Introduction to Accelerators. Scientific Tools for High Energy Physics and Synchrotron Radiation Research
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1 Introduction to Accelerators. Scientific Tools for High Energy Physics and Synchrotron Radiation Research Pedro Castro Introduction to Particle Accelerators DESY, July 2010
2 What you will see Pedro Castro Introduction to Accelerators July 2010 Page 2
3 How to build colliders Linear colliders: E E Circular colliders: E B B Pedro Castro Introduction to Accelerators July 2010 Page 3
4 Superconducting magnets LHC superconducting magnets HERA Pedro Castro Introduction to Accelerators July 2010 Page 4
5 How electromagnetic fields accelerate particles Pedro Castro Introduction to Accelerators July 2010 Page 5
6 Differences between proton and electron accelerators HERA (Hadron Electron Ring Accelerator) tunnel: proton accelerator electron accelerator Pedro Castro Introduction to Accelerators July 2010 Page 6
7 Fundamental principles at work mass energy equivalence E = mc 2 wave particle duality λ = h p (de Broglie wavelength) Lorenzt force r F = q r r r ( E + v B) relativity Ampère s law superconductivity Poynting vector Q quantum effects Pedro Castro Introduction to Accelerators July 2010 Page 7
8 Accelerators as tools for researchers > 1. Mass energy equivalence: E E 2 E = mc creation of much heavier particles Pedro Castro Introduction to Accelerators July 2010 Page 8
![Electrons 27.6 GeV HERA: the super electron microscope Resolution = de Broglie wavelength λ[fm] = 1.2 p[gev/c] 1.6 fm = diameter of proton Protons 920 GeV HERA: Hadron-Electron Ring Accelerator, 6.](/docs-images/77/75021385/images/9-2.jpg "3 km ring, DESY (physics: 1992-2007), max. E = 27.5 GeV for electrons, 920 GeV for protrons collision energy at center of mass frame = 318 GeV 1.2 λ[ fm ] = = 318 GeV/c 0.")
9 Electrons 27.6 GeV HERA: the super electron microscope Resolution = de Broglie wavelength λ[fm] = 1.2 p[gev/c] 1.6 fm = diameter of proton Protons 920 GeV HERA: Hadron-Electron Ring Accelerator, 6.3 km ring, DESY (physics: ), max. E = 27.5 GeV for electrons, 920 GeV for protrons collision energy at center of mass frame = 318 GeV 1.2 λ[ fm ] = = 318 GeV/c fm Pedro Castro Introduction to Accelerators July 2010 Page 9
10 Accelerators as light sources dipole magnet synchrotron light N S electrons spectroscopy, X-ray diffraction, X-ray microscopy, crystallography (of proteins), Pedro Castro Introduction to Accelerators July 2010 Page 10
11 Other applications of accelerators? > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) Pedro Castro Introduction to Accelerators July 2010 Page 11
12 Other applications of accelerators > About 120 accelerators for research in nuclear and particle physics > About 70 electron storage rings and electron linear accelerators used as light sources (so-called synchrotron radiation sources ) Other applications: > More than 7,000 accelerators for medicine radiotherapy (>7,500), radioisotope production (200) < 1% > More than 18,000 industrial accelerators ion implantation (>9,000), electron cutting and welding (>4,000) Pedro Castro Introduction to Accelerators July 2010 Page 12
13 How to build colliders Linear colliders: E E Circular colliders: E B B Pedro Castro Introduction to Accelerators July 2010 Page 13
14 Motion in electric and magnetic fields Equation of motion under Lorentz Force r dp dt = r F = r r ( r ) q E + v B magnetic field momentum charge velocity electric field of the particle Pedro Castro Introduction to Accelerators July 2010 Page 14
