1. 1 Cobbled together from: i) “The quest for luminosity”, by Dr. Rob Appleby ii) “An introduction to particle accelerators,” by Erik Adli

2. Particle accelerators are everywhere! Daily applications Daily applications TV, computer monitor TV, computer monitor Microwave oven, oscilloscopes Microwave oven, oscilloscopes Industrial Industrial Food sterilization Food sterilization Electron microscopes Electron microscopes Radiation treatment of materials Radiation treatment of materials Nuclear waste treatment Nuclear waste treatment

3. Particle accelerators are everywhere! Medical applications Medical applications Cancer therapy, Radiology Cancer therapy, Radiology Instrument sterilization Instrument sterilization Isotope production Isotope production Research tools for many scientific fields Research tools for many scientific fields High energy physics experiments High energy physics experiments Light sources for chemistry, biology etc Light sources for chemistry, biology etc Optics, neutron sources Optics, neutron sources Inertial fusion Inertial fusion

4. The technologies used Large scale vacuum Large scale vacuum High power microwaves High power microwaves Superconducting technology Superconducting technology Very strong and precise magnets Very strong and precise magnets Computer control Computer control Large scale project management Large scale project management Accelerator physics (beam dynamics) Accelerator physics (beam dynamics)

5. What is an accelerator? Put simply, an accelerator takes a stationary particle, with energy E 0, and accelerates it to some final energy E. Put simply, an accelerator takes a stationary particle, with energy E 0, and accelerates it to some final energy E. This is achieved using electric fields for acceleration and magnetic field for beam control This is achieved using electric fields for acceleration and magnetic field for beam control The uses are many…we are interested mainly in colliding beam applications The uses are many…we are interested mainly in colliding beam applications

6. Why do we need them? We want to study the building blocks of nature We want to study the building blocks of nature Very small structure, 10 -10 m to 10 -15 m Very small structure, 10 -10 m to 10 -15 m Our probe is electromagnetic radiation Our probe is electromagnetic radiation To probe 10 -15 m, we need =10 -15 m To probe 10 -15 m, we need =10 -15 m

7. The best accelerator in the universe…

8. A basic 9eV accelerator The single electron passes through a potential difference of 1.5 volts, thus gaining 1.5 electron-volts of energy (The simplest in the universe!)

9. An aside on electron volts Make sure you understand the units of particle and accelerator physics! Make sure you understand the units of particle and accelerator physics! 1 eV = 1.602 x 10 -19 joules So we speak of GeV (Giga-electron-volts) and TeV (Tera-electron volts) So we speak of GeV (Giga-electron-volts) and TeV (Tera-electron volts)

10. The development of accelerators Accelerators have gone through a long development process, including Accelerators have gone through a long development process, including Electrostatic accelerators Electrostatic accelerators The Van de Graaff accelerator The Van de Graaff accelerator The Cyclotron The Cyclotron The Synchrotron The Synchrotron

11. The Cyclotron A vertical B-field provides the force to maintain the electron’s circular orbit A vertical B-field provides the force to maintain the electron’s circular orbit The particles pass repeatedly from cavity to cavity, gaining energy. The particles pass repeatedly from cavity to cavity, gaining energy. As the energy of the particles increases, the radius of the orbit increases until the particle is ejected As the energy of the particles increases, the radius of the orbit increases until the particle is ejected AC voltage between “D”s timed so electric field always accelerates

12. The first million volt cyclotron “we were concerned about how many of the protons would succeed in spiralling around a great many times without getting lost on the way." 08/01/32 Lawrence and Livingston at Berkeley

13. 13 Modern Particle Accelerators The particles gain energy by surfing on the electric fields of well-timed radio oscillations (in a cavity like a microwave oven)

14. Accelerating cavities Accelerating cavities Modern machines use a time-dependent electric field in a cavity to accelerate the particles Modern machines use a time-dependent electric field in a cavity to accelerate the particles

15. How we manipulate the beam The charged particle beam is then manipulated by the use of powerful magnets The charged particle beam is then manipulated by the use of powerful magnets In analogy with light optics, we call this process magnetic beam optics In analogy with light optics, we call this process magnetic beam optics The beam is bent using dipole magnets and focusing using quadrupole magnets The beam is bent using dipole magnets and focusing using quadrupole magnets The magnets are very strong, often several Tesla, and use normal conducting, superconducting or permanent magnet technology The magnets are very strong, often several Tesla, and use normal conducting, superconducting or permanent magnet technology

