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An Introduction to Particle Accelerators Erik Adli,, University of Oslo/CERN November, 2007 [email protected] v1.32 References • Bibliograp hy: – 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! Part 1 Introduction Particle accelerators for HEP •LHC:theworld: the world biggest accelerator, both in energy and size ((gas big as LEP) •Under construction at CERN today •End of magnet installation in 2007 •First collisions expected summer 2008 Particle accelerators for HEP The next big thing. After LHC, a Linear Collider of over 30 km lengg,th, will probably be needed (why?) Others accelerators • Histor ica lly: t he ma in dr iv ing force o f acce lerator deve lopment 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: Medical applications • Therapy – The last decades: electron accelerators (converted to X-ray via a target) are used very successfully for cancer therapy) – Todayyp's research: proton accelerators instead (hadron therapy): energy deposition can be controlled better, but huge technical challenges • Imaging – Isotope production for PET scanners Advantages of proton / ion-therapy (() Slide borrowed from U. Am aldi ) Proton therapy accelerator centre HIBAC in Chiba What is all this? Follow the ( Slide borrowed from U. Am aldi ) lectures... :) Synchrotron Light Sources • the las t two deca des, enormous increase in the use o f sync hrony ra dia tion, 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 Outline of presentation Part 1: Intro + Main parameters + Basic Concepts Part 2: Longgyitudinal 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 Main Parameters Main parameters: particle type • Hadron collisions: compoundild particles – Mix of quarks, anti-quarks and gluons: variety of processes – Parton energy sp read – Hadron collisions ⇒ large discovery range • Lepton collisions: elementary particles – Collision process known – Well defined energy – Lepton co llisi ons ⇒ preciiision measurement “If you know what to look for, collide leptons, if not collide hadrons” Main parameters: particle type Discovery Precision SS/LHCSppS / LHC LEP / LC Main parameters: particle energy • NhibfdtlNew physics can be found at larger unpro bdibed energies • Energy for p article creation: centre-of-mass energy, ECM • Assume particles in beams with parameters m, E, E >> mc2 = – Particle beam on fixed target: ECM mE = – Colliding particle beams: ECM 2E • ⇒ Colliding beams much more efficient Main parameters: luminosity • Hig h energy is no t enoug h ! • Cross-sections for interestinggp processes are ver y small (~ pb = 10−36 cm² ) ! σ 2 2, 2 – (gg → H) = 23 pb [ at s pp = (14 TeV) mH = 150 GeV/c ] R = Lσ – 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) σ σ – bunch transverse size at the interaction point ( x, y ) – bunch collision rate ( f) n n L = f 1 2 πσ σ 4 x y Main parameters: LEP and LHC LEP LHC Particle type(s) e+ and e- p, ions (Pb, Au) (~ Collision energy (Ecm) 209 GeV (max) p: 14 TeV at p 2-3 TeV mass reach, depending on physics) Pb: 1150 TeV Luminosity (L) Peak: 1032 cm-2s-1 Peak: 1034 cm-2s-1 Daily avg last years: (IP1 / IP5) 1031 cm-2s-1 Integrated: ~ 1000 pb-1 (per experiment) Capabilities of particle accelerators • A mo dern HEPtilHEP particle acce ltlerator can acce ltlerate par tilkticles, keep ithing them within millimeters of a defined reference trajectory, and transport them over a distance of several times the size of the solar system HOW? HOW? • In this presen ta tion we try t o expl a in this by s tu dy ing: – 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 Part 2 Basic concepts An accelerator • Structures in which the particles will move • Structures to accelerate the particles • Structures to steer the particles • Structures to measure the particles Lorentz equation • The two ma in tas ks of an accel era tor – Increase the particle energy – Change the particle direction (follow a given trajectory, focusing) • Lorentz equation: r r r r r r r r r F = q(E + v × B) = qE + qv × B = FE + FB ⊥ • FB v ⇒ FB does no wor k on the par tic le – 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 Acceleration techniques: DC field • The s imp les t acce lera tion me tho d: DC vo ltage • Energy kick: ΔE=qV • Can accelerate particles over many gaps: electrostatic accelerator • Problem: breakdown voltage at ~10MV • DC field still used at start of injector chain Acceleration techniques: RF field • Osc illa ting RF (ra dio-f)fildfrequency) field • “Widerøe accelerator”, after the pioneering work of the Norwegian Rolf Widerøe (b roth er of th e avi ator Vi ggo Widerøe ) • Particle must sees the field onlyyg when the field is in the accelerating direction – Requires the synchronism condition to hold: Tparticle =½TRF L = (1/ 2)vT • Problem: high power loss due to radiation Principle of phase focusing ...what happens to particles with energies slightly off the nominal values...? 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 Klys trons • RF power oscillating (from magnetic to electric energy), at the didfdesired frequency • RF cavities requires bunched beams (as opposed to coasting beams ) – particles located in bunches separated in space Acceleration techniques: Pill-Box cavity • Ideal cyli nd ri cal cav ity: • 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 – λ010 = 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“ eEˆ cos(ωt)dz ΔE ∫ z eVˆT sin(θ / 2) ωl T = var = = = , θ = Δ ˆ θ Econst eEˆ dz eV / 2 v ∫ z – Example: l = λ / 2 gives θ=π and T=0.64 From pill -box to real cavities (from A. Chao) LHC cavity module ILC cavity Why circular accelerators? • Technological limit on the electrical field in an RF cavity (breakdown) • Gives a limited ΔE 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) The synchrotron • Acce lera tion i s perf ormed b y RF cav ities • (Piecewise) circular motion is ensured by a guide field FB •FB : Bending magnets with a homogenous field 2 v 1 qB 1 − B[T ] • In the arc section: F = m ⇒ = ⇔ [m 1] ≈ 0.3 B ρ ρ p ρ p[GeV / c] •RF freqqyuency must stay locked to the revolution fre qypquency of a particle (later slide) • Almost all ppypresent day particle accelerators are s ynchrotrons Digression: other accelerator types • CltCyclotron: – 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 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 ? Part 3 LidildiLongitudinal dynamics and acceleration LitdilDidLongitudinal Dynamics: degrees o ffdtf freedom tangen tiltthftial to the reference tjttrajectory us: tangential to the reference trajectory RF acceleration = ˆ ω • We assume a cavity with an oscillating RF-field: Ez Ez sin( RF t) • 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: W = Fdz = q E dz = q Eˆ sin(ω t)dz = qVˆ sin(ω t) ∫ ∫ z ∫ z RF RF Synchrotron with one cavity • The energy kick of a particle, ΔE, depends on the RF phase seen, φ Δ = = ˆ ω = ˆ φ E W qV sin( RF t) qV sin • We define a “synchronous particle”, s, which always sees the same phase φ s passihing the cav ity ω ω ⇒ RF =h rs ( h: “harmonic number” ) • E.g.
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