15 Motion in magnetic fields if the electric field is zero (E=0), then r F = r dp dt = r q v r B r F r v v electron r B (perpendicular) Magnetic fields do not change the particles energy, only electric fields do! Pedro Castro Introduction to Accelerators July 2010 Page 15
16 Acceleration with an electrostatic field r r dp r F = = q E dt principle: beam maximum voltage ~ 5-10 MV in Van der Graaff generators Pedro Castro Introduction to Accelerators July 2010 Page 16
17 Acceleration with an electrostatic field beam V=10 MV V=0 V=0 V=0 V=0 Tandem Van der Graff accelerator tandem = two things placed one behind the other Pedro Castro Introduction to Accelerators July 2010 Page 17
18 Acceleration with an electrostatic field beam V=10 MV V=0 V=0 V=0 V=0 12 MV-Tandem van de Graaff Accelerator at MPI Heidelberg, GE Pedro Castro Introduction to Accelerators July 2010 Page 18
19 Acceleration with an electrostatic field 20 MV-Tandem at Daresbury, UK 12 MV-Tandem van de Graaff Accelerator at MPI Heidelberg, GE Pedro Castro Introduction to Accelerators July 2010 Page 19
20 Acceleration using Radio-Frequency (RF) generators Wideroe (1928): apply acceleration voltage several times to particle beam charged particle p - E RF-generator half a period later: E p RF-generator Pedro Castro Introduction to Accelerators July 2010 Page 20
21 Acceleration using Radio-Frequency (RF) generators charged particle p - E RF-generator quarter of a period later: p RF-generator Pedro Castro Introduction to Accelerators July 2010 Page 21
22 Acceleration using Radio-Frequency (RF) generators quarter of a period later: p RF-generator half a period later: + E p RF-generator Pedro Castro Introduction to Accelerators July 2010 Page 22
23 Acceleration using Radio-Frequency (RF) generators Drift-tube principle p RF-generator jargon: synchronous condition Pedro Castro Introduction to Accelerators July 2010 Page 23
24 Restrictions of RF > particles travel in groups called bunches > bunches are travelling synchronous with RF cycles synchronous condition > ΔE Δv Pedro Castro Introduction to Accelerators July 2010 Page 24
25 Velocity as function of energy β as function of γ Newton: E kin = 1 mv 2 2 Einstein: E = E o + E kin = γmc 2 = mc β β = v c relativistic relativistic γ = 3 : 2.8 GeV protron 1.5 MeV electron Pedro Castro Introduction to Accelerators July 2010 Page 25
26 Accelerator beams are ultra relativistic β>0.999 injection E=40 GeV maximum E=920 GeV injection E=7 GeV maximum E=27.5 GeV maximum E=7 TeV maximum E=105 GeV HERA: 6.3 km LEP/LHC: 26.7 km record: γ= Pedro Castro Introduction to Accelerators July 2010 Page 26
27 Acceleration using Radio-Frequency (RF) generators β = 1 (ultra relativistic particles) p RF-generator λ RF / 2 Pedro Castro Introduction to Accelerators July 2010 Page 27
28 Acceleration using Radio-Frequency (RF) generators β < 1 original Wideroe drift-tube principle Pedro Castro Introduction to Accelerators July 2010 Page 28
29 Drift tube accelerators Limitations of drift tube accelerators: > only low freq. (<10 MHz) can be used λ c L tube β = β 2 2 f = 30 m for β=1 and f=10 MHz drift tubes are impracticable for ultra-relativistic particles (β=1) only for very low β particles Pedro Castro Introduction to Accelerators July 2010 Page 29
30 Resonant cavities Alvarez drift-tube structure: RF resonator E E Pedro Castro Introduction to Accelerators July 2010 Page 30
31 E total = 988MeV E = E m c E Examples DESY proton linac (LINAC III) kin kin total E = c p + m0 c p = 310 MeV / c β 0.3 = 50 MeV 0 2 GSI Unilac (GSI: Heavy Ion Research Center) Darmstadt, Germany Protons/Ions E 20 MeV per nucleon β Pedro Castro Introduction to Accelerators July 2010 Page 31