16. Lorentz equation The two main tasks of an accelerator –Increase the particle energy –Change the particle direction (follow a given trajectory, focusing) Lorentz equation: F B  v  F B does no work on the particle –Only F E can increase the particle energy F E or F B for deflection? v  c  Magnetic field of 1 T (feasible) same bending power as en electric field of 3  10 8 V/m (NOT feasible) –F B is by far the most effective in order to change the particle direction

17. Magnetic lattices Magnets are combined to form a magnet lattice Magnets are combined to form a magnet lattice The lattice steers and focuses the beam The lattice steers and focuses the beam Dipole F Quadrupole D Quadrupole

19. A mini tour Now we’ll look at some of the world’s biggest circular accelerators Now we’ll look at some of the world’s biggest circular accelerators Just LEP and the LHC Just LEP and the LHC Note that I only scratch the surface, miss many out and spend very little time on non-colliding machines Note that I only scratch the surface, miss many out and spend very little time on non-colliding machines There is much more life than I show! There is much more life than I show!

20. What was LEP? LEP was a circular electron-positron collider, built at Cern, Geneva. LEP was a circular electron-positron collider, built at Cern, Geneva. The ring design (c=27km) meant that the accelerating structures are seen many times by the circulating beams of particles The ring design (c=27km) meant that the accelerating structures are seen many times by the circulating beams of particles The ring had 4 experimental sites - ALEPH, DELPHI, L3 and OPAL. The ring had 4 experimental sites - ALEPH, DELPHI, L3 and OPAL. Final collision energy was 209 GeV (2 x E beam ) Final collision energy was 209 GeV (2 x E beam ) It almost discovered the Higgs boson! It almost discovered the Higgs boson!

21. L (arge) E (lectron) P (ositron)

22. The LEP tunnel (this is one of LEPs superconducting cavities)

23. 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

24. From pill-box to real cavities LHC cavity moduleILC cavity (from A. Chao)

25. 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 F B in order to follow a circular trajectory (later slide)

26. The synchrotron Acceleration is performed by RF cavities (Piecewise) circular motion is ensured by a guide field F B F B : Bending magnets with a homogenous field In the arc section: RF frequency must stay locked to the revolution frequency of a particle (later slide) Synchrotrons are used for most HEP experiments (LHC, Tevatron, HERA, LEP, SPS, PS) as well as, as the name tells, in Synchrotron Light Sources (e.g. ESRF)

27. Focusing field: quadrupoles Quadrupole magnets gives linear field in x and y: B x = -gy B y = -gx However, forces are focusing in one plane and defocusing in the orthogonal plane: F x = -qvgx (focusing) F y = qvgy (defocusing) Opposite focusing/defocusing is achieved by rotating the quadrupole 90  Analogy to dipole strength: normalized quadrupole strength: inevitable due to Maxwell

28. Optics analogy Physical analogy: quadrupoles  optics Focal length of a quadrupole: 1/f = kl –where l is the length of the quadrupole Alternating focusing and defocusing lenses will together give total focusing effect in both planes (shown later) –“Alternating Gradient” focusing

29. The Lattice An accelerator is composed of bending magnets, focusing magnets and non-linear magnets (later) The ensemble of magnets in the accelerator constitutes the “accelerator lattice”

30. Example: lattice components

31. Conclusion: transverse dynamics We have now studied the transverse optics of a circular accelerator and we have had a look at the optics elements, –the dipole for bending –the quadrupole for focusing –the sextupole for chromaticity correction All optic elements (+ more) are needed in a high performance accelerator, like the LHC

32. But particles radiate energy! Synchrotron Radiation from an electron in a magnetic field: Energy loss per turn of a machine with an average bending radius  : Energy loss must be replaced by RF system cost scaling $  E cm 2 ~3400 MeV for LEP200 (18 MW)

33. End of the road? So, because of the low mass of an electron, LEP is the end of the road for circular electron machines! So, because of the low mass of an electron, LEP is the end of the road for circular electron machines! The higher proton mass means that we can build the LHC (what matters is  =E/E 0 ) The higher proton mass means that we can build the LHC (what matters is  =E/E 0 ) So the next generation of electron colliders cannot use a ring…so we need to stretch out that ring into a straight line So the next generation of electron colliders cannot use a ring…so we need to stretch out that ring into a straight line

34. A linear machine e+e+ e-e- ~15-20 km For a E cm = 1 TeV machine: Effective gradient G = 500 GV / 14.5 km = 35 MV/m Note: for LC, $ tot  E

35. The International Linear Collider The International Linear Collider (ILC) is a proposed machine, to complement the LHC The International Linear Collider (ILC) is a proposed machine, to complement the LHC It shall collider electron and positrons together at a centre-of-mass energy of 1 TeV It shall collider electron and positrons together at a centre-of-mass energy of 1 TeV The anticipated cost is a cool $8,000,000,000! The anticipated cost is a cool $8,000,000,000! Currently, a detailed physics case and accelerator design is being formulated, in an attempt to get someone to pay for it! Currently, a detailed physics case and accelerator design is being formulated, in an attempt to get someone to pay for it!

