Introduction to Accelerator Physics
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1 Intoduction to Acceleato Physics Pat 3 Pedo Casto / Acceleato Physics Goup (MPY) Intoduction to Acceleato Physics DSY, 5th July 017 acceleating devices vacuum chambe injecto acceleating device staight sections magnet vacuum chambe linea acceleato (linac) cicula acceleato: synchoton Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 1
2 Motion in electic and magnetic fields dp dt quation of motion unde Loentz Foce = F = q ( v B) magnetic field momentum chage velocity electic field of the paticle Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 3 Motion in magnetic fields if the electic field is zeo (=0), then F v electon dp = dt = q v B B (pependicula) F v Magnetic fields do not change the paticles enegy, only electic fields do! Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 4
3 Motion in magnetic fields if the electic field is zeo (=0), then F dp = dt p c = q v B = enegy-momentum elation in special elativity 0 total enegy enegy at est momentum Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 5 Motion in magnetic fields if the electic field is zeo (=0), then F dp = dt = p c = q v B 0 d dt = c dp p dt = c q p( v B) = c q since p v B cosφ = 0 o φ = 90 Magnetic fields do not change the paticles enegy, only electic fields do! Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 6 3
4 In geneal: Static magnetic fields to guide (bend focus) paticle s Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 7 acceleation with DC electic fields p V V V 3 V Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 8 4
5 In geneal: Static magnetic fields to guide (bend focus) paticle s Static electic fields acceleate paticle s (low enegy) Radio-fequency M fields acceleate paticle s (high ) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 9 RF cavity basics: the pill box cavity p a quate of a peiod late: B I B Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 10 5
6 RF cavity basics: the pill box cavity - p - -- L a quate of a peiod late: LC cicuit (o esonant cicuit) analogy: B B L.... I half a peiod late: angula fequency: 1 L I - - C C C Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 11 Maxwell's equations (diffeential fomulation in SI units) 0 bounday conditions TM modes (tansvese magnetic modes) set of solutions with 0 (that is, is tansvese) set of solutions with 0 (that is, is tansvese) T modes (tansvese electic modes) : cavity adius : cavity length Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 1 6
7 Maxwell's equations (diffeential fomulation in SI units) 0 bounday conditions : cavity adius : cavity length set of solutions with 0 (that is, is tansvese)! "!# $ cos () cos *,-./ indices: 0 * 4 * 0 $ "! "!#!# cos () sin *,-./ ( "!# $ $! "!# sin () sin *,-./ 0 5 ( "!# $6! "!# $ sin () cos *,-./ 4 5 "!# 6 $! "!# cos () cos *,-./ ( 0,1,, : numbe of full peiod vaiations in ) of the fields : 1,, : numbe of zeos of the axial field component in $ * 0,1,, : numbe of half peiod vaiations in z of the fields! : Bessel s functions! : deivative of the Bessel s functions "!# : n-th oot of! (that is,! "!# 0) angula fequency : 6 "!# Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 13 *! : Bessel s functions < "! "! "! " " " " " "!# : n-th oot of! (that is,! "!# 0) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 14 7
8 bounday conditions : cavity adius : cavity length " $,-./ fundamental solution with 0 (that is, is tansvese) " 6 $ ",-./ : otation symmety of the fields A B : no zeos of the axial field component in C : no vaiation in of the fields! : Bessel s functions angula fequency : 6 "! : deivative of the Bessel s functions ".405 Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 15 bounday conditions : cavity adius : cavity length " $,-./ fundamental solution with 0 (that is, is tansvese) " 6 " $,-./ : otation symmety of the fields A B : no zeos of the axial field component in C : no vaiation in of the fields! : Bessel s functions angula fequency : 6 "! : deivative of the Bessel s functions ".405 Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 16 8
9 Pill box cavity: 3D visualisation of and B B Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 17 xamples of pill box cavities DSY cavity (pill box) ADON cavity 51 MHz (pill box) Fascati lab, Italy Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 18 9
10 xamples of pill box cavities ADON cavity 51 MHz (pill box) Fascati lab, Italy ADON in 1963, Laboatoi Nazionali di Fascati, Italy Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 19 Supeconducting cavity used at DSY 1 m mateial: pue Niobium opeating tempeatue: K acceleating field gadient: up to 35 MV/m Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 0 10
11 Supeconducting cavity used at DSY Supeconducting cavity used in FLASH (0.3 km) and in XFL (3 km) 1 m Fee-electon LASe in Hambug uopean X-ay Fee-lecton Lase Intenational Linea Collide Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 1 Cavities inside a cyostat Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 11
12 Cavities inside a cyostat 1. m Numbe of cavities 8 Cavity length m Opeating fequency 1.3 GHz Opeating tempeatue K Acceleating Gadient MV/m Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 3 Cavities inside a cyostat Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 4 1
13 Cavities inside an acceleato module (cyostat) module installation in FLASH (004) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 5 Fee-electon LASe in Hambug (FLASH) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 6 13
14 Fee-electon LASe in Hambug (FLASH) 7 SC acceleation modules 300 m, 1. GeV λ = 4-45 nm 1 undulato modules 6 undulato modules photon exp. halls Pedo Casto / MPY Acceleato Physics 5 th July 017 Page acceleato modules (cyostats) in XFL uopean X-ay Fee-lecton Lase (XFL) (3 km, 17.5 GeV) λ = nm Schleswig- Holstein Hambug Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 8 14
