface of radius ρ 0 = 9 mm and length L = 1 m. [2 STUDENT NAME: STUDENT ID: ELEC ENG FH3: MIDTERM EXAMINATION QUESTION SHEET This emitio is TWO HOURS log. Oe double-sided cib sheet is llowed. You c use the McMste ppoved clculto Csio f99. You c tke y mteil