32 Charges, currents and electromagnetic fields LC circuit analogy: Alvarez drift-tube L E p C a quarter of a period later: a quarter of a period later: L B I p.... B I Pedro Castro Introduction to Accelerators July 2010 Page 32
33 Charges, currents and electromagnetic fields half a period later: Alvarez drift-tube half a period later: L - E p C 3 quarters of a period later: L 3 quarters of a period later:... B I p B I Pedro Castro Introduction to Accelerators July 2010 Page 33
34 Resonant cavities Alvarez drift-tube structure: RF resonator βλ RF twice longer tubes higher frequencies possible shorter accelerator V length of the tube t still preferred solution for ions and protons up to few hundred MeV Pedro Castro Introduction to Accelerators July 2010 Page 34
35 Examples Pedro Castro Introduction to Accelerators July 2010 Page 35
36 Alvarez drift-tube E a quarter of a period later: B.... B I Pedro Castro Introduction to Accelerators July 2010 Page 36
37 RF cavity basics: the pill box cavity E p a quarter of a period later: B I B Pedro Castro Introduction to Accelerators July 2010 Page 37
38 Pill box cavity: 3D visualisation of E and B E B beam beam Pedro Castro Introduction to Accelerators July 2010 Page 38
39 In reality Superconducting cavity used in FLASH (0.3 km) and in XFEL (3 km) 1 m RF input port called input coupler or power coupler beam pill box called cell Higher Order Modes port (unwanted modes) beam RF input port called input coupler Pedro Castro Introduction to Accelerators July 2010 Page 39
40 Superconducting cavity used in FLASH and in XFEL Simulation of the fundamental mode: electric field lines beam E π - mode acceleration Higher Order Modes port (unwanted modes) beam Pedro Castro Introduction to Accelerators July 2010 Page 40
41 Artistic view? Electromagnetic fields accelerate the electrons in a superconducting resonator Pedro Castro Introduction to Accelerators July 2010 Page 41
42 Advantages of RF superconductivity resistance for DC currents! critical temperature (Tc): at radio-frequencies, there is a microwave surface resistance which typically is 5 orders of magnitude lower than R of copper Pedro Castro Introduction to Accelerators July 2010 Page 42
43 Advantages of RF superconductivity Example: comparison of 500 MHz cavities: superconducting cavity normal conducting cavity for E = 1 MV/m 1.5 W / m 56 kw / m at 2 K dissipated at the cavity walls T 300 T Carnot efficiency: η = = c x cryogenics efficiency 20-30% for E = 1 MV/m 1 kw / m 56 kw / m for E = 1 MV/m 1 kw / m 112 kw / m including RF generation efficiency (50%) >100 power reduction factor Pedro Castro Introduction to Accelerators July 2010 Page 43
44 Cavities inside of a cryostat beam Pedro Castro Introduction to Accelerators July 2010 Page 44
45 How to build colliders Linear colliders: E E Circular colliders: E B B Pedro Castro Introduction to Accelerators July 2010 Page 45
46 HERA: the super electron microscope HERA (Hadron Electron Ring Accelerator) tunnel: protons ( samples ) at 920 GeV electrons at 27.5 GeV Why do they look so different? Pedro Castro Introduction to Accelerators July 2010 Page 46
47 Implications of ultra relativistic approximations B v electron F r dp dt = r F = r q v r B γm v r 2 = qvb 1 r = qb γmv = qb p β 1 cqb E v electron r B (perpendicular) Pedro Castro Introduction to Accelerators July 2010 Page 47
48 Dipole magnet permeability of iron = larger than air Pedro Castro Introduction to Accelerators July 2010 Page 48
49 Dipole magnet beam air gap flux lines Pedro Castro Introduction to Accelerators July 2010 Page 49
