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    August 2018
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Elementary Particles Instrumentation Accelerators Dec 15, 2014 1 First accelerator: cathode ray tube 2 Efield = V / D heated filament With electron charge q: F = q . Efield distance D Potential diffence V electron kinetic energy: Ee- =  F dD = q.V Ee- independent of: - distance D - particle mass 3 ElectronVolt: eV Energy unit: ElectronVolt: eV 1000 eV = 1 keV = 103 eV 1 MeV = 106 eV 1 GeV = 109 eV 1 TeV = 1012 eV 1 eV = |q| Joules = 1.6 x 10-19 Joules 4 Wimshurst’s electricity generator, Leidsche Flesschen 5 Van de Graaff accelerator Corona discharge deposits charge on belt Left: Robert van de Graaff Vertical construction is easier as support of belt is easier From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p. 222. 6 Faraday Cage! HV = 10 kV gnd belt 7 Beam pipe From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p. 223. 8 Hoogspanning (hoge potentiaal) met: Rumkorffse Klos transformator bobine vonkenzender Marconi bobine: ontsteking voor explosie motoren 9 Practical limit to transformers Cockcroft-Walton high-voltage generator Sir John Douglas Cockroft Ernest Walton Nobel Prize 1951 From: Principles of Charged Particle Acceleration Stanley Humphries, Jr., on-line edition, p. 210 10 Cockroft Walton generator at Fermilab, Chicago, USA High voltage = 750 kV Structure in the foreground: ion (H-) source 11 Motion of charged particle in magnetic field Lorentz force: dp  q v B dt The speed of a charged particle, and therefore its g, does not change by a static magnetic field 12 Motion of charged particle in magnetic field If magnetic field direction perpendicular to the velocity: g mv 2   q v  B which can be written as : p =  q B → p = 0.2998 B  radius of curvature (p in GeV/c, B in T,  in m, for 1 elementary charge unit = 1.602177x10-19 C, and obtained using 1 eV/c2 = 1.782663x10-36 kg and c = 299792458 m/s ) D Sh ρ 13 Force on charged particle due to electric and magnetic fields: dp = q(E + v ´ B) dt perpendicular to motion: deflection In direction of motion -> acceleration or deceleration -> For acceleration an electric field needs to be produced: • static: need a high voltage: e.g. Cockroft Walton generator, van de Graaff accelerator • with a changing magnetic field: e.g. betatron • with a high-frequent voltage which creates an accelerating field across one or more regions at times that particles pass these regions: e.g. cyclotron • with high-frequency electro-magnetic waves in cavities 14 The cyclotron "Dee": conducting, non-magnetic box Top view Constant magnetic field Side view ~ r.f. voltage Ernest O.Lawrence at the controls of the 37" cyclotron in 1938, University of California at Berkeley. 1939 Nobel prize for "the invention and development of the cyclotron, and for the results thereby attained, especially with regard to artificial radioelements." (the 37" cyclotron could accelerate deuterons to 8 MeV) Speed increase smaller if particles become relativistic: special field configuration or synchro-cyclotron (uses particle bunches, frequency reduced at end of acceleration cycle) 15 From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: 16 From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: 17 Superconducting cyclotron (AGOR), KVI, Groningen Protons up to ~ 190 MeV, heavy ions (C, N, Ar, ...) ~ 50-60 MeV per nucleon 18 Eindhoven: new cyclotron for isotope production (2002) IBA Cyclone 30, 18 - 30 MeV protons, 350 mA 19 Linear Drift Tube accelerator, invented by R. Wideröe ~ r.f. voltage: frequency matched to velocity particles, so that these are accelerated for each gap crossed Particles move through hollow metal cylinders in evacuated tube 20 Linear Drift Tube accelerator, Alvarez type Metal tank ~ small antenna injects e.m. energy Particles move through into resonator, e.m. wave in tank hollow metal cylinders in accelerates particles when they cross evacuated tube gaps, particles are screened from e.m. wave when electric field would decelerate Luis Walter Alvarez Nobel prize 1968, but not for his work on accelerators: "for his decisive contributions to elementary particle physics, in particular the discovery of a large number of resonance states, made possible through his development of the technique of using hydrogen bubble chamber and data analysis" 21 Inside the tank of the Fermilab Alvarez type 200 MeV proton linac 22 R.f. cavity with drift tubes as used in the SPS (Super Proton Synchrotron) at CERN NB: traveling e.m. waves are used Frequency = 200.2 MHz Max. 790 kW 8MV accelerating voltage 23 Standing waves in cavity: particles and anti-particles can be accelerated at the same time Superconducting cavity