15 Supeconducting cavities at HRA Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 9 Othe acceleatos using supeconducting cavities 5 de-commissioned 11 in opeation 4 in constuction 9 in design phase Total = 9 full list: Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 30 15
16 Supeconducting cavity used in FLASH and in XFL Supeconducting cavity used in FLASH (0.3 km) and in XFL (3 km) 1 m pill box called cell iis equato pill box called cell Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 31 Acceleating field map Simulation of the fundamental mode: electic field lines F GH 1.3 GHz micowaves: (L-band) iis equato Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 3 16
17 Fequently Asked Questions 1) Why this shape? ) 3) 4) 5) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 33 Multipacting mitigation in supeconducting cavities iis equato Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 34 17
18 1) Why this shape? to educe/avoid multipacting ) How to feed in? 3) 4) 5) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 35 Supeconducting cavity used in FLASH and in XFL Supeconducting cavity used in FLASH (0.3 km) and in XFL (3 km) 1 m RF input pot called input couple o powe couple pill box called cell iis equato pill box called cell RF input pot called input couple Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 36 18
19 Fundamental mode couple (input couple) electic field Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 37 1) Why this shape? to educe/avoid multipacting ) How to feed in? with input couples 3) How to measue? 4) 5) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 38 19
20 Supeconducting cavity used in FLASH and in XFL Supeconducting cavity used in FLASH (0.3 km) and in XFL (3 km) 1 m RF input pot called input couple o powe couple pill box called cell pick up antenna iis equato pill box called cell RF input pot called input couple Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 39 Supeconducting cavity used in FLASH and in XFL Supeconducting cavity used in FLASH (0.3 km) and in XFL (3 km) HOM couple 1 m RF input pot called input couple o powe couple pick up antenna pill box called cell iis equato Highe Ode Modes pot HOM couple (unwanted modes) HOM couple pill box called cell RF input pot called input couple o powe couple Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 40 0
21 1) Why this shape? to educe/avoid multipacting ) How to feed in? with input couples 3) How to measue? with pick up antennas 4) What ae HOM couples fo? 5) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 41 Wakefields vacuum chambe wall mio cuents Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 4 1
22 1) Why this shape? to educe/avoid multipacting ) How to feed in? with input couples 3) How to measue? with pick up antennas 4) What ae HOM couples fo? to educe HOM (wakefields) 5) Is thee a net acceleation? Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 43 Acceleating field map Simulation of the fundamental mode: electic field lines F GH 1.3 GHz micowaves: (L-band) iis equato Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 44
23 Simulation of the fundamental mode: electic field lines Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 45 (electons) Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 46 3
24 (electons) t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 47 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 48 4
25 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 49 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 50 5
26 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 51 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 5 6
27 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 53 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 54 7
28 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 55 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 56 8
29 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 57 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 58 9
30 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 59 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 60 30
31 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 61 t Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 6 31
32 1) Why this shape? to educe/avoid multipacting ) How to feed in? with input couples 3) How to measue? with pick up antennas 4) What ae HOM couples fo? to educe HOM (wakefields) 5) Is thee a net acceleation? timing is the key Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 63 Summing-up of this pat Paticle acceleation using adio-fequency fields: basic cavity: pill box analogy to an LC cicuit infinite numbe of solutions fo and eq. fo the fundamental solution fo and supeconducting cavity multipacting mitigation RF couples and antennas wakefields and HOMs FLASH and XFL Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 64 3
33 xecise Calculate the esonant fequency of the fundamental mode in a coca-cola tin assume a cylindical shape with a diamete of 6.4 cm and a height of 1.1 cm Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 65 xecise Calculate the diamete of the ADON pill box cavity fo a fundamental fequency of 51 MHz ADON cavity 51 MHz (pill box) Fascati lab, Italy Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 66 33
34 bounday conditions : cavity adius : cavity length " $,-./ fundamental solution with 0 (that is, is tansvese) " 6 $ ",-./ : otation symmety of the fields A B : no zeos of the axial field component in C : no vaiation in of the fields! : Bessel s functions angula fequency : 6 "! : deivative of the Bessel s functions ".405 Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 67 xecise Calculate the esonant fequency of the fundamental mode in a coca-cola tin assume a cylindical shape with a diamete of 6.4 cm and a height of 1.1 cm 6 " L $MN O P F 3.6 RS Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 68 34