50 Dipole magnet cross section Max. B max. current large conductor cables Power dissipated: P = R I 2 Pedro Castro Introduction to Accelerators July 2010 Page 50
51 Dipole magnet cross section water cooling channels Pedro Castro Introduction to Accelerators July 2010 Page 51
52 Dipole magnet cross section Pedro Castro Introduction to Accelerators July 2010 Page 52
53 Dipole magnet iron beam current loops Pedro Castro Introduction to Accelerators July 2010 Page 53
54 Dipole magnet cross section C magnet + C magnet = H magnet Pedro Castro Introduction to Accelerators July 2010 Page 54
55 Dipole magnet cross section (another design) Pedro Castro Introduction to Accelerators July 2010 Page 55
56 Dipole magnet cross section (another design) beam Pedro Castro Introduction to Accelerators July 2010 Page 56
57 Dipole magnet cross section (another design) beam water cooling tubes Power dissipated: current leads P = R I Pedro Castro Introduction to Accelerators July 2010 Page 57 2
58 Superconducting dipole magnets LHC superconducting dipoles HERA Pedro Castro Introduction to Accelerators July 2010 Page 58
59 Superconducting dipole magnets Pedro Castro Introduction to Accelerators July 2010 Page 59
60 Superconductivity 12.5 ka normal conducting cables 12.5 ka superconducting cable Pedro Castro Introduction to Accelerators July 2010 Page 60
61 LHC cables 1 cable houses 36 strands 1 strand = mm diameter houses 6300 filaments cross section Copper is the insulation material between two filaments (around each filament: 0.5 µm Cu) 1 filament = 6 µm cables from Rutherford company Pedro Castro Introduction to Accelerators July 2010 Page 61
62 Dipole field from 2 coils J = uniform current density Ampere s law: r r B ds = μ0i r B J B ds = current through the circle μ Jr π rb = μ0π r J B = r θ B B x μ J = 2 B y = μ J 2 0 r 0 r sinθ cosθ Pedro Castro Introduction to Accelerators July 2010 Page 62
63 Dipole field from 2 coils J = uniform current density r B J B J Pedro Castro Introduction to Accelerators July 2010 Page 63
64 Dipole field from 2 coils J = uniform current density J. J = 0 J Pedro Castro Introduction to Accelerators July 2010 Page 64
65 Dipole field from 2 coils J = uniform current density B = μ 0Jr 2 B x μ J = 2 B y = μ J 2 0 r 0 r sinθ cosθ. J J = 0 J B x μ J = 0 ( r1 sinθ1 + r2 sinθ2) 0 2 = μ J 0J B y = 0 ( r1 cosθ1 r2 cosθ2) = μ 2 2 d d r 1 r 2 θ θ 2 1 h = r = = r1 cosθ1 + ( r2 cosθ2) 1 sinθ1 r2 sin θ 2 Pedro Castro Introduction to Accelerators July 2010 Page 65
66 Dipole field from 2 coils J = uniform current density. J B J B x μ0 J = ( r1 sinθ1 r2 sinθ2) = 0 2 μ J 0J B y = 0 ( r1 cosθ1 r2 cosθ2) = μ 2 2 d constant vertical field Pedro Castro Introduction to Accelerators July 2010 Page 66
67 From the principle to the reality. B Aluminium collar Pedro Castro Introduction to Accelerators July 2010 Page 67
68 Simulation of the magnetic field B Pedro Castro Introduction to Accelerators July 2010 Page 68
69 From the principle to the reality. B Aluminium collar Pedro Castro Introduction to Accelerators July 2010 Page 69
70 LHC dipole coils in 3D I B p beam p beam Pedro Castro Introduction to Accelerators July 2010 Page 70
71 LHC dipole magnet (cross-section) Pedro Castro Introduction to Accelerators July 2010 Page 71
72 Superconducting dipole magnets LHC dipole magnet interconnection: p p Pedro Castro Introduction to Accelerators July 2010 Page 72
73 Damping rings Linear colliders: Damping rings E E Circular colliders: E B B Pedro Castro Introduction to Accelerators July 2010 Page 73
74 HERA: the super electron microscope HERA (Hadron Electron Ring Accelerator) tunnel: protons ( samples ) at 920 GeV electrons at 27.5 GeV Why are the energies so different? Pedro Castro Introduction to Accelerators July 2010 Page 74