for the LEP-II e+e- collider (2000: last year of operation) t1 "iris" t2 The direction of E is indicated Cavities in cryostat in LEP 24 Non-superconducting cavity as used in LEP-I. The copper sphere was used for low-loss temporary storage of the e.m. power in order to reduce the power load of the cavity 25 Generation of r.f. e.m waves with a klystron * The electron gun 1 produces a flow of electrons. * The bunching cavities 2 regulate the speed of the electrons so that they arrive in bunches at the output cavity. * The bunches of electrons excite microwaves in the output cavity 3 of the klystron. * The microwaves flow into the waveguide 4, which transports them to the accelerator. * The electrons are absorbed in the beam stop 5. from 26 Synchrotron : circular accelerator with r.f. cavities for accelerating the particles and with separate magnets for keeping the particles on track. All large circular accelerators are of this type. Injection During acceleration the magnetic field needs to be "ramped up". Focussing magnet r.f. cavity Vacuum beam line Bending magnet Extracted beam 27 CERN, Geneve 28 29 During acceleration the magnetic field needs to be "ramped up". Slow extraction Fast extraction of part of beam At time of operation of LEP Fast extraction of remainder of beam SPS used as injector for LEP For LHC related studies 30 Collider: two beams are collided to obtain a high Centre of Mass (CM) energy. Colliders are usually synchrotrons (exception: SLAC). In a synchrotron particles and anti-particles can be accelerated and stored in the same machine (e.g. LEP (e+e-), SppS and Tevatron (proton - anti-proton). This is not possible for e.g. a proton-proton collider or an electron-proton collider. Important parameter for colliders : Luminosity L N = L s cross-section number of events /s Unit L: barn-1 s-1 or cm-2 s-1 31 CERN accelerator complex to Gran-Sasso (730 km) 32 Charged particles inside accelerators and in external beamlines need to be steered by magnetic fields. A requirement is that small deviations from the design orbit should not grow without limit. Proper choice of the steering and focusing fields makes this possible. Consider first a charged particle moving in a uniform field and in a plane perpendicular to the field: design orbit displaced orbit In the plane a deviation from the design orbit does not grow beyond a certain limit: it exhibits oscillatory behavior. However, a deviation in the direction perpendicular to the plane grows in proportion to the number of revolutions made and leads to loss of the particle after some time. 33 To prevent instabilities a restoring force in the vertical direction is required. Possible solution : "weak focusing" with a "combined function magnet" pole shoe design orbit plane (seen from the side) pole shoe field component causes downward force field component causes upward force Components of magnetic field parallel to the design orbit plane force particles not moving in the plane back to it, resulting in oscillatory motion1) perpendicular to plane. The field component perpendicular to the plane now depends on the position in the design orbit plane: the period of the oscillatory motion1) in this plane around the design orbit becomes larger than a single revolution. 1) "betatron oscillations" 34 Dipoles and quadrupoles in LEP Quadrupole Dipole 35 Large Hadron Collider LHC: proton-proton collider Interaction point Bunch size squeezed near interaction point • Crossing angle to avoid long range beam beam interaction • R ~4 km, E ~ 7 TeV (2x!)  B ~ 7 T! 36 37 Superconducting magnets: no pole shoes Current distributions 38 39 LHC dipoles 40 pp collisions 2) heavy collisions: A proton is a bag filled with quarks en gluons 41 With van de Graaff accelerator: simple: E = q V, so E = V eV From Einstein’s Special Theory on Relativity: E2 = mo2 c4 + p2c2 With:  = v / c, and the Lorentz factor γ: relativistic mass mr = γ m0 γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ So: total energy E = m0 c2 sqrt(1+ 2 γ2) [= rest mass eq. + kinetic energy] = γ m0 c 2 = mr c 2 42 Remember: TOTAL energy E2 = mo2 c4 + p2c2 Note ‘restmass’ term and ‘kinetic’ term (squared!) relativistic mass mr = γ m0 p = m v = γ m0 v (for high energy particles: p = γ m0 c) γ = 1 / sqrt(1- 2) For high-energy particles (E >> m0c2): E2 = mo2 c4 + p2c2 = E2 = p2c2  E = pc  p = E/c 43 Examples: electron: rust mass m0 = 511 keV With total energy 1 GeV: kinetic energy = 1 GeV Momentum p: 1GeV/c Other example: electron with [kinetic] energy of 1 MeV (~1/2 m0 c2) Total energy ET = 1 MeV + 511 keV = 1511 keV Momentum p follows from ET2 = mo2 c4 + p2c2 Gamma factor γ = ET / moc2 Speed follows from γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ 44