Introduction to Accelerator Physics. DESY Summer Student Lecture 2008 Winni Decking DESY –MPY- Accelerator: A Definition Device that provides accelerated particles with defined and controllable properties: – Particle Species (electron, proton, ion) –Energy – Direction – Time structure – Intensity –Density Accelerators are tailored to applications needs Employ cutting edge and special developed technology to advance parameter space in any of the above areas Accelerator Physics Winni Decking Accelerator Applications • Direct particle beams on specific targets or collide beams with each other • Produce thin beams for synchrotron light • HEP: structure of atom, standard model, … • Bombard targets to obtain new materials with different properties • Synchrotron radiation: spectroscopy, X-rat diffraction, X-ray microscopy, crystallography (of proteins), … • Medicine: use for Positron Emission Tomography (PET, cancer therapy, surgery • Nuclear waste transmutation (conversion of long lived into short lived nuclides) Accelerator Physics Winni Decking Accelerators Worldwide CATEGORY NUMBER Ion implanters 7000 Industry 1500 Radiotherapy 7500 Medical isotopes 200 Hadron therapy 20 non-nuclear research 1000 SR sources 70 Nuclear & Particle physics res. 120 TOTAL 17390 courtesy W. Mondelaers, JUAS 2004 Accelerator Physics Winni Decking Accelerator Physics – What’s needed • Basic knowledge – relativistic particle dynamics – classical theory of electromagnetism (Maxwell’s equations) • Advanced Studies – Hamiltonian mechanics, optical concepts – Quantum scattering, radiation of charged particles – Statistical mechanics – Surface physics – Computing, …. Accelerator Physics Winni Decking What we will do • Historical introduction • Review of relativity • Acceleration concepts • Ring concepts • Optical Functions • Luminosity • Synchrotron Radiation • PETRA III as an example • Questions and discussions Accelerator Physics Winni Decking Rutherford Scattering 1906 – 1913 using α particles from a radioactive N(θ) source to bombard a thin gold foil: Thomson-Model Discovery of massive, non point-like structure of the of Atom nucleus Measurement and Rutherford-Model 1927 E. Rutherford says, addressing the Royal Prediction Society : “... if it were possible in the laboratory to have a supply of electrons and atoms of matter in θ general, of which the individual energy of motion is greater even than that of the alfa particle, .... this would open up an extraordinary new field of investigation....” But bright sources with such energies were not yet available: man-made devices, mainly built to produce X-rays, operated at the time in the hundred KV range. Villard X-ray Tube 1898-1905 Accelerator Physics Winni Decking Basic Principles: Relativity Relativistic Energy 2 2 E = mc = m0γc Relativistic Momentum p = mv = m0γβc v v2 β = γ = 1 1- = 1 1− β 2 c c2 Relationship between Momentum E 2 = p2c2 + m2c4 and Energy 0 2 2 Kinetic Energy T = E − m0c = m0c (γ −1) Accelerator Physics Winni Decking Basic Principles: Relativity c = 2.9979×108 m Speed of Light s m = 511 keV Electron Rest Mass 0,electron c2 Proton Rest Mass m = 938.3 MeV 0, proton c2 Electron Charge e = 1.6021×10−19 Coulomb −19 Electron Volts 1eV = 1.6021×10 Joule 2 2 mc m0c Energy in eV E[]eV = = γ e e Energy and rest mass 1eV c2 = 1.78×10−36 kg Accelerator Physics Winni Decking Motion in Electric and Magnetic Fields Equation of motion under Lorentz Force r dpr r r F = = q(E + v× B) dt 2 r 2 2 2 4 E = p c + m0 c r dE 2 r dp 2 r r r r 2 r r ⇒ E = c p = qc p()E + v × B = qc pE dt dt Magnetic Fields do not change the particles energy, only electric fields do! Technical challenge: provide large enough electric fields Accelerator Physics Winni Decking Electrostatic Accelerators Cockroft & Walton: r r U F = qE = q d b b r U ΔE = Fdrr = q drr =qU ∫ ∫ d a a useful unit charge×voltage = eV 1932: First particle beam (protons) produced Today: Proton Pre- for nuclear reactions: splitting of Li- accelerator at nuclei with a proton beam of 400 keV PSI (Villingen) Accelerator Physics Winni Decking Electrostatic Accelerators Van de Graaff: • Mechanical transport of charges creates high voltages • Maximum potential around 20 MV (needs already SF6 gas surrounding to prevent discharges) Today: 12 MV-Tandem van de Graaff Accelerator at MPI Heidelberg Accelerator Physics Winni Decking Linear Accelerators (Basic Principle) Wideroe (1928): apply acceleration voltage several times to particle beam + -̶ ++-̶ -̶ + • acceleration of the particle in the gap between the tubes • voltage has to be „flipped“ to get the right sign in the next gap Æ RF voltage Æ shield the particle in drift tubes during the negative half wave of the RF voltage Æ vary the tube length with increasing energy/velocity Accelerator Physics Winni Decking Acceleration in the Wideroe Structure Energy gained after n acceleration gaps n number of gaps between the drift tubes EnqUns= **0 *sinψ q charge of the particle U0 Peak voltage of the RF System ΨS synchronous phase of the particle Kinetic energy of the particles 1 Emv= * 2 nn2 valid for non relativistic