An Introduction to Particle Accelerators

1. An Introduction to Particle Accelerators Erik Adli, University of Oslo/CERN November, 2007 Erik.Adli@cern.ch v1.32

2. References • Bibliography: • CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992 • LHC Design Report [online] • K. Wille, The Physics of Particle Accelerators, 2000 • Other references • USPAS resource site, A. Chao, USPAS January 2007 • CAS 2005, Proceedings (in-print), J. Le Duff, B, Holzer et al. • O. Brüning: CERN student summer lectures • N. Pichoff: Transverse Beam Dynamics in Accelerators, JUAS January 2004 • U. Am aldi, presentation on Hadron therapy at CERN 2006 • Various CLIC and ILC presentations • Several figures in this presentation have been borrowed from the above references, thanks to all!

3. Part 1 Introduction

4. Particle accelerators for HEP • LHC: the world biggest accelerator, both in energy and size (as big as LEP) • Under construction at CERN today • End of magnet installation in 2007 • First collisions expected summer 2008

5. Particle accelerators for HEP The next big thing. After LHC, a Linear Collider of over 30 km length, will probably be needed (why?)

6. Others accelerators • Historically: the main driving force of accelerator development was collision of particles for high-energy physics experiments • However, today there are estimated to be around 17 000 particle accelerators in the world, and only a fraction is used in HEP • Over half of them used in medicine • Accelerator physics: a disipline in itself, growing field • Some examples:

7. Medical applications • Therapy • The last decades: electron accelerators (converted to X-ray via a target) are used very successfully for cancer therapy) • Today's research: proton accelerators instead (hadron therapy): energy deposition can be controlled better, but huge technical challenges • Imaging • Isotope production for PET scanners

8. Advantages of proton / ion-therapy ( Slide borrowed from U. Am aldi )

9. Proton therapy accelerator centre HIBAC in Chiba What is all this? Follow the lectures... :) ( Slide borrowed from U. Am aldi )

10. Synchrotron Light Sources • the last two decades, enormous increase in the use of synchrony radiation, emitted from particle accelerators • Can produce very intense light (radiation), at a wide range of frequencies (visible or not) • Useful in a wide range of scientific applications

11. Outline of presentation Part 1: Intro + Main parameters + Basic Concepts Part 2: Longitudinal Dynamics Part 3: Transverse Dynamics Case: LHC Part 4: Intro to synchrotron radiation Part 5: The road from LEP via LHC to CLIC Case: CLIC

12. Main Parameters

13. Main parameters: particle type • Hadron collisions: compound particles • Mix of quarks, anti-quarks and gluons: variety of processes • Parton energy spread • Hadron collisions  large discovery range • Lepton collisions: elementary particles • Collision process known • Well defined energy • Lepton collisions  precision measurement “If you know what to look for, collide leptons, if not collide hadrons”

14. Main parameters: particle type Discovery Precision SppS / LHC LEP / LC

15. Main parameters: particle energy • New physics can be found at larger unprobed energies • Energy for particle creation: centre-of-mass energy, ECM • Assume particles in beams with parameters m, E, E >> mc2 • Particle beam on fixed target: • Colliding particle beams: •  Colliding beams much more efficient

16. Main parameters: luminosity • High energy is not enough ! • Cross-sections for interesting processes are very small (~ pb = 10−36 cm² ) ! • s(gg → H) = 23 pb [ at s2pp = (14 TeV)2, mH = 150 GeV/c2 ] • We need L >> 1030 cm-2s-1 in order to observe a significant amount of interesting processes! • L [cm-2s-1] for “bunched colliding beams” depends on • number of particles per bunch (n1, n2) • bunch transverse size at the interaction point (x, y ) • bunch collision rate ( f)

17. Main parameters: LEP and LHC

18. Capabilities of particle accelerators • A modern HEP particle accelerator can accelerate particles, keeping them within millimeters of a defined reference trajectory, and transport them over a distance of several times the size of the solar system HOW?

