1 / 85

860 likes | 902 Views

An Introduction to Particle Accelerators. Erik Adli , University of Oslo/CERN November, 2007 Erik.Adli@cern.ch. v1.32. References. Bibliography: CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992 LHC Design Report [online]

Download Presentation
## An Introduction to Particle Accelerators

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**An Introduction to Particle Accelerators**Erik Adli, University of Oslo/CERN November, 2007 Erik.Adli@cern.ch v1.32**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!**Part 1**Introduction**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**Particle accelerators for HEP**The next big thing. After LHC, a Linear Collider of over 30 km length, will probably be needed (why?)**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:**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**Advantages of proton / ion-therapy**( Slide borrowed from U. Am aldi )**Proton therapy accelerator centre**HIBAC in Chiba What is all this? Follow the lectures... :) ( Slide borrowed from U. Am aldi )**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**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**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”**Main parameters: particle type**Discovery Precision SppS / LHC LEP / LC**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**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)**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?**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**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 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 3108 V/m (NOT feasible) • FB is by far the most effective in order to change the particle direction**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**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**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 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**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**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 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)**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**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**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**Longitudinal dynamicsand acceleration Longitudinal Dynamics: degrees of freedom tangential to the reference trajectory us: tangential to the reference trajectory**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:**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**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!**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”**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**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 )**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**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"**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]**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**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**Part 4**Transverse dynamics Transverse dynamics: degrees of freedom orthogonal to the reference trajectory ux: the horizontal plane uy: the vertical plane**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)**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**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

More Related