Overview. Basic Accelerator Principles : units and equations. acceleration concepts. storage rings. trajectory stability.

Transcription

1 Overview Basic Accelerator Principles : units and equations acceleration concepts storage rings trajectory stability collider concept vacuum requirements synchrotron radiation design parameters for the LHC school/hst Lecture.pdf

2 Overview and History: M.S. Livingston and E.M. McMillan, History of the Cyclotron, Physics Today, 1959 S. Weinberg, The Discovery of Subatomic Particles, Scientific American Library, (ISBN or [pbk]) ( WEI) C. Pellegrini, The Development of Colliders, AIP Press, (ISBN ) (93: PEL) P. Waloschek, The Infancy of Particle Accelerators, DESY , R. Carrigan and W.P. Trower, Particles and Forces - At the Heart of the Matter, Readings from Scientific American, W.H. Freeman and Company, Leon Lederman, The God Particle, Delta books 1994 Lillian Hoddeson (editor), The rise of the standard model: particle physics in the 1960s and 1970s, Cambridge University Press, 1997 S. Weinberg, Reflections on Big Science, MIT Press, 1967 (5(04) WEI)

3 Introduction to Particle Accelerator Physics: J.J. Livingood, Principles of Cyclic Particle Accelerators, D. Van Nostrand Company, 1961 M.S. Livingston and J.P. Blewett, Partticle Accelerators, McGraw- Hill, 1962 Mario Conte and William McKay, An Introduction to the Physics of Particle Accelerators, Word Scientific, 1991 H.Wiedemann, Particle Accelerator Physics, Springer Verlag, CERN Accelerator School, General Accelerator Physics Course, CERN Report 85-19, CERN Accelerator School, Second General Accelerator Physics Course, CERN Report 87-10, CERN Accelerator School, Fourth General Accelerator Physics Course, CERN Report 91-04, M. Sands, The Physics of Electron Storage Rings, SLAC-121, E.D. Courant and H.S. Snyder, Theory of the Alternating-Gradient Synchrotron, Annals of Physics 3, 1-48 (1958). CERN Accelerator School, RF Engeneering for Particle Accelerators, CERN Report 92-03, CERN Accelerator School, 50 Years of Synchrotrons, CERN Report 97-04, E.J.N. Wilson, Accelerators for the Twenty-First Century - A Review, CERN Report 90-05, 1990.

4 Special Topics and Detailed Information: J.D. Jackson, Calssical Electrodynamics, Wiley, New York, Lichtenberg and Lieberman, Regular and Stochastic Motion, Applied Mathematical Sciences 38, Springer Verlag. A.W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, New York M. Diens, M. Month and S. Turner, Frontiers of Particle Beams: Intensity Limitations, Springer-Verlag 1992, (ISBN or ) (Hilton Head Island 1990) Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, New York R.A. Carrigan, F.R. Huson and M. Month, The State of Particle Accelerators and High Energy Physics, American Institute of Physics New Yorkm 1982, (ISBN ) (AIP ) Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, New York 1993.

5 Choices for the LHC super conducting RF R = 2784 meter B max = 8.38 T iron sarturation: 2 Tesla 4 earth: 0.3 * 10 Tesla super conducting magnet technology FODO lattice proton collider 2 in 1 magnet design 2835 bunche with 10 particles per bunch 11 high luminosity insertions beam screen cryo pump at 2K

6 Search for Elementary Particles Stage I: Nuclear Physics Chronology: 1803: 1896: 1896: Dalton M & P Currie Thomson Atom Atoms can decay Electron 1906: Rutherford Nucleus + Electron 1911: Rutherford α+ N O + H + Disintegration of Nuclei! Particle Accelerators

7 Stage II: Particle Physics Chronology (Theory): 1905: Einstein 2 E = mc 1930: 1935: Dirac Yukawa Antimatter π - Meson Chronology (Experiments): (Cosmic Rays) 1932: Anderson 1937: Anderson e µ + p - } π? Accelerators

8 Acceleration Concepts Lorentz Force: dp dt = Q * ( E + v x B ) magnetic fields: B v F Trajectory curvature due to B field! Energy gain only due to E field!