35 xecise Calculate the diamete of the ADON pill box cavity fo a fundamental fequency of 51 MHz ADON cavity 51 MHz (pill box) Fascati lab, Italy πf 6 " 6 " πf 3 10L.405 π U.5 ( N 4.5 ( Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 69 Intoduction to Acceleato Physics Pat 4 Pedo Casto / Acceleato Physics Goup (MPY) Intoduction to Acceleato Physics DSY, 5th July
36 Cicula acceleatos: the synchoton acceleating device magnet vacuum chambe injecto staight sections Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 71 Cicula acceleatos: the synchoton acceleating device magnet vacuum chambe injecto staight sections Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 7 36
37 Cicula acceleatos: the synchoton Low negy Antipoton Ring (LAR) at CRN Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 73 Dipole magnet Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 74 37
38 Cicula acceleatos: the synchoton injecto acceleating device staight sections magnet vacuum chambe W X W W ( (cicula motion) X ( Y(Z![\ 6]:OM: X
39 Dipole magnet ^ ` c[d NO f e ^ e ^ f gap height Ampee s law: _ S NO ^g#hibjgk e^ N flux lines ai gap _ S NO ` S NO ` S NO e ^ a0b# c[d ` a0b# NO ` a0b# c[d NO e ^ S Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 77 Dipole magnet coss section incease B incease cuent, but powe dissipated P ^ lage conducto cables Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 78 39
40 Dipole magnet coss section incease B incease cuent, but powe dissipated P ^ lage conducto cables Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 79 Dipole magnet coss section wate cooling channels Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 80 40
41 Dipole magnet coss section Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 81 Dipole magnet ion cuent loops Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 8 41
42 Dipole magnet coss section C magnet C magnet = H magnet Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 83 Dipole magnet coss section (anothe design) wate cooling tubes Powe dissipated: cuent leads P = R I Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 84 4
43 Supeconductivity 1.5 ka nomal conducting cables 1.5 ka supeconducting cable Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 85 Satuation of ion: 1.6 T incease B incease cuent, but powe dissipated P ^ lage conducto cables satuation effects feomagnets pemeability paamagnets fee space diamagnets I Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 86 43
44 Satuation of ion: 1.6 T B vs H cuve fo ion I [A] Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 87 Supeconducting dipole magnets LHC supeconducting dipoles HRA Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 88 44
45 Supeconducting dipole magnets: coss section Tevaton HRA RHIC LHC Femilab DSY Bookhaven CRN Chicago (USA) Hambug (Gemany) Long Island (USA) Geneva (Switzeland) 4.5 T 5.3 T 3.5 T 8.3T Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 89 Supeconducting dipole magnets Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 90 45
46 Dipole field inside 1 conducto : unifom cuent density Ampee s law: _ NO ^ B _ NO _ NO $ $ θ NO B x µ J = µ J B y = 0 0 sinθ cosθ $ Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 91 Dipole field inside conductos J = unifom cuent density B J B J Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 9 46
47 Dipole field inside conductos J = unifom cuent density one conducto: B x µ J = µ J B y = 0 0 sinθ cosθ. J J = 0 J supeposition: µ 0J B x = ( 1 sinθ1 sinθ) B y µ 0J = ( 1 cosθ1 cosθ ) 1 θ 1 θ Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 93 Dipole field inside conductos J = unifom cuent density one conducto: B x µ J = µ J B y = 0 0 sinθ cosθ. J J = 0 J B x µ J = 0 ( 1 sinθ1 sinθ) 0 = B y µ 0J = ( 1 cosθ1 cosθ ) 1 θ 1 θ h = = 1 sinθ1 sin θ Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 94 47
48 Dipole field inside conductos J = unifom cuent density one conducto: B x µ J = µ J B y = 0 0 sinθ cosθ. J J = 0 J B x µ J = 0 ( 1 sinθ1 sinθ) 0 = µ J 0J B y = 0 ( 1 cosθ1 cosθ ) = µ d 1 θ θ 1 h = = d = 1 cosθ1 ( cosθ) 1 sinθ1 sin θ Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 95 Dipole field inside conductos J = unifom cuent density. J B J B x µ 0 J = ( 1 sinθ1 sinθ) = 0 µ J 0J B y = 0 ( 1 cosθ1 cosθ ) = µ d constant vetical field Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 96 48
49 Dipole field inside conductos. J B J µ 0 J B y = d constant vetical field Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 97 Fom the pinciple to the eality. B 56 mm 15 mm x mm Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 98 49
50 LHC dipole coils in 3D p p Aluminium colla 15 mm x mm Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 99 LHC dipole coils in 3D I B p p Pedo Casto / MPY Acceleato Physics 5 th July 017 Page
51 Computed magnetic field nonmagnetic collas B feomagnetic ion 56 mm Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 101 LHC dipole magnet (coss-section) 1 m feomagnetic ion nonmagnetic collas supeconducting coils tubes steel containe fo He insulation vacuum vacuum tank suppots Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 10 51
52 Supeconducting dipole magnets LHC dipole magnet inteconnection: p p Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 103 Summing-up of this pat Cicula acceleatos: the synchoton RF cavities: pill-box cavity supeconducting cavities Dipole magnets: nomal conducting dipoles supeconducting dipoles Pedo Casto / MPY Acceleato Physics 5 th July 017 Page 104 5
53 Thank you fo you attention Pedo Casto / MPY Acceleato Physics 5 th July 017 Page
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