Accelerators. The following are extracts from a lecture course at Nikhef (Amsterdam).

Transcription

1 Accelerators The following are extracts from a lecture course at Nikhef (Amsterdam). You are not required to know this information for this course, but you will find it interesting as background information There are, of course, many other good resources for this subject on the web! Particle Detection UVA/VU 2003 III 1

2 Force on charged particle due to electric and magnetic fields: dp dt = q(e + v B) In direction of motion -> acceleration or deceleration perpendicular to motion: deflection -> For acceleration an electric field needs to be produced: static: need a high voltage: e.g. Cockroft Walton generator, van de Graaff accelerator with a changing magnetic field: e.g. betatron with a high-frequent voltage which creates an accelerating field across one or more regions at times that particles pass these regions: e.g. cyclotron with high-frequency electro-magnetic waves in cavities Particle Detection UVA/VU 2003 III 2

3 Cockcroft-Walton high-voltage generator Sir John Douglas Cockroft Ernest Walton Nobel Prize 1951 From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p Particle Detection UVA/VU 2003 III 3

4 Cockroft Walton generator at Fermilab High voltage = 750 kv Structure in the foreground: ion (H - ) source CERN had a similar 750 kv setup, this has been replaced by a RFQ (Radio-Frequency Quadrupole) Particle Detection UVA/VU 2003 III 4

5 Van de Graaff accelerator Corona discharge deposits charge on belt Vertical construction is easier as support of belt is easier Left: Robert van de Graaff From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p Particle Detection UVA/VU 2003 III 5

6 Beam pipe From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p Particle Detection UVA/VU 2003 III 6

7 Tandem Van de Graaff accelerator: doubling of beam energy From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p Particle Detection UVA/VU 2003 III 7

8 6 MV tandem Van de Graaff accelerator, University of Utrecht Particle Detection UVA/VU 2003 III 8

9 Betatron: "beam transformer": increasing magnetic field accelerates particles (electrons) From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p Curved magnetic field focuses electrons Particle Detection UVA/VU 2003 III 9

10 The cyclotron Top view "Dee": conducting, non-magnetic box Side view ~ r.f. voltage Constant magnetic field Ernest O.Lawrence at the controls of the 37" cyclotron in 1938, University of California at Berkeley Nobel prize for "the invention and development of the cyclotron, and for the results thereby attained, especially with regard to artificial radioelements." (the 37" cyclotron could accelerate deuterons to 8 MeV) Speed increase smaller if particles become relativistic: special field configuration or synchro-cyclotron (uses particle bunches, frequency reduced at end of acceleration cycle) Particle Detection UVA/VU 2003 III 10

11 From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: Particle Detection UVA/VU 2003 III 11

12 From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: Particle Detection UVA/VU 2003 III 12

13 Linear Drift Tube accelerator, invented by R. Wideröe ~ r.f. voltage: frequency matched to velocity particles, so that these are accelerated for each gap crossed Particles move through hollow metal cylinders in evacuated tube Particle Detection UVA/VU 2003 III 13

14 Linear Drift Tube accelerator, Alvarez type Metal tank ~ small antenna injects e.m. energy Particles move through into resonator, e.m. wave in tank hollow metal cylinders in accelerates particles when they cross evacuated tube gaps, particles are screened from e.m. wave when electric field would decelerate Luis Walter Alvarez Nobel prize 1968, but not for his work on accelerators: "for his decisive contributions to elementary particle physics, in particular the discovery of a large number of resonance states, made possible through his development of the technique of using hydrogen bubble chamber and data analysis" Particle Detection UVA/VU 2003 III 14

15 Inside the tank of the Fermilab Alvarez type 200 MeV proton linac Particle Detection UVA/VU 2003 III 15

16 R.f. cavity with drift tubes as used in the SPS (Super Proton Synchrotron) at CERN NB: traveling e.m. waves are used Frequency = MHz Max. 790 kw 8MV accelerating voltage Particle Detection UVA/VU 2003 III 16

17 Generation of r.f. e.m waves with a klystron * The electron gun 1 produces a flow of electrons. * The bunching cavities 2 regulate the speed of the electrons so that they arrive in bunches at the output cavity. * The bunches of electrons excite microwaves in the output cavity 3 of the klystron. * The microwaves flow into the waveguide 4, which transports them to the accelerator. * The electrons are absorbed in the beam stop 5. from Particle Detection UVA/VU 2003 III 17