9 Energy Gain: Units 1 ev 19 (1.6 * 10 J) 1 Volt e E Common Units: kev, MeV, GeV, TeV ( ) 10, 10, 10, 10 Total Particle Energy: Relativity: 2 E = mc ; m = γ * m 0 γ = 1/ 1 β 2 ; β = v/c electron: 0.51 MeV proton: 0.94 GeV

10 Particle Sources: - e : e Cathode Rays p + : Cathode Tube withh - H +e H + 2 e H e- + H + H + e 2 H + e- + H + 2 e- + - Antimatter: Pair Production

11 Electrostatic Fields High Voltage Unit: ion source high voltage unit + acceleration tube V = 200 kv max target Cascade Generator: 0 2U 4U 6U o o o U = U osin ωt capacitors diodes 1928: 1932: Cockroft + Walton p + Li 2 He (Nobel Prize 1951) 800kV 700kV (p)

12 Van de Graaf Generator Single Unit: charge collector charge conveyor belt + 50 kv dc ion + source + spraycomb top terminal + 10 MV + evacuated acceleration channel spectrometer magnet experiment V = 10 MVolt max

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

14 Time Varying Fields E = - 1 A c t e e E rot B = µε c e e E t capacitor beam AC generator Resonator: capacitor coil B L = C = ε 2 µ 0 N A l 0 A d beam E beam cavity f; Q; R cavity

15 Circular Accelerators Synchrotron: ω r = = Q m m Q 0 γ B B γ v R = const. (LHC/LEP: ω = 11.3kHz) B = const. injection magnet B RF cavity vacuum chamber extraction / target

16 Why 8.4 Tesla? Synchrotron: R = const. r = m Q 0 γ B v B γ B[T] = p[gev/c] R[meter] Physics: LEP tunel: p = 7000 GeV/c L = meter arcs: L = meter R = 3500 meter Bending and Focusing: R = 2784 meter B max = 8.38 T iron sarturation: 2 Tesla 4 earth: 0.3 * 10 Tesla

17 Power Consumption LEP: B = Tesla P = R I 2 I = 4500A; R = 1m Ω ca. 500 magnets P = 20 kw / magnet P = 10 MW LHC: B I B max = 8.38 T I = A P = 78 MW / magnet ca. 500 magnets P > 39 GW superconducting technology! 8.4 T is at the limit of available technology!

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

19 Strong Focusing oscillator (spring): F = g y Ω A 2 g 1 g for a fixed energy strong focusing: small amplitudes small vacuum chamber efficient magnets high oscillation frequency

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

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

22 Circular Accelerators uniform B field: R = const. r = m0 Q γ B v p = Q B L 2π E / c for E >> E 0 realistic synchrotron: B field is not uniform: drift space for installation different types of magnets space for experiments etc E = Q c 2π B d l high beam energy requires: high magnetic field large packing factor F

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

24 Sources for Orbit Errors Alignment: +/ 0.1 mm Ground motion slow drift civilisation moon seasons civil engineering Error in dipole strength power supplies calibration Energy error of particles

25 Synchrotron: the orbit determines the particle energy! assume: L > design orbit V b) a) t energy increase Equilibrium: f RF = h f rev f = rev 1 2 π q m γ B E depends on orbit and magnetic field!

26 momentum compaction factor: increase particle energy velocity increase shorter revolution time momentum increase longer revolution time transition energy R = α p R p α = 1 γ t 2 α 1 Q 2 E error depends on transition energy!

27 Orbit Correction aim at a local correction of the dipole error due to the quadrupole alignment errors place orbit corrector and BPM next to the main quadrupoles horizontal BPM and corrector next to QF vertical BPM and corrector next to QD BPM BPM QF MB QD HX HV relative alignment of BPM and quadrupole?

28 Orbit Stability dipole error and Q = N: Kick the perturbation adds up watch out for integer tunes! field errors: the perturbations add up for Q = 1/n watch out for fractional tunes! minimise field errors and avoid strong resonances!

