Accelerators LISHEP Lecture II Oliver Brning CERN - PDF document

Accelerators LISHEP Lecture II Oliver Brüning CERN http://bruening.home.cern.ch/bruening

Summary Lecture I Motivation & History Particle Sources Acceleration Concepts: Equations and Units DC Acceleration RF Acceleration Electro−Magnetic Waves & Boundary Conditions Summary

Circular Accelerators II) Cyclotron Synchrotrons beam energy Collider Concepts: need for focusing collider versus fixed target particle − anti particle collider luminosity Summary

Time Varying Fields beam E Linear Acceleration: E beam bunched beam long accelerator! E Circular Accelerator: beam

Circular Accelerators I Cyclotron Lawrence 1929: Q ω = B m m v r = Q B m = const f = const orbits RF B = const dee orbits beam extraction RF - H to 80 keV Livingston 1931: Lawrence 1932: p to 1.2 MeV (NP 1939)

Cyclotron 1931: 4.5 inch cyclotron by Livingston − H to 80 keV 11 inch cyclotron by Lawrence: p to 1.2 MeV 12 inch build by T. Koeth (1999)

Disadvantage: High Energy: γ >> 1 f = const. RF short bunch trains large dipole magnet R = const. Synchrotron: Q B ω = γ m 0 0 m γ 0 r = v B = const. Q B small magnets, f = const. v = c RF high beam energy requires strong magnets & large storage ring!

Bending Magnet µ µ B = H H = I N 0 µ < 1: Dia ����������� ����������� µ >> 1 ����������� ����������� � � ����������� ����������� coil µ > 1: Para � � ����������� ����������� ����������� ����������� h H 0 ����������� ����������� µ >> 1: Ferro ����������� ����������� ����������� ����������� ������������ ������������ l H ������������ ������������ E yoke beam vacuum chamber Maxwell Equations: B = B 0 E µ H = H E 0 H = h H + l H H = h H + l H H = h H + l H 0 E B = N I 0 µ 0 B h H B [T] 1 e B -1 = 0.3 [m ] = p p [GeV] ρ

Bending Magnet LEP injection area dipole magnet: Ω B = 0.135 T; I = 4500 A; R = 1 m P = 20 kW / magnet ca. 500 magnets P = 10 MW

Circular Accelerators II Synchrotron: Cosmotron 3 GeV protons 1952: electrons 1949: injection �������� �������� magnet �������� �������� B �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� �������� RF cavity vacuum chamber extraction / target 1955: Bevatron 6 GeV protons - p (fixed-target experiment) E 2 E = 2 m c 1 + - 1 cm 0 2 m c 2 0

Berkeley Bevatron

Synchrotron Radiation Quantum Picture: q γ B γ bending magnet radiation fan in bending plane 1 opening angle γ synchrotron 4 particle γ light cone 2 q N trajectory P ρ 2 3 γ <E > ρ γ polarised

Synchrotron Radiation Acceleration: uniform motion E E acceleration 4 γ P 2 ρ polarised

Examples ρ E N U E P γ 12 [keV] [MeV] [GeV] [MW] [km] [10 ] 2.1 90 3.1 4.7 260 45 LEP 1 2800 23 100 3.1 4.7 LEP 2 715 7000 3.1 312 0.007 0.005 LHC 0.04 γ 1.3 MeV −rays: Co 60 keV X−rays: Visible Light: eV X−rays LEP 1 γ LEP 2 −rays LHC UV light

Summary Acceleration Concept: 25 MeV Static field discharge AC field no limit length multiple passages Circular Acceleration: Cyclotron 25 MeV non−relativistic Synchrotron no limit small magnets synchrotron radiation In Practice: Combination of several options

CERN Accelerator Complex searching at each acceleration stage for the most efficient acceleration concept one uses in practice a combination of several types!

Collider Rings 1960: fixed target physics (bubble chamber) But: E 2 E = 2 m c 1 + − 1 cm 0 2 2 m c 0 E = 2 E Collider: p CM GeV 2000 Tevatron center of mass energy 1500 1000 collider SppS 500 ISR fixed target Tevatron SPS 400 600 800 1000 200 GeV particle energy + − 1960 : e / e collider + − p / p collider 1970 :

+/ - Features ( ) Advantages: E = 2 E p CM Disadvantages: not all particles collide in one crossing long storage times requires 2 beams: two rings anti-particles collision collision point regions beam-beam interaction

Luminosity −2 −1 [ L ] = cm s N / sec = L σ ev interaction region ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� N N 2 1 area A n N N f L = b 1 rev 2 A high bunch current beam−beam; collective effects many bunches total current (RF); collective effects small beam size hardware

Beam−Beam Parameter the electro−magnetic fields of beam2 act on the particles of beam1 transform into moving frame of test particle and calculate Lorentz force r β F = q (E + v B) =q (E + c B ) r x φ Gauss theorem and Ampere’s law: r 2 r E = 1 π ρ 2π r 2 r E = (r ) dr ε r 0 0 r µ ρ π 2π β c r (r ) dr 2 r B = 2 r E = 0 φ 0 Gaussian distribution for round beam: 2 β 2 r N q q (1 + ) 2 1 2 1 − exp(− ) F (r) = 2 π ε r 2σ 2 0 force acts in the radial direction

Beam−Beam Parameter F r 1σ small amplitudes (with v c): r F N r p 2 quadrupole γ 2 σ v p 2 e 1 with: r = p 4 π ε 2 m c 0 p strong non−linear field: tune depends on oscillation amplitude strong non−linear field bunch intensity limited by non−linear resonances

Lepton versus Hadron Collider Leptons: elementary particles well defined energy γ light particles ( >> 1) synchrotron radiation (size, damping, magnet type) Hadrons: multi particle collisions energy spread (discovery range vs. background) γ heavy particles ( < 10000) no synchrotron radiation (no damping, superconducting magnets) - + p p Example: 1985 SppS Z 0 + - e e 1990 LEP

Collider Rings + − 1960 : e / e collider E = 2 E p CM + − p / p collider 1970 : Synchrotron rings as collider:

Stanford: e− / e− collisions in 1959 Ada: electron − positron collision 1961

VEP−1: electron / positron collider build in 1961 but no physics before ´64

ISR: proton − proton collider 1971

Trajectory Stability Vertical Plane: 1 2 gravitation: Δ Δ s = g t 2 −2 g = 10 m s Δ t = 60 msec Δ s = 18 mm 660 Turns! requires focusing! y B (y) ideal orbit x B particle trajectory v F x F B v

Quadrupole Focusing Quadrupole Magnet B = −g y x N S B = −g x y F = g x R x S N F = −g y y defocusing in horizontal plane! Alternate Gradient Focusing cut the arc sections in Idea: focusing and defocusing elements ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ω > ω 0 β

Strong Focusing ISR quadrupole magnet at CERN: SPS magnet sequence in the tunnel:

Storage Ring Tune: number of oscillations Q = turn Q ; Q ; Q s x y Envelope Function: 2π φ 0 β y(s) = A sin( Q s + ) L sorage ring circumference amplitude term amplitude term due to focusing due to injector s β( ) = β( ) s + L Q = 1 1 ds 2π β( ) s

Closed Orbit D B B F B F D B B D F B B = -g y x B = -g x y Orbit Offset in Quadrupole: x = x + x 0 quadrupole B = -g y x B = -g x - g x y 0 dipole component orbit error

Dipole Error and Orbit Stability Q = N with dipole field perturbations: Kick the perturbation adds up resonance with instability! arbitrary field imperfections: similar instabilities for: n Q + m Q = p x y avoid resonances!