Particle Accelerators

Transcription

1 Experimental Methods of Particle Physics Particle Accelerators Andreas Streun, PSI Andreas Streun, PSI 1

2 Particle Accelerators 1. Introduction 2. Accelerator basics and types 3. Single particle dynamics 4. Multi-particle dynamics 5. Longitudinal beam dynamics 6. Synchrotron radiation 7. Luminosity 8. Muons and neutrinos Andreas Streun, PSI 2

3 1. Introduction u Books & webs u Why accelerators? u Particles Particles of interest Particle wavelength and momentum Particles to accelerate Particle production u A beam of particles Beam quality Accelerator peformance u Particle Physics experiments Center-of-mass energy Luminosity Andreas Streun, PSI 3

4 Books & Webs & Lectures u K. Wille, Physik der Teilchenbeschleuniger und Synchrotronstrahlungsquellen, Teubner Studienbücher, Stuttgart u K. Wille, The physics of particle accelerators, Oxford university press, u S. Y. Lee, Accelerator Physics, World Scientific, Singapore 1999 u H. Wiedemann, Particle Accelerator Physics I+II, Springer, Berlin Heidelberg New York u Proceedings of The CERN Accelerator School u A. W. Chao and M.Tigner, Handbook of Accelerator Physics and Engineering, World Scientific, Singapore u Proceedings of the Accelerator Conferences u ETH 2-semester lecture on accelerators and modeling Andreas Streun, PSI 4

5 Why accelerators? I. Applications length scale m = 1 Å / atomic m / nuclear m / electroweak Materials Research (MR) Physics Chemistry Biology Pharmacy Nuclear Physics (NP) Particle Accelerators Particle Physics (PP) Energy frontier Particle factories Exotic particles Medical applications Industrial applications Andreas Streun, PSI 5

6 Why accelerators? II. Connections Engineering Radio-frequency Magnet technology Ultra high vacuum Classical Physics Mechanical engineering Alignment & Survey Electronics Control systems Particle Accelerators Computing Hamiltonian Mechanics Electrodynamics High performance computing Accelerator design codes Digital signal processing s/w Application programming Modern Physics Quantum mechanics Particle Physics Andreas Streun, PSI 6

7 Why accelerators? III. common PP & MR interests Particle Physics (PP) Materials Research (MR) High energy colliders Particle factories Neutrino factories Spallation neutron sources Photon sources Linear colliders Circular colliders High power proton accelerators Storage rings Free electron lasers (FEL) A c c e l e r a t o r s Linear accelerators Cyclotrons Synchrotrons PP & MR scientists: ð understand potential and limitations of accelerators ð help to specify future machines Andreas Streun, PSI 7

8 Particles of interest (PP) Particle Physics: interested in all particles! presently: particular interest in u new and unknown particles: W ± (80.4 GeV), Z (91.2 GeV), H o (126 GeV),...? produced in e + e - or pp or pp collision ð highest energies: e.g. LEP, LHC u meson pairs (e.g. K S K L, B o B o ) at high rate ð meson factories: e.g. KEK-B, DAFNE. u muons (m ± ) and neutrinos (n e,n m ) ð long baseline experiments: e.g. CNGS, JPARC ð muon accelerator and neutrino factory projects Andreas Streun, PSI 8

9 Particles of interest (MR) Materials Research: neutral particles ð high penetration depth in materials u Neutrons (n) penetrate high Z materials depth not a steep function of Z have a magnetic moment and a spin explore structure and dynamics of materials rather low flux (= particles per time and area) u Photons (g) available at (very!) high flux penetrate well low Z materials have polarization complementary to neutrons ( surface vs. bulk ) Andreas Streun, PSI 9

10 Particle wavelength Size of structure ó Size of probe MR ð l ~ m NP ð l ~ m PP ð l ~ m De-Broglie wavelength Planck constant h = Js = ev s Particle momentum p = m v = m o c bg l = h p non relativistic p = m o v high relativistic p= m o c g = E / c Andreas Streun, PSI 10

11 Momentum p = m v = m o c bg non-relativistic high relativistic Total energy 2 2 E = mc = m c g = Kinetic energy p = m o v p = m o c g = E/c E kin = m o c 2 (g-1) = q U = charge voltage. E kin in units of ev is equivalent to the accelerating voltage for a particle with charge q = 1e (p, e +, Na +, m +...) non-relativistic E kin = ½ m o v 2 high relativistic Recall: momentum & energy o ( moc ) + ( pc) = Ekin + moc E kin = pc norm. velocity b = v / c Lorentz factor g = E / m o c 2 rest energy E o = m o c 2 useful relations: b = 1- g = bg = g g 2 1- b 2-1 Andreas Streun, PSI 11