75 Particles moving in a magnetic field B v electron F r dp dt = r F = r qv r B Charged particles when accelerated, emit radiation tangential to the trajectory: B Pedro Castro Introduction to Accelerators July 2010 Page 75
76 Synchrotron radiation Total energy loss after one full turn: ΔE turn [ GeV] = γ r[m] ALL charged particles when accelerated, emit radiation tangential to the trajectory: B 4 γ = E m c 2 0 r electron Pedro Castro Introduction to Accelerators July 2010 Page 76
77 Synchrotron radiation Total energy loss after one full turn: ΔE turn [ GeV] = γ r[m] 4 γ = E m c 2 0 HERA electron ring: r = 580 m E = 27.5 GeV ΔE 80 MeV (0.3%) HERA proton ring: r = 580 m E = 920 GeV ΔE 10 ev (10-9 %) need acceleration = 80 MV per turn Pedro Castro Introduction to Accelerators July 2010 Page 77
78 Synchrotron radiation Total energy loss after one full turn: ΔE turn [ GeV] = γ r[m] 4 γ = E m c 2 0 HERA electron ring: r = 580 m E = 27.5 GeV ΔE 80 MeV (0.3%) need acceleration = 80 MV per turn HERA proton ring: r E = = ΔE 580 m 920 GeV 10 ev (10-9 %) the limit is the max. dipole field = 5.5 Tesla 1 r = qb p Pedro Castro Introduction to Accelerators July 2010 Page 78
79 Synchrotron radiation Total energy loss after one full turn: ΔE turn [ GeV] = γ r[m] 4 γ = E m c 2 0 HERA electron ring: r = 580 m E = 27.5 GeV x5 ΔE 80 MeV (0.3%) LEP collider: r = 2800 m E = 105 GeV ΔE 3 GeV (3%) need acceleration = 80 MV per turn need 3 GV per turn!! Pedro Castro Introduction to Accelerators July 2010 Page 79
80 Synchrotron radiation Total energy loss after one full turn: ΔE HERA electron ring: r = 580 m turn E = 27.5 GeV ΔE 80 MeV (0.3%) [ GeV] = γ r[m] x5 LEP collider: r = m E = 105 GeV ΔE 3 GeV (3%) γ = LEP = LastElectron- Positron Collider? E m c 2 0 need acceleration = 80 MV per turn need 3 GV per turn!! Pedro Castro Introduction to Accelerators July 2010 Page 80
81 Radiation of a Hertz dipole under relativistic conditions dipole radiation: electron trajectory PETRA: γ =14000 Lorentz-contraction = v = 0. 9c v 0. 5c electron trajectory electron trajectory Pedro Castro Introduction to Accelerators July 2010 Page 81
82 Synchrotron radiation Pedro Castro Introduction to Accelerators July 2010 Page 82
83 Development of synchrotron light sources FELs lecture on Friday, by M. Dohlus Pedro Castro Introduction to Accelerators July 2010 Page 83
84 Damping rings Damping rings E E E B B Pedro Castro Introduction to Accelerators July 2010 Page 84
85 Concept of beam emittance plasma beam Pedro Castro Introduction to Accelerators July 2010 Page 85
86 Concept of beam emittance p r y x p r beam z Pedro Castro Introduction to Accelerators July 2010 Page 86
87 Concept of beam emittance beam p r p x r p = dx dz x y x p r z phase space diagram x Pedro Castro Introduction to Accelerators July 2010 Page 87
88 Concept of beam emittance beam p r p x r p = dx dz x y x p r z phase space diagram x emittance definition: ε = 2 2 x x xx 2 area/π = emittance (units: mm.mrad) Pedro Castro Introduction to Accelerators July 2010 Page 88
89 Concept of beam emittance x as beam p r function of x p x r p = dx dz x y x p r transverse phase space diagram ε x = x 2 z 2 2 x' xx' y as function of y x ε y = 2 y' yy' transverse emittance (units: mm.mrad) y 2 2 Pedro Castro Introduction to Accelerators July 2010 Page 89
90 Concept of beam emittance beam p r y x z p r Δp longitudinal phase space diagram Δp as function of z z ε z longitudinal emittance (units: mm.ev/c) Pedro Castro Introduction to Accelerators July 2010 Page 90