18 Synchrotron : circular accelerator with r.f. cavities for accelerating the particles and with separate magnets for keeping the particles on track. All large circular accelerators are of this type. Injection During acceleration the magnetic field needs to be "ramped up". r.f. cavity Focussing magnet Bending magnet Vacuum beam line Extracted beam Particle Detection UVA/VU 2003 III 18

19 During acceleration the magnetic field needs to be "ramped up". Slow extraction Fast extraction of part of beam Fast extraction of remainder of beam At time of operation of LEP SPS used as injector for LEP For LHC related studies Particle Detection UVA/VU 2003 III 19

20 Direct acceleration with e.m. waves in cavities (i.e. without using drift tubes) Consider an e.m. wave in a cylindrical conducting enclosure. The phase velocity of the wave will be larger than the speed of light, i.e. maxima and minima in electric field strength will move faster than light (not in conflict with relativity, as energy does not propagate faster than light) interfering waves Explanation: the e.m. wave can be regarded as a superposition of e.m. waves bouncing from the walls, each moving with the speed of light wave crest 2 wave crest 1 resultant wave crest travels over larger distance than original wave crests in the same time Particle Detection UVA/VU 2003 III 20

21 wave α Energy propagates with group velocity, v g = c sin α wall TM waves: magnetic field transversal, electric field longitudinal TE waves: electric field transversal, magnetic field longitudinal, unless distorted not usable for acceleration The phase velocity needs to be < c to make acceleration possible. This is possible with a disc loaded cylindrical cavity with holes ("irisses") in the centre of the discs. r.f. energy in r.f. energy out part of cavity (cut open) used in SLAC linear accelerator Particle Detection UVA/VU 2003 III 21

22 Standing waves in cavity: particles and anti-particles can be accelerated at the same time Superconducting cavity for the LEP-II e + e - collider (2000: last year of operation) t 1 "iris" t 2 The direction of E is indicated Cavities in cryostat in LEP Particle Detection UVA/VU 2003 III 22

23 Non-superconducting cavity as used in LEP-I. The copper sphere was used for low-loss temporary storage of the e.m. power in order to reduce the power load of the cavity Particle Detection UVA/VU 2003 III 23

24 Collider: two beams are collided to obtain a high CM energy. Colliders are usually synchrotrons (exception: SLAC). In a synchrotron particles and anti-particles can be accelerated and stored in the same machine (e.g. LEP (e + e - ), SppS and Tevatron (proton - anti-proton). This is not possible for e.g. a proton-proton collider or an electron-proton collider. Important parameter for colliders : Luminosity L number of events /s N = L σ cross-section Unit L: barn -1 s -1 or cm -2 s -1 Particle Detection UVA/VU 2003 III 24

25 Charged particles inside accelerators and in external beamlines need to be steered by magnetic fields. A requirement is that small deviations from the design orbit should not grow without limit. Proper choice of the steering and focusing fields makes this possible. Consider first a charged particle moving in a uniform field and in a plane perpendicular to the field: design orbit displaced orbit In the plane a deviation from the design orbit does not grow beyond a certain limit: it exhibits oscillatory behavior. However, a deviation in the direction perpendicular to the plane grows in proportion to the number of revolutions made and leads to loss of the particle after some time. Particle Detection UVA/VU 2003 III 25

26 To prevent instabilities a restoring force in the vertical direction is required. Possible solution : "weak focusing" with a "combined function magnet" design orbit plane (seen from the side) pole shoe pole shoe field component causes downward force field component causes upward force Components of magnetic field parallel to the design orbit plane force particles not moving in the plane back to it, resulting in oscillatory motion 1 ) perpendicular to plane. The field component perpendicular to the plane now depends on the position in the design orbit plane: the period of the oscillatory motion 1 ) in this plane around the design orbit becomes larger than a single revolution. 1 ) "betatron oscillations" Particle Detection UVA/VU 2003 III 26