19. HOW? • In this presentation we try to explain this by studying: • the basic components of an accelerator • the physical mechanisms that determines the particle motion • how particles (more or less) follow a specified path, even if our accelerator is not designed perfectly • At the end, we use what we have learned in a case-study: the LHC

20. Part 2 Basic concepts

21. An accelerator • Structures in which the particles will move • Structures to accelerate the particles • Structures to steer the particles • Structures to measure the particles

22. Lorentz equation • The two main tasks of an accelerator • Increase the particle energy • Change the particle direction (follow a given trajectory, focusing) • Lorentz equation: • FB v  FB does no work on the particle • Only FE can increase the particle energy • FE or FB for deflection? v  c  Magnetic field of 1 T (feasible) same bending power as en electric field of 3108 V/m (NOT feasible) • FB is by far the most effective in order to change the particle direction

23. Acceleration techniques: DC field • The simplest acceleration method: DC voltage • Energy kick: DE=qV • Can accelerate particles over many gaps: electrostatic accelerator • Problem: breakdown voltage at ~10MV • DC field still used at start of injector chain

24. Acceleration techniques: RF field • Oscillating RF (radio-frequency) field • “Widerøe accelerator”, after the pioneering work of the Norwegian Rolf Widerøe (brother of the aviator Viggo Widerøe) • Particle must sees the field only when the field is in the accelerating direction • Requires the synchronism condition to hold: Tparticle =½TRF • Problem: high power loss due to radiation

25. Principle of phase focusing ...what happens to particles with energies slightly off the nominal values...?

26. Acceleration techniques: RF cavities • Electromagnetic power is stored in a resonant volume instead of being radiated • RF power feed into cavity, originating from RF power generators, like Klystrons • RF power oscillating (from magnetic to electric energy), at the desired frequency • RF cavities requires bunched beams (as opposed to coasting beams) • particles located in bunches separated in space

27. Acceleration techniques: Pill-Box cavity • Ideal cylindrical cavity: • Solution for E and H are oscillating modes (of increasing frequency) • The fundamental mode normally used for acceleration is named TM010 with the following features: • Ez is constant in space along the axis of acceleration, z, at any instant • l010 = 2.6a, l < 2 a • Acceleration efficiency of cavity depends on the transit-time factor • Ratio of “actual energy gain”, versus “energy gain if the field was constant in time“ • Example: l = l / 2 gives q=p and T=0.64

28. From pill-box to real cavities (from A. Chao) LHC cavity module ILC cavity

29. Why circular accelerators? • Technological limit on the electrical field in an RF cavity (breakdown) • Gives a limited E per distance •  Circular accelerators, in order to re-use the same RF cavity • This requires a bending field FB in order to follow a circular trajectory (later slide)

30. The synchrotron • Acceleration is performed by RF cavities • (Piecewise) circular motion is ensured by a guide field FB • FB : Bending magnets with a homogenous field • In the arc section: • RF frequency must stay locked to the revolution frequency of a particle (later slide) • Almost all present day particle accelerators are synchrotrons

31. Digression: other accelerator types • Cyclotron: • constant B field • constant RF field in the gap increases energy • radius increases proportionally to energy • limit: relativistic energy, RF phase out of synch • In some respects simpler than the synchrotron, and often used as medical accelerators • Synchro-cyclotron • Cyclotron with varying RF phase • Betatron • Acceleration induced by time-varying magnetic field • The synchrotron will be the only type discussed in this course

32. Particle motion • We separate the particle motion into: • longitudinal motion: motion tangential to the reference trajectory along the accelerator structure, us • transverse motion: degrees of freedom orthogonal to the reference trajectory, ux, uy • us, ux, uy are unit vector in a moving coordinate system, following the particle

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34. Part 3 Longitudinal dynamicsand acceleration Longitudinal Dynamics: degrees of freedom tangential to the reference trajectory us: tangential to the reference trajectory

35. RF acceleration • We assume a cavity with an oscillating RF-field: • In this section we neglect the transit-transit factor • we assume a field constant in time while the particle passes the cavity • Work done on a particle inside cavity:

36. Synchrotron with one cavity • The energy kick of a particle, DE, depends on the RF phase seen, f • We define a “synchronous particle”, s, which always sees the same phase fs passing the cavity  wRF =h wrs ( h: “harmonic number” ) • E.g. at constant speed, a synchronous particle circulating in the synchrotron, assuming no losses in accelerator, will always see fs=0

37. Non-synchronous particles • A synchronous particle P1 sees a phase fs and get a energy kick DEs • A particle N1 arriving early with f=fs-d will get a lower energy kick • A particle M1 arriving late with f=fs+d will get a higher energy kick • Remember: in a synchrotron we have bunches with a huge number of particles, which will always have a certain energy spread!