particles ... => velocity of the particle 22****sinEnqUψ v ==nS0 n mm shielding of the particles during the negative half wave of the RF U 0 Length of the n-th drift tube: τ RF 1 t lvnn==** v n 22ν RF Accelerator Physics Winni Decking Examples DESY proton linac (LINAC III) Etotal =988MeV 2 EEkin=− total mc0 EMeVkin = 50 22224 E =+cp m0 c p = 310MeV / c GSI Unilac E ≈ 20 MeV per Nukleon β≈0.04 … 0.6 Protons/Ions ν = 110 MHz Accelerator Physics Winni Decking What is relativistic? Electrons: β > 0.99 at 3.7 MeV Protons: β > 0.99 at 6.7 GeV Accelerator Physics Winni Decking Acceleration in RF fields Traveling wave structure: • Particles in phase with waveform • Reduce phase velocity in waveguide with irises Example: SLAC 2 mile LINAC E up to 50 GeV in operation since mid 60’s Electrons/Positrons ν = 2.8 GHz, 35 MV/m Accelerator Physics Winni Decking Klystron • Energy/velocity modulated electron beam in first resonator • After drift density modulation • Electric field extracted in second resonator courtesy E. Jensen, RF for LINACS, CAS 2005 Accelerator Physics Winni Decking Motion in a constant B-field (E=0) • Energy stays constant • Spiraling trajectory along the uniform magnetic field Lorentz Force →→→ F = qvB*(× ) Zentrifugal Force mv* 2 F = ρ mv* 2 qvB**=→= B *ρ pq / ρ Accelerator Physics Winni Decking Cyclotron Uses magnetic field to force particles to pass through accelerating fields at regular intervals Cyclotron: • Constant B-field • Time for one revolution ρ m T ==22ππ vqB* z • Constant revolution frequency = constant accelerating frequency 1 q ==2*π B z →=ω const . ω z Tm z • Works only if m=const => non-relativistic particles • Large momentum => large magnets p B* ρ = E. Lawrence and his first q cyclotron Accelerator Physics Winni Decking Synchrotron • Varying B-field B* ρ = p • Constant ρ q • Increase B-field synchronous to momentum p Where is the acceleration? • RF field in accelerating cavity with the right (synchronous) phase Δp = eU sin(φ ) q 0 Increase B → decreases ρ → particle comes early → gains more energy Accelerator Physics Winni Decking Synchrotron Synchronous accelerator where there is a synchronous RF phase for which the energy gain fits the increase of B-field at each turn. revolution time revolution frequency RF frequency h = harmonic number =number of possible bunches Magnetic rigidity Accelerator Physics Winni Decking Magnetic Dipole Fields Technical design of a dipole magnet: a magnet with two flat, parallel pole shoes creates a homogeneous dipole field r rrr δ D Maxwells equations: ∇×Hj = + δt r r r ∇ × H nr da = Hdsr = h* H + l *H = nI ∫ ( ) ∫ 0 Fe Fe A n*I = number of coil windings, BB HH==00, each carrying the current I 0 Fe μr = rel. permeability of the material, μ00μμ* Fe μr (Fe) ≈ 3000 the magnetic field B depends on μ *nI *the current B = 0 0 h * the number of windings * the gap height Accelerator Physics Winni Decking Dipole Fields and Max. Energies For high energy machines (γ >> 1) 2 2 2 2 4 E = p c + m0 c ⇒ E ≈ pc B* ρ = p ⇒ B* ρ = E ⇒ E ≈ 0.3× B[T]× ρ[m] q ce Technology Size (= money) normal conducting: Bmax ≈ 2 T super conducting : Bmax ≈ 7 T Accelerator Physics Winni Decking Example: HERA p 920 GeV Proton storage ring dipole magnets N = 416, l = 8.8m, ρ=580 m, B = 5.5 T total length 6.3 km (3.6 km dipoles) 1990 till 2007 Accelerator Physics Winni Decking Example LHC 7 TeV Proton storage ring dipole magnets ρ=2810 m, B = 8.3 T total length 27 km (17.6 km dipoles) turns on know !!!!!!!!! Accelerator Physics Winni Decking HEP: The energy frontier ILC RA E H CESR, DORIS II SPEAR, DORIS (charm quark, τ lepton) Accelerator Physics Winni Decking Luminosity RL= *Σ production rate of (scattering) events is determined react. by the cross section Σreact and a parameter L that is given by the design of the accelerator: … the luminosity p-Bunch 7*10^10 particles e-Bunch IP 2 σ 3*10^10 particles 1 Iep I L*= 2 ∗ ∗ 4efπ 0 n b σ x σ y Accelerator Physics Winni Decking Focusing Magnet imperfections, misalignments, gravitation, earth magnetic field, …. Particles will not stay on a stable circular orbit (or follow a long straight pass) => need a magnet with increasing B-field away from the centre axis four iron pole shoes of hyperbolic contour By = −g * x, Bx = g * y Fx = −g * x, Fy = g * y focusing in one plane, defocusing in the other 2μ nI g = 0 R 2 Accelerator Physics Winni Decking Focusing Net focusing effect Put many quadrupoles in a row – motion is confined ‘FODO’ structure Accelerator Physics Winni Decking Focusing forces and particle trajectories normalise magnet fields to momentum (remember: B*ρ = p / q ) Dipole Magnet Quadrupole Magnet BB1 g == k := pq/ Bρ ρ pq/ Example: HERA Ring Momentum: p = 920 GeV/c Bending field: B = 5.5 Tesla Quadrupol Gradient G= 110 T/m Æ k = 33.64*10-3 /m2 Æ 1/ρ = 1.7 *10-3 /m Accelerator Physics Winni Decking Equation of Motion Under the influence of the focusing and defocusing forces the differential equation of the particles trajectory can be developed: x = distance of a single particle to the center of the beam xkx''+= * 0 horizontal plane dx x′ := ds if we assume ...