Theory of accelerators

1. by Ted Wilson Theory of accelerators I. Electrostatic Machines II. Cyclotrons III. Linacs IV. Synchrotrons V. Colliders VII. Synchrotron Radiation Sources VIII. Other Applications

2. → → → → Centripetal Force Lorentz force Fixes the relation between magnetic field and particle’s energy ρ Magnetic rigidity LHC: ρ = 2.8 km given by LEP tunnel! Basic concepts Charged particles are accelerated, guided and confined by electromagnetic fields. - Bending: Dipole magnets - Focusing: Quadrupole magnets - Acceleration: RF cavities In synchrotrons, they are ramped together synchronously to match beam energy. - Chromatic aberration: Sextupole magnets

3. Newton & Einstein

4. Some relativity

5. LHC injector complex 450 GeV 1.4 GeV 26 GeV

6. The Large Hadron Collider (LHC)

7. Superconducting magnets

8. B field I I I F force p B B p F Bending Two-in-one magnet design LHC: B = 8.33 T ⇒ E = 7 TeV

9. N S Fy By Fx S N Focusing Transverse focusing is achieved with quadrupolemagnets, which act on the beam like an optical lens. Linear increase of the magnetic field along the axes (no effect on particles on axis). Focusing in one plane, de-focusing in the other! x y

10. s y x Alternating gradient lattice An illustrative scheme (LHC: 2x3 dipoles per cell) One can find an arrangement of quadrupole magnets that provides net focusing in both planes (“strong focusing”). Dipole magnets keep the particles on the circular orbit. Quadrupole magnets focus alternatively in both planes. Coordinate system

11. Alternating gradients

12. Hill’s equation K(s) describes the distribution of focusing strength along the lattice. G. Hill, 1838-1914 Transverse equation of motion Magnetic field [T] : Field gradient [T m-1] : Normalized grad. [m-2] : and its solution

13. LHC layout and accelerator systems Eight arcs and eight straight sessions: Point 1: Atlas, LHCf Point 2: Alice, injection Point 3: Momentum cleaning Point 4: RF Point 5: CMS, TOTEM Point 6: Beam Dumps Point 7: Betatron cleaning Point 8: LHCb, injection

14. LHC design parameters - These are the key parameters of a collider – the LHC - Why are they important for physics? - What is the basic theory which limits each one of them?

15. Imagine a blue particle colliding with a beam of cross section area - A Probability of collision for an interaction is For N particles in both beams Suppose they meet f times per second at the revolution frequency Event rate Luminosity (single bunches) Make big Make small • LUMINOSITY

16. s Acceleration Acceleration is performed with electric fields fed into Radio-Frequency (RF) cavities. RF cavities are basically resonators tuned to a selected frequency. In circular accelerators, the acceleration is done with small steps at each turn. LHC: 8 RF cavities per beam (400 MHz), located in point 4 At the LHC, the acceleration from 450 GeV to 7 TeV lasts ~ 20 minutes (nominal!), with an average energy gain of ~ 0.5 MeV on each turn. [Today, we ramp at a factor 4 less energy gain per turn than nominal!]

17. ΔE LHC bunch spacing = 25 ns = 10 buckets ⇔ 7.5 m RF bucket time 2.5 ns 450 GeV 7 TeV RMS bunch length 11.2 cm 7.6 cm RMS energy spread 0.031% 0.011% Buckets and bunches The particles oscillate back and forth in time/energy The particles are trapped in the RF voltage: this gives the bunch structure RF Voltage 2.5 ns time

18. Synchroton Radiation • Electrons accelerating by running up and down in a radio antenna emit radio waves • Radio waves are nothing more than Long Wavelength Light-

19. Synchroton Light Sources When the electron speed gets close to the speed of light, e radiation comes out only in a narrow forward cone; a laser-like concentrated stream

20. This 300 MeV electron synchroton at the General Electric Co. at Schenectady, built in the late 1940s. The photograph shows a beam of synchrotron radiation emerging.

21. Spring 8, a synchrotron light source located in Japan. Synchrotron Light Sources This intricate structure of a complex protein molecule structure has been determined by reconstructing scattered synchrotron radiation

22. Engines of Discovery Linac Coherent Light Source and the European Union X-Ray Free Electron Laser(Fourth Generation) FELs, invented in the late 1970’s at Stanford are now becoming the basis of major facilities in the USA (SLAC) and Europe (DESY) .They promise intense coherent radiation. The present projects expect to reach radiation of 1 Angstrom (0.1 nano-meters, 10kilo-volt radiation) ↓

23. Basis of muon collider

24. Spallation Neutron Sources (SNS) 1GeV protons mean current 1 mA = 1.4 MW of power In a 0.7 microsecuond burst Cost is about 1.5 B$ An overview of the Spallation Neutron Source (SNS) site at Oak Ridge National Laboratory.

25. Unstable Isotopes and their Ions The Rare Isotope Accelerator (RIA) scheme. The heart of the facility is composed of a driver accelerator capable of accelerating every element of the periodic table up to at least 400 MeV/nucleon. Rare isotopes will be produced in a number of dedicated production targets and will be used at rest for experiments, or they can be accelerated to energies below or near the Coulomb barrier.

26. Energy amplifier

27. Proton Drivers for Power Reactors A linac scheme for driving a reactor. These devices can turn thorium into a reactor fuel, power a reactor safely, and burn up long-lived fission products.

28. I have not mentioned Sterilisation Chip manufacture Art and archaeology National Security Surface treatment Etc. etc….

29. Author’s e-mail: ted.wilson@cern.ch “Engines of Discovery”: http://www.worldscientific.com/worldscibooks/10.1142/8552 “Particle Accelerators” http://www.oup.com/uk/catalogue/?ci=9780198508298 Links