27 θ=0 θ s ρ x z Lorentz force In-plane stability: qvb z (r) < γmv 2 /r for r<ρ qvb z (r) > γmv 2 /r for r>ρ centrifugal force Assume x<<ρ: With: r= ρ+x= ρ(1+x/ρ) we write: γmv 2 /r (1-x/ρ) γmv 2 /ρ B z r ()= B 0 1+ x B z B 0 r r=ρ = B 0 1 n x ρ n = "field index" The conditions now become: 1-nx/ρ < (1-x/ρ) for x<0 1-nx/ρ > (1-x/ρ) for x>0 n<1 Particle Detection UVA/VU 2003 III 27

28 Out-of-plane stability: B x = -Cz (C is a constant) θ=0 θ s ρ x z B = 0 B x z = B z x = C -> B z has to decrease with increasing x, therefore: n > 0. Note: C=0 for n=0, which corresponds to B z being independent of x For small n the amplitude of the vertical oscillations around the design orbit can be large, i.e. a large vacuum chamber will be required to contain the beam => a large value of n is desirable, but n < 1 for horizontal stability Particle Detection UVA/VU 2003 III 28

29 pole shoe pole shoe The inventors pole shoe pole shoe Here is the magnetic field not strong enough for stability if n 1 and if the orientation of all magnets in the ring is the same and another independent inventor => Alternate magnets with field lines bending to outside and bending to inside, n can be much larger than 1, and the amplitude for oscillations around the design orbit is much smaller. This is "strong focusing" Particle Detection UVA/VU 2003 III 29

30 CERN proton synchrotron (28 GeV protons), photograph taken in 1959 clearly shows the alternation of the combined function magnets Particle Detection UVA/VU 2003 III 30

31 Size comparison between Cosmotron and AGS magnet. AGS = Alternating Gradient Synchrotron, a strong-focusing, 33 GeV proton synchrotron, in operation from 1960 at Brookhaven The Cosmotron at Brookhaven, a 3.3 GeV proton synchrotron, weak- focusing, in operation from (photograph taken before concrete shielding was installed) The AGS: the field gradient is alternating between successive magnets (240 in total) Particle Detection UVA/VU 2003 III 31

32 The field of the combined function magnets used in the PS and in the AGS is a combination of a dipole field (for bending) and a quadrupole field (for focusing). In modern machines these functions are separated. Coil Magnetic field lines N S y x Cross-section of quadrupole magnet S N Hyperbolic pole contour B y = gx and B x = gy, where g is a constant The quadrupole focuses in one plane, but defocuses in the perpendicular plane. Two quadrupoles, rotated over 90 0 with respect to each other have a net focusing effect Particle Detection UVA/VU 2003 III 32

33 Dipoles and quadrupoles in LEP Quadrupole Dipole Particle Detection UVA/VU 2003 III 33

34 Focusing of a system of two lenses for both planes To focuse the beams in both planes, a succession of focusing and defocusing quadrupole magnets is required: FODO structure f 1 := 100 m horizontal plane f 2 := 100 m d := 50m d = 50 m F := f 1 f 2 d f 1 f 2 1 F = 200 m vertical plane Particle Detection UVA/VU 2003 III 34

35 LHC FODO structure QF dipole decapole QD sextupole QF magnets magnets magnets small sextupole corrector magnets Dipole- und Quadrupol magnets Particle trajectory stable for particles with nominal momentum Sextupole magnets LHC Cell - Length about 110 m (schematic layout) To correct the trajectories for off momentum particles Particle trajectories stable for small amplitudes (about 10 mm) Multipole-corrector magnets Sextupole - and decapole corrector magnets at end of dipoles Particle trajectories can become instable after many turns (even after, say, 10 6 turns) Particle Detection UVA/VU 2003 III 35

36 Superconducting magnets: no pole shoes Current distributions Particle Detection UVA/VU 2003 III 36

37 Particle Detection UVA/VU 2003 III 37

38 LHC string under test Particle Detection UVA/VU 2003 III 38

39 Calculation of the luminosity in a circular collider for head-on collisions k particle bunches moving in same direction simultaneously present in ring n particles per bunch surface of bunch is A one bunch is circling the machine with frequency f Interaction cross-section is σ For a particle in the left bunch the probability for an interaction with a particle in the right bunch is: nσ/a. For one bunch-bunch encounter the probability is n 2 σ/a. There are fk bunch-encounters per second in one interaction region With L = (# of interactions/s) / σ we find: L = fkn 2 /A -> minimizing the beam size and many bunches help to maximize the luminosity Particle Detection UVA/VU 2003 III 39