91 Concept of beam emittance parallel beam converging beam diverging beam x x x x x x Pedro Castro Introduction to Accelerators July 2010 Page 91
92 Concept of beam emittance y x p r r p = r p r + Δ p z z acceleration (only in z direction) p x r p gets smaller linear accelerators: ε ε 1 E definition: normalized emittance: ε N = ε γ = constant E geometrical emittance Pedro Castro Introduction to Accelerators July 2010 Page 92
93 Damping rings Damping rings E E E B B Pedro Castro Introduction to Accelerators July 2010 Page 93
94 Quatum excitation dipole magnet Nominal E Trajectory Low E Trajectory > Quantum excitation Radiation is emitted in discrete quanta Number and energy distribution etc. of photons obey statistical laws Increase emittance Pedro Castro Introduction to Accelerators July 2010 Page 94
95 Need of focusing quadrupole magnet: four iron pole shoes of hyperbolic contour hyperbola B y = g x F x = g x focusing! Pedro Castro Introduction to Accelerators July 2010 Page 95
96 Quadrupole magnets quadrupole magnet: four iron pole shoes of hyperbolic contour B x = g y F y = g y defocusing B y = g x F x = g x focusing! Pedro Castro Introduction to Accelerators July 2010 Page 96
97 Quadrupole magnets QD + QF = net focusing effect: charged particle center of quad x x 1 2 x 1 < x 2 defocusing quadrupole focusing quadrupole beam defocusing quadrupole focusing quadrupole Pedro Castro Introduction to Accelerators July 2010 Page 97
98 Quadrupole magnets QD + QF = net focusing effect: charged particle center of quad x x 1 2 x 1 < x 2 defocusing quadrupole focusing quadrupole Pedro Castro Introduction to Accelerators July 2010 Page 98
99 Circular accelerator beam cell focusing quadrupole dipole magnet defocusing quadrupole dipole magnet focusing quadrupole Pedro Castro Introduction to Accelerators July 2010 Page 99
100 Circular accelerator PETRA beam cell focusing quadrupole dipole magnet defocusing quadrupole dipole magnet focusing quadrupole Pedro Castro Introduction to Accelerators July 2010 Page 100
101 HERA collider and injector chain HERA: 4 arcs + 4 straight sections PETRA: 8 arcs + 8 straight sections arc straight section Pedro Castro Introduction to Accelerators July 2010 Page 101
102 Damping rings for high luminosity Linear colliders: Damping rings E E e+ e- production rate of a given event (for example, Z particle production): R Z = dn dt z = Σ z number of events L luminosity (independent of the event type) cross section of Z production Pedro Castro Introduction to Accelerators July 2010 Page 102
103 Damping rings for high luminosity Linear colliders: Damping rings E E e+ e- P Z e = Σ + e ( 1 ) z 4π σ x e+ N σ y e- e σ y density σ x N 4π σ = e x σ y Pedro Castro Introduction to Accelerators July 2010 Page 103
104 Damping rings for high luminosity Linear colliders: Damping rings E E e+ e- number of colliding bunches per second R Z = Σ z L = Σ z nb Ne+ N 4π σ σ x e y number of positrons per bunch number of electrons per bunch luminosity transverse bunch sizes (at the collision point) Pedro Castro Introduction to Accelerators July 2010 Page 104
105 Certification of knowledge in accelerator physics and technology: magnet dipoles basics (normal conducting and superconducting) RF cavity basics (normal conducting and superconducting) synchrotron radiation effects quadrupole focusing concept of emittance concept of luminosity Hamburg, 21 st July 2010 Pedro Castro Introduction to Accelerators July 2010 Page 105
106 Thank you for your attention Pedro Castro Introduction to Accelerators July 2010 Page 106
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