38. Frequency dependence on energy • In order to see the effect of a too low/high DE, we need to study the relation between the change in energy and the change in the revolution frequency (h: "slip factor") • Two effects: • Higher energy  higher speed (except ultra-relativistic) • Higher energy  larger orbit “Momentum compaction”

39. Momentum compaction • Increase in energy/mass will lead to a larger orbit • We define the “momentum compaction factor” as: • a is a function of the transverse focusing in the accelerator, a=<Dx> / R • a is a well defined quantity for a given accelerator

40. Calculating h • Logarithmic differentiation gives: • For a momentum increase dp/p: • h>0: velocity increase dominates ( fr increases ) • h<0: circumference increase dominates ( fr decreases )

41. Phase stability • h>0: velocity increase dominates, fr increases • Synchronous particle stable for 0º<fs<90º • A particle N1 arriving early with f=fs-d will get a lower energy kick, and arrive relatively later next pass • A particle M1 arriving late with f=fs+d will get a higher energy kick, and arrive relatively earlier next pass • h<0: stability for 90º<fs<180º • h=0 is called transition. When the synchrotron reaching this energy, the RF phase needs to be switched rapidly from fsto 180-fs

42. Longitudinal phase-space (from A. Chao) d = Dp/p Phase-space for a harmonic oscillator: H = p2 / 2 + x2 / 2 Longitudinal phase-space showing the synchrotron motion Synchrotron motion: "particles rotate in the phase-space"

43. Synchrotron oscillations • Analysis of small amplitude oscillations gives: • As result of the phase stability, the energy and phase will oscillate, resulting in longitudinal synchrotron oscillations: • Equation of an Harmonic Oscillator • For derivations, please refer to [Wille2000]

44. Synchrotron: energy ramping • We now wish to ramp up the energy of the particle. What do we do? • Each time the synchronous particle passes the cavity it will receive a momentum kick: • We want the synchronous particle to on the same trajectory (reference trajectory) regardless of particle energy. Therefore, we require the field and the particle momentum to increase proportionally: • Combining gives: • Thus, for a given dB/dt profile the synchronous phase is given as: • For a given B’ , the synchronous particles will, by definition, see the phase fs

45. Summary: longitudinal dynamicsfor a synchrotron • Summary: to ramp up the energy in a synchrotron • Simply ramp up the magnetic field • With the (automatic) RF frequency modulation the synchronous particle will stay on the reference orbit • Due to the phase-stability, the particles in the phase-space vicinity of the synchronous particle will be captured by the RF and will also be accelerated at the same rate, undergoing synchrotron oscillations

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47. Part 4 Transverse dynamics Transverse dynamics: degrees of freedom orthogonal to the reference trajectory ux: the horizontal plane uy: the vertical plane

48. Bending field • Circular accelerators: deflecting forces are needed • Circular accelerators: piecewise circular orbits with a defined bending radius  • Straight sections are needed for e.g. particle detectors • In circular arc sections the magnetic field must provide the desired bending radius: • For a constant particle energy we need a constant B field  dipole magnets with homogenous field • In a synchrotron, the bending radius,1/=eB/p, is kept constant during acceleration (last section)

49. The reference trajectory • We need to steer and focus the beam, keeping all particles close to the reference orbit Dipole magnets to steer Focus? or cosq distribution homogenous field

50. Focusing field: quadrupoles • Quadrupole magnets gives linear field in x and y: Bx = -gy By = -gx • However, forces are focusing in one plane and defocusing in the orthogonal plane: Fx= -qvgx (focusing) Fy = qvgy (defocusing) Alternating gradient scheme, leading to betatron oscillations