1. 1 Experimental aspects: Lectures 5/6: Accelerators Double lecture on accelerators 2 on examples of complete systems These are an important part of the subject, but I will not go too far into maths

2. 2 A useful reference CERN Accelerator school (slightly dated, good) http://cas.web.cern.ch/cas/CAS_Proceedings.html

3. 3 Introduction Particle physicists want high energy to discover/study new particles Cosmic rays become rare at high energies, not repeatable Therefore particle accelerators are required The subject has been driven by accelerator technology for 50 years.

4. 4 Livingstone Plot No longer straight Energy gains harder to achieve New ideas needed: Wakefield acceleration? Laser acceleration? Muon colliders?

5. 5 Basics of acceleration Of the known forces, only EM is conceivable Gravity not controllable Nuclear forces too short range alpha particles! So this lecture is about:

6. 6 The Basic accelerator: ~1931: Cockcroft and Walton Source, e.g. hot wire for electrons; H - plasma Appropriate high voltage to attract ions/electrons High voltage 800kV Very hard to go beyond few MV, due to breakdown. Folded tandem: Accelerate H - ions, strip to H + with thin foil, bend in B-field, accelerate down. 'Free' doubling of energy Used as a first stage on some machines

7. 7 ISIS Cockcroft Walton Good for Dr. Who Now being replaced (RFQ)

8. 8 Oscillating fields Drift in tubes Accelerate in gaps Wideroe Drift Tube Linac 1928

9. 9 Motion in Magnetic fields Particles spiral round field lines Frequency is energy independent f=qB/2  m 1T: 15MHz(protons) 28GHz(electrons) Radius increases with energy Non relativistic

10. 10 The Cyclotron: ~1930s: Lawrence Use B-field oscillations Pole pieces give vertical magnetic field D shaped metal cans have alternating power supply attached E Field in gap region Frequency tuned to match particles Those particles with the correct phase will always be accelerated in the gap Radius increases with energy

11. 11 Real Cyclotrons Field (accidentally originally) spreads Gives vertical force Taylor curl B=0 SHM: Tune

12. 12 Cyclotron Tune We just saw Tune must be real, or particles are not captured k is negative (field decreasing with R) But there are also radial oscillations: Similar condition holds: hence -1<k<0 for stable operation

13. 13 The Cyclotron: relativity Use relativistic formulae Highest energy particles de-phase, e.g. γ of 1.01 will be out of phase after 50 turns This is β=0.14c, or E k =13MeV for proton This seemed to be the limit for years

14. 14 Can variable field cheat relativity? Change B field changes with r so that B  γ. This gives But we know that -1 < k < 0 A relativistic cyclotron must be unstable! or must it?

15. 15 A variable field can cheat relativity! AVF or Thomas focusing B field arranged such that B  γ Alternate sectors of field and drift Original configuration defocussing Edges provide vertical focusing If insufficient, can insert reverse field sectors Fixed Field, Alternating Gradient (FFAG) Spiral sector boundaries give even more focusing

16. 16 Worlds largest Cyclotron: Triumf Tri- University Meson facility, Vancouver, BC, Canada E=505MeV

17. 17 Cyclotron Summary Fixed magnetic fields make for simple operation No ramping of magnets, with associated stress High proton current as always on Most economical way to achieve 1MW? Beam energy record is ~600MeV Used for high intensity pion/muon/neutron sources

18. 18 Cycling Magnetic Field For many years the AVF was ignored Time varying magnetic field seemed only solution Synchro-cyclotrons: raise cyclotron B-field as beam energy rises maintain non-relativistic cyclotron behaviour Not often used Synchrotrons Keep r fixed, put all variation into the field.

19. 19 The Synchrotron: Constant radius orbit Time Varying magnetic field Acceleration at 'cavities' in ring Dipoles provide bending field Quadrupoles/Sextupoles focus, steer Strong focusing, Thomas-like

20. 20 Storage Ring One ring or two? Particles & antiparticles going opposite directions can use same ring

21. 21 Anti-protons? Where from? Anti-protons are in short supply! 10 6 120GeV protons collide 20 antiprotons collected 0.00002% eff Forget 'Angels and Demons' LHC pp! n.b. Positrons (fairly) easy to make Fermilab Source

22. 22 Luminosity Define: Collision rate is luminosity times cross-section For a circular machine – f is interaction rate, – n the number of particles –  the beam size n1n1 n2n2 xx yy

23. 23 Luminosity - practical example LEP claims Luminosity 10 32 cm 2 /s Use 10 7 seconds in a year (4 months working) 10 39 cm 2 /year 1b = 10 -28 m 2 1000pb -1 per year But actually 200pb -1 recorded – factor 1/5 for filling, breakage, average-to-peak ● 10 30 gives 2 events for 1pb cross-section

24. 24 Emittance `Envelope of beam particles’ Define  x  x  ’ x  units mm mRad (assumes uncorrelated) 3D/6D emittance The 6-dimensional particle correlation x,y,z,x', y', z'  a conserved quantity (Liouville's theorem): Reduce one , other grows Normalised emittance: normalised emittance invariant under acceleration It is so useful, it is often called emittance. xx ’x’x 1/  = brightness

25. 25 Emittance examples All these have zero emittance

26. 26 More Emittance examples Finite emittance Initially x' small Lense correlates x,x' Drift to focus makes x small. Area is conserved

27. 27 Luminosity and Emittance Define   is  x /  ’ x, This is small if beam is focused 'Low Beta quads'

28. 28 Beam Emittance e + e - rings set by synchrotron radiation Electron machines `have no memory’ pp machines by beam preparation – Stochastic cooling – emittance growth is cumulative For linear accelerators preparation and beam blowup contribute.

29. 29 Luminosity Optimisation Increase f – Bunch separation, power constraints Increase n i – Space charge, power, particle availability Decrease   – Strong Quads in apparatus, blowup, bunch length Decrease  – ‘colder beams’ improve performance

30. 30 Beam-spot size The size affects b-tagging as well as luminosity Typical track resolution:   =20 2 +(50/p t ) 2  in  m, p t in GeV These figures vary with beampipe radius detector technology If beam is small w.r.t. this it helps. – True for all planned colliders bar  H

31. 31 Other Luminosity limits beam beam interaction: Each beam feels field of the other: Disruptive if beams very small (linear v circular collider) accelerating power Available Watts of RF power limit currents cooling power Not usually critical, but need enough cooling pile-up LHC aims for 25 collisions per bunch crossing – more would swamp detectors Causes radiation damage

32. 32 Example of LEP luminosity tuning Deterministic and empirical optimization!

33. 33 Tevatron Luminosity 1.5fb -1 after 5 years

34. 34 Tevatron Goals Tevatron enters Higgs search with 2fb -1 Needs 20+ to make a discovery

35. 35 Bunch Stability Why does a bunch of particles stay together? r v Gauss's law: Ampere's law: Electric and magnetic forces cancel at high energy

36. 36 Picture of CERN 1hr return drive © Photo CERN

37. 37 Tunnel up to ~100 m below ground. Injection from the SPS. e + e - collisions simultaneously in four interaction points.

38. 38 Close up of DELPHI Note 1 cooling tower - old photo! 66 cars? © Photo CERN

39. 39 In the LEP tunnel Part of the 27km of dipoles © PhotoC ERN

40. 40 Now to be the LHC tunnel 27km of vacuum pipe 8.3Tesla bending magnets, 3 o above absolute zero © Photo CERN

41. 41 The simulation being made real... The first of over 1000 8.3Tesla bending magnets, © Photo CERN

42. 42 Dipoles being connected