40 LHC: Luminosity can be increased by increasing n 1 and n 2, but the counterrotating beams interact electro-magnetically: "beam-beam" interactions Number of protons per bunch limited to about Assume the probability distribution to be Gaussian: L = fkn 1n 2 4πσ x σ y f = Hz Beam size 16 μm L = n 1 n 2 f k / 4π σ x σ y = [cm -2 s -1 ] with one bunch with 2808 bunches (every 25 ns one bunch) L = [cm -2 s -1 ] Particle Detection UVA/VU 2003 III 40

41 LHC: Large number of bunches Interaction point Bunch size squeezed near interaction point Crossing angle to avoid long range beam beam interaction Interaction region quadrupoles with gradient of 250 T/m and 70 mm aperture Particle Detection UVA/VU 2003 III 41

42 SLAC accelerator complex Damping rings: see section 3.3 Present lay-out, showing the Babar experiment : Particle Detection UVA/VU 2003 III 42

43 Particle Detection UVA/VU 2003 III 43

44 DESY accelerator complex (Hamburg) 8 km circumference Particle Detection UVA/VU 2003 III 44

45 CERN accelerator complex to Gran-Sasso (730 km) Particle Detection UVA/VU 2003 III 45

46 Particle Detection UVA/VU 2003 III 46

47 ESRF: European Synchrotron Radiation Facility, Grenoble, France 300 m circumference booster synchrotron, 6 GeV 16 m linac, 200 MeV Particle Detection UVA/VU 2003 III 47

48 Photon beams From electron beam by bremsstrahlung, using thin, high Z target. By measuring the energy and the direction of the electron before and after creation of the photon, the photon energy can be determined ("tagged" photon beam). From proton beam via π 0 decays. The beam may contain a significant fraction of neutrons, passing the beam through deuterium may improve the photon / neutron ratio. Charged particles are removed with bending magnets. Particle Detection UVA/VU 2003 III 48

49 π, K and anti-proton beams Production by interactions of primary protons from a proton accelerator with a suitable target. Typical fractions of particles for 400 GeV/c primary protons: Positive beam: 83.5 % p, 14.0 % π +, 2.5% K + Negative beam: 95.7% π, 3.5% K -, 0.8 % anti-proton At low energy electrostatic separators can be used for improving purity beam It may be possible to use Cerenkov counters in the beam to determine the beam composition on an event-by-event basis Particle Detection UVA/VU 2003 III 49

50 μ beams From decays of pions, hadrons absorbed in low Z absorber to minimize multiple scattering of muons High-intensity muon beam at CERN Absorber: 9.9 m Be Particle Detection UVA/VU 2003 III 50

51 Electron or positron beams From pair production in thin high Z radiator by photons produced by decays of neutral pions. Neutron, anti-neutron and K 0 beams From proton interactions in a production target, charged particles can be removed with magnetic fields, photons can be removed by passing the beam through a radiator, leading to conversion into e + e - pairs. Spallation source: accelerator + production target optimized for neutron beam production, example: ISIS, Rutherford lab, UK (800 MeV proton synchrotron and Ta target, see Hyperon (Λ, Σ ±,Ξ -, Ξ 0, Ω - ) beams Particles have short lifetimes -> short beamlines. Production with proton interactions, "tagging" of particles (e.g. using Cerenkov detector) in beam essential Particle Detection UVA/VU 2003 III 51

52 Neutrino beams From decays of charged pions and K-mesons: π + -> μ + ν μ π -> μ ν μ Κ + -> μ + ν μ Κ -> μ ν μ Κ + -> e + π 0 ν μ Κ -> e π 0 ν μ Electron neutrino flux ~ 1% of muon neutrino flux Beamline: thin production target, decay region and massive absorber (earth, iron) for removing everything else than neutrinos from beam. Wide band beam: collection of π's and K's from production target over wide range of momenta and large solid angle -> broad energy spectrum, high neutrino flux Narrow band beam: momentum (and charge) selection of π's and K's -> neutrino's or anti-neutrino's, lower intensity, better defined energy than in wide band beam. Particle Detection UVA/VU 2003 III 52

53 The future CNGS neutrino beam line at CERN, pointing to Gran Sasso Horn: pulsed magnet focusing particles produced Particle Detection UVA/VU 2003 III 53