29 Tune Diagram resonances: n Q x + m Q + r Q = p y s strength: h A n+m+s Q x 1 avoid low order resonances! Q x 0.3 Q y Q y limits for b and tune changes n

30 Collider Rings 1960: fixed target physics (bubble chamber) But: E E = 2 m c cm 0 2 m 2 0 c Collider: E = 2 E CM p center of mass energy GeV ISR collider SppS SPS Tevatron Tevatron fixed target particle energy GeV 1960 : 1970 : + + e / e collider p / p collider

31 + / Features ( ) not all particles collide in one crossing long storage times requires 2 beams: two rings anti particles collision regions collision point anti particles hard to produce beam beam interaction requires beam separation

32 LHC Layout 2 Ring Layout: RF IP4 CMS TOTEM IP5 extraction IP6 collimation machine protection IP3 beam1 beam2 IP7 IP2 ALICE injection b1 IP1 ATLAS IP8 LHCb injection b2 2 in 1 magnet design 4 proton experiments + 1 ion experiment beam cross over in 4 IR s

33 Lepton versus Hadron Collider Leptons: ( e + / e ) elementary particles well defined energy precision experiments Hadrons: + ( p / p ) multi particle collisions energy spread discovery potential Example: 1985 SppS p Z + p LEP e + e

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

35 Luminosity: Beam Size interaction region N N 1 2 area A L = LHC: n N N f A b 1 2 rev A = π β ε <β> arc = 80 meter β IP = 0.5 meter Limit: magnet strength aperture x = A β sin( φ ) A x = sin( φ ) β

36 Synchrotron Radiation Electro Magnetic Waves : accelerated charge emits electro magnetic waves radio signal X rays radiation fan in bending plane bending plane synchrotron light cone P <E > γ opening angle γ 4 ρ 2 γ 3 ρ particle trajectory 1 γ LEP: γ = γ = 7000 LHC:

37 Examples E [GeV] ρ [km] N 12 [10 ] U [MeV] P [MW] u c [kev] LEP LEP LEP LHC LEP 1 LEP 2 LHC X rays γ rays UV light

38 Vacuum Bremsstrahlung + Coulomb Scattering beam blow up particle loss background in experiments loss in luminosity! equipment damage!

39 LHC Beam Parameter L = N 2 p ε β n b f rev 2 π 34 2 L = 10 cm s 1 Beam Beam Interaction: Beam Size: Q magnet quality + N b ε < aperture 11 N = 10 p ε β: quadrupole strength + β = 0.5 meter n = 2835 b I beam = 0.5 A aperture Beam Power E = 300 MJ = 120 kg TnT Synchrotron Radiation P = 0.5 W/m

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

41 Drift Tubes 1924: Ising AC Voltage: Symmetric line: V t + BEAM l = v part T/2 1928: demonstrated by Wideroe 1MHz, 25kV oscillator 50kV potassium ions Lawrance: 1.3MV mercury ions with 48kV But: f < 7MHz (l = 21 meter)!

42 Time Varying Fields Maxwell Equations without Sources a) * E = 0 b) x E + 1 B = 0 c t e e c) * B = 0 d) µε E x B = 0 c t e e Rotation on b) and d) plus: x ( x V ) = ( V ) V Wave equation: 2 E e e t 2 c 2 = E µε 2 2 B e e c 2 2 t = B 2 µε

43 E = E e 0 Time Varying Fields Plane Electro Magnetic Wave: ik n x ω t ik n x ωt B = B e 0 B = µε n x E 0 0 k = 2 π λ No acceleration in the direction of propagation!

44 Boundary ConditionsI Transverse Electric Waves (TE): E z= 0 everywhere; e e B n Boundary condition: = 0 s Transverse Magnetic Waves (TM): B = 0 everywhere; z Boundary condition: E = 0 n s E E 01 mode H wall currents λ 2 displacement currents Problem: v > c ph Shielding or change v ph

45 Alvarez: Resonance Tank l = v part T support BEAM posts Tubes are passive higher frequencies! (f = 200 MHz gives good tube size) Posts v = 0 gr Pre accelerator for most acclelerators proton

46 Boundary ConditionsII Cavity Resonator: TM mode with longitudinal boundary; beam axis H E Short Section: multi cell multi passage

47 Boundary ConditionsIII Loaded Wave Guide: v ph = v particle iris beam path But: Concept of linear acceleration is limited by power of RF generator! Not feasible before World War II