4511_Lec_23Jan08

1
Beam Stability and Focusing

• Particles need gt105 revolutions to reach full
  energy. Excellent beam stability/ focusing
  needed
• Weak focusing discovered in cyclotrons Constant
  field gradient, field decreasing toward outside.
  Beam confined, but with a large envelope

• Strong focusing (Courant, Livingston, Snyder
  52)
• Alternate focusing and defocusing elements for
  net focusing effect

Allows much smaller apertures ? smaller (cheaper)
magnets
2
Quadrupole Fields (focusing elements)
Luckily
FODO cell
Net focusing in both planes!

• Real world accelerator is far from the idealized
  picture
• Orbits are not circles! Chain of arcs of local
  radius of curvature ?(s)
• Complicated oscillations about average orbit

3
y
Synchrotron Beams Transverse Motion

• Beam particles oscillate in x and y about ideal
• Injected beam spread, imperfect components, other
  disturbances
• Oscillation length depends on optics (quadrupole
  focal length)

Beam particles travel in a potential gutter in
x and y
Betatron Oscillations Envelope of motion
determines required magnet aperture

• Detailed parameters of the motion depend on the
  design and operating settings (currents) of the
  magnets ? LATTICE

CERN SPS
400 GeV, with 108 of these FODO cells
4
Synchrotron Beams Longitudinal Motion

• Beam particles oscillate longitudinally about the
  ideal synchronization point (synchrotron
  oscillations)
• Need precise synchronization or a way to
  compensate for particle-to-particle energy
  differences, mistiming accelerating fields,
  magnetic field variations that can lead to beam
  loss
• Answer principle of phase stability
  (Veksler/McMillan 44-45)
• Time ideal particle to ride displaced from the
  crest of the accelerating wave. Real particles
  that are lagging behind get bigger-than-normal
  boost and particles that are ahead get a smaller
  one

5
Synchrotron Components

• Particle source
• H- ions produced from H2 gas
• Electrons by thermionic emission
• Pre-accelerator (C-W, linac perhaps multiple
  stages)
• Injection magnet
• Dipole bending magnets
• Quadrupole focusing magnets
• RF accelerating cavity (required because flux
  linked by orbit is small)
• Driven by klystron generator
• One well-timed kick (few MeV) per orbit
• Kicker magnet for extraction of full-energy
  beam to
• Fixed-target beam lines
• Colliding-beam storage ring

6
Synchrotron Radiation

• Bad news Accelerated charges radiate EM energy
  as synchrotron radiation

S.R. losses are huge for electrons and small for
protons
7
Synchrotron Radiation

• Good news Accelerated electrons radiate EM
  energy as synchrotron radiation
• Damping essential for good performance
• Late 40s, early 50s first detection and power
  measurements of S.R.
• 1968 first storage ring to produce S.R. for
  materials science (TANTALUS in Madison)

1st Generation (70s) mostly parasitic X-ray
production 2nd Generation (80s) many dedicated
X-ray sources 3rd Generation (90s) several
rings with special radiation devices 4th
Generation (now) Free Electron Lasers driven by
Linacs
8
Trade-offs in Synchrotron Design
(? )

• Electrons RF!
• Because of S.R., lots of energy must be provided
  to sustain stored beams
• ee- beams in 27-km (circ.) LEP (now LHC) tunnel
  radiated _at_ 20 MW 4 GeV per turn per electron
• RF and power lots of cavities, superconducting
  cavities
• Ultimate solution back to the future with linear
  collider

• Protons Magnets!
• S.R. not significant, so make ? as small as
  bending magnet technology allows
• 1.4 T with Cu
• Steady development of SC dipole magnets
• SSC design (1990) 20 TeV protons in 87-km
  tunnel 6.8 T
• LHC (2009?) - 14 TeV protons in 27-km tunnel 8.4
  T

LHC Dipole Magnet Assembly
SRF Accelerating Cavities
9
Linacs Synchrotrons
Colliding Beams
vs.

• Advantages of Colliders
• Efficient use of energy

• Disadvantages of Colliders
• Low-density target

1030?1032 ?1034 ???? Fixed target 1038

• Need to store beams for many hours ? very high
  vacuum
• Only stable charged particles

• Control over kinematics, event topology (CM at
  rest or boosted)

• First storage rings 1960, ee- collider AdA in
  Frascati, Italy (250 MeV) in 1961
• Most major discoveries since 1974 from colliders
  c, b, and t quarks, gluons/QCD, Z0, W? bosons,
  etc. Exceptions neutrino mass,
  astrophysics/cosmology

10
Collider Components

• Basic accelerator requirements bending and
  focusing magnets, RF systems, vacuum. Tighter
  tolerances store up to many hours
• Complicated injection system perhaps two kinds
  of particles in same ring store one (positrons
  or pbars) while injecting the other
• Separators need to keep beams from colliding
  outside the detectors.
• Compensation/avoidance for beam-beam interactions
• Final focus make beams as small as possible
  at the interaction point

11
Challenge Mass Production of Antiparticles

• Positrons are easy Linac-accelerated electron
  beam of a few hundred MeV hits a metal target and
  showers Positrons are separated magnetically and
  collected into bunches for injection. High
  efficiency not needed
• Antiprotons are hard!

CESR
Tevatron pbar Target 120 GeV protons hit Ni
target (bunches every 1.5 s). Lots of stuff
separate pbars with pulsed magnet. 1M protons
give 20 pbars!
Debuncher Large energy spread, small time spread
? small energy spread, large time spread with
phase stability effect
Accumulator Stacks pbars over many hours. Uses
RF and stochastic cooling (S. van der Meer -
Nobel 1984)
12
Fermilab Accelerator Complex
13
The CERN Accelerator Complex
14
Medical Applications of Accelerators
1939 Using the 60 cyclotron at the Berkeley
Radiation Lab (now LBNL), Lawrence et al. tested
tumor therapy with 9 MeV protons, 19 MeV
deuterons, 10 MeV neutrons (d t ? n ??)

• Mechanism like all radiation therapy, kills
  tumor cells by damaging DNA
• Proton therapy advantages
• Precise targeting for both near-surface and deep
  tumors
• Well-defined range
• Less dispersion in tissue
• Less tissue damage
• Reduced side effects
• Extensive application in treating specific cancers