36. The parts of a linear collider

37. The key parameters The linear collider is driven by 2 key parameters The linear collider is driven by 2 key parameters The collision energy The collision energy The luminosity The luminosity The two beams collide head-on, so the collision energy is the sum of the beam energies E=2E beam The two beams collide head-on, so the collision energy is the sum of the beam energies E=2E beam The luminosity tells us the probability of the two beams interacting – essentially the overlap of the two colliding beams The luminosity tells us the probability of the two beams interacting – essentially the overlap of the two colliding beams

38. Event rate vs. Luminosity Rate = L*s Rate = L*s e + e - annihilation cross-section approximately e + e - annihilation cross-section approximately L=10E 34 /cm 2 s = 0.00001/fb/s luminosity results in rate 0.0015/s = 5.4/hr. L=10E 34 /cm 2 s = 0.00001/fb/s luminosity results in rate 0.0015/s = 5.4/hr. Presumably interested in much more rare processes Presumably interested in much more rare processes High luminosity is very important at high energy High luminosity is very important at high energy

39. To increase probability of direct e + e - collisions (luminosity) and birth of new particles, beam sizes at IP must be very small To increase probability of direct e + e - collisions (luminosity) and birth of new particles, beam sizes at IP must be very small How to get Luminosity Beam size: 250 * 3 * 110000 nanometers (x y z) (We shall derive this next lecture)

40. The Livingstone plot

41. The large hadron collider The large hadron collider (LHC) uses the same tunnel as LEP, at Cern in Geneva The large hadron collider (LHC) uses the same tunnel as LEP, at Cern in Geneva The machine is a 14 TeV proton-proton collider, so each stored beam will have an energy of 7 TeV The machine is a 14 TeV proton-proton collider, so each stored beam will have an energy of 7 TeV It is being built now, and shall start operation sometime in 2007no 2009oops 2011 It is being built now, and shall start operation sometime in 2007no 2009oops 2011 There are a number of experiments There are a number of experiments

43. The LHC tunnel

44. LHC layout circumference = 26658.9 m 8 interaction points, 4 of which contains detectors where the beams intersect 8 straight sections, containing the IPs, around 530 m long 8 arcs with a regular lattice structure, containing 23 arc cells Each arc cell has a FODO structure, 106.9 m long FODO = focus-drift-defocus-drift

45. LHC main parameters at collision energy Particle typep, Pb Proton energy E p at collision7000 GeV Peak lumin. (ATLAS, CMS)10 34 cm -2 s -1 Circumference C26 658.9 m Bending radius  2804.0 m RF frequency f RF 400.8 MHz # particles per bunch n p 1.15 x 10 11 # bunches n b 2808 1400 in 2011-2 4000 in 2012

46. Colliding Proton/Antiproton Beams No problem with synchrotron radiation energy loss, but… Like throwing bags of marbles at each other at high velocity: Marble-marble collisions are interesting, not bag-bag collisions Fortunately, the number and arrangements of the “marbles” has been measured by other experiments

47. Timeline of Proton Colliders 1975198019851990199520002005201020152020 W/Z bosons Top quark Higgs, Supersymmetry etc Proton- proton Proton-antiproton Proton-proton

48. Proton-Antiproton Collisions at Fermilab (Chicago) The Tevatron accelerator, 6 km circumference The Tevatron accelerator, 6 km circumference The CDF (Collider Detector at Fermilab) experiment

49. 49 LHC Dipole Design

50. 50 LHC Dipole Magnet (3D)

51. 51 References Bibliography: K. Wille, The Physics of Particle Accelerators, 2000...and the classic: E. D. Courant and H. S. Snyder, "Theory of the Alternating- Gradient Synchrotron", 1957 CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992 LHC Design Report [online] 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. Amaldi, presentation on Hadron therapy at CERN 2006