12 Examples: momentum and wavelength MR: 1Å neutron (m o c 2 = MeV, m o = kg) ð p = 12.4 kev/c ð v = 3960 m/s << c ð E kin = 0.08 ev ð <E kin > = kt Ê ð temperature equivalent T = 930 K MR: 1Å photon (no rest mass) ð v = c, E g = pc = 12.4 kev X-ray NP: m electron (m o c 2 = 511 kev) ð p = 1.24 GeV/c ð v = c = c 90 km/h! ð E kin = pc = 1.24 GeV PP: m proton (m o c 2 = MeV) ð p = 1.24 TeV/c ð v = c ð E kin = pc = 1.24 TeV ( LHC 7 TeV) Andreas Streun, PSI 12

13 Particles to accelerate Requirements for acceleration: charge q ¹ 0 and lifetime t ³»1 ms üstandard: electron e - and proton p üantiparticles: positron e + and antiproton p üions: ümuons: m +, m - t = 2.2 ms û pion p ± (t = 26 ns), neutron n, neutrino n, photon g... Andreas Streun, PSI 13

14 Particle Production how to get the particles of interest from the particles that can be accelerated how many? Principle Products Performance Beam on target electrons e - protons p spallation target Colliding beams leptonic e + e - hadronic pp Synchrotron radiation electrons e - pairs e + e -, pp mesons p m n neutrons n anything... mesons KK, BB... Higgs H o photons g Flux ò chapter 8 Luminosity ò chapter 7 Brightness ò chapter 6 Andreas Streun, PSI 14

15 A beam of particles Particle beam (n, m, g, e -, p...) = ensemble of N particles in 6-dimensional phase space ( x, y, z; p x, p y, p z ) 1 st order Beam centroid mean values < r i > beam momenta p x, p y, p z moving along z p z» p >> p x, p y beam location z (t) beam positions x, y beam angles x» p x /p, y 2 nd order Beam distribution rms values s i 2 = < r i 2 > and correlations < r i r j > momentum spread s Dp/p bunch length s Dz beam sizes s x, s y beam divergences s x, s y... correlations... Andreas Streun, PSI 15

16 Beam quality I. phase space density Criterion for beam quality (n, m, g, e -, p...) : density in 6-d phase space ð performance of experiment flux, luminosity, brightness, ð threshold phenomena coherence, non-linearity... Theorem of Liouville: (holds under several conditions...) The 6-d phase space density is an invariant. or The 6-d phase space occupied by a beam behaves like an incompressible liquid. Andreas Streun, PSI 16

17 Beam quality II. Emittance Decoupling of 6-d phase space density into 3 2 dimensions (this is often» possible): longitudinal horizontal vertical Dp/p, Dz x, p x (or x ) y, p y (or y ) momentum transverse emittances e x, e y spread 2-d phase space area: pulse (bunch*) e 2 x = < x 2 >< x 2 > - < xx > 2 length invariant along beam transport line ð chapter 4 * beams are usually bunched, not continuous ð chapter 2 Andreas Streun, PSI 17

18 Beam quality III. Accelerator performance u Momentum ( high relativistic: energy E = pc ) u Momentum spread u Bunch length u Emittances u Beam current p s Dp/p s Dz e x, e y I = q dn/dt u Higher orders... ( non-gaussian, halo, tails etc. ) u Polarization (spin orientation) è u Time structure: [continuous or] bunched repetition rate u Stability: position, angle, momentum, timing... jitter as function of frequency 6-d phase space density ò Experiment performance: Luminosity (PP) Brightness (MR) Andreas Streun, PSI 18

19 p 2 = 0 E 1 = E E = (E 1 +E 2 ) 2 ( p 1 c+ p 2 c) 2 p 2 = p 1 E 1 = E 2 = E E 2Em 2 c 2 β = p 1c+ p 2 c E 1 +E 2 γ = E 1+E 2 E E = 2E e + p π,... µ [ ν µ ] n e + e E = 14 Φ,B... β E 1 E 2

20 E β E 1, E 2 p N 1 p (p = N 2 N N ) N ǫ T = R 1 = N ǫt σ 2 = = R = σl L 2 1

21 = L = N 1 T N 2 A A L = N 1,N 2,T A E 1 E 2 E β =

22 e + e