ACCELERATORS

1
ACCELERATORS
2
Topics

• types of accelerators
• relativistic effects
• Fermilab accelerators
• Fermilab proton-antiproton collider
• beam cooling
• summary

3
Luminosity and cross section

• Luminosity is a measure of the beam intensity
  (particles per
  area per second) ( L1031/cm2/s )
• integrated luminosity is a measure of the
  amount of data collected (e.g. 100 pb-1)
• cross section s is measure of effective
  interaction area, proportional to the probability
  that a given process will occur.
• 1 barn 10-24 cm2
• 1 pb 10-12 b 10-36 cm2 10-40 m2
• interaction rate

4
How to make qq collisions
_

• Quarks are not found free in nature!
• But (anti)quarks are elements of (anti)protons.
• So, if we collide protons and anti-protons we
  should get some qq collisions.
• Proton structure functions give the probability
  that a single quark (or gluon) carries a
  fraction x of the proton momentum (which is 980
  GeV/c at the Tevatron)

_
_
-
5
ACCELERATORS

• are devices to increase the energy of charged
  particles
• use magnetic fields to shape (focus and bend) the
  trajectory of the particles
• use electric fields for acceleration.
• types of accelerators
• electrostatic (DC) accelerators
• Cockcroft-Walton accelerator (protons up to 2
  MeV)
• Van de Graaff accelerator (protons up to 10 MeV)
• Tandem Van de Graaff accelerator (protons up to
  20 MeV)
• resonance accelerators
• cyclotron (protons up to 25 MeV)
• linear accelerators
• electron linac 100 MeV to 50 GeV
• proton linac up to 70 MeV
• synchronous accelerators
• synchrocyclotron (protons up to 750 MeV)
• proton synchrotron (protons up to 900 GeV)
• electron synchrotron (electrons from 50 MeV to 90
  GeV)
• storage ring accelerators (colliders)

6
ACCELERATORS, contd

• electrostatic accelerators
• generate high voltage between two electrodes ?
  charged particles move in electric field,
  energy gain
  charge times voltage drop
• Cockcroft-Walton and Van de Graaff accelerators
  differ in method to achieve high voltage.

7
Cockcroft-Walton generator

• C-W generator uses diodes and capacitors in a
  rectifier and voltage-multiplier circuit

8
Van de Graaff accelerator

• use powersupply to deposit charges on belt pick
  charges off at other end of belt and deposit on
  terminal
• now rubber belt replaced by pellet chain
  pelletron

9
Van de Graaff accelerator -- 2

• tandem VdG use potential difference twice,
  with change of charges in the middle (strip off
  electrons)

10
Proton Linac

• proton linac (drift tube accelerator)
• cylindrical metal tubes (drift tubes) along axis
  of large vacuum tank
• successive drift tubes connected to opposite
  terminals of AC voltage source
• no electric field inside drift tube ? while in
  drift tube, protons move with constant velocity
• AC frequency such that protons always find
  accelerating field when reaching gap between
  drift tubes
• length of drift tubes increases to keep drift
  time constant
• for very high velocities, drift tubes nearly of
  same length (nearly no velocity increase when
  approaching speed of light)

11
CYCLOTRON

• cyclotron
• consists of two hollow metal chambers called
  (dees for their shape, with open sides which
  are parallel, slightly apart from each other
  (gap)
• dees connected to AC voltage source - always one
  dee positive when other negative ? electric field
  in gap between dees, but no electric field inside
  the dees
• source of protons in center, everything in vacuum
  chamber
• whole apparatus in magnetic field perpendicular
  to plane of dees
• frequency of AC voltage such that particles
  always accelerated when reaching the gap between
  the dees
• in magnetic field, particles are deflected p
  q?B?R p momentum, q charge,
  B magnetic field strength, R radius of
  curvature
• radius of path increases as momentum of proton
  increases time for passage always the same as
  long as momentum proportional to velocity
  
  this is not true when velocity becomes too big
  (relativistic effects)

12
Cyclotron
13
Accelerators relativistic effects

• relativistic effects
• special relativity tells us that certain
  approximations made in Newtonian mechanics break
  down at very high speeds
• relation between momentum and velocity in old
  (Newtonian) mechanics p m v
  relativistically this becomes p mv ?, with ?
  1/?1 - (v/c)2
  m rest
  mass, i.e. mass is replaced by rest mass times
  ? - relativistic
  growth of mass
• factor ? often called Lorentz factor
  ubiquitous in relations from special relativity
  energy E mc2?
• acceleration in a cyclotron is possible as long
  as relativistic effects are negligibly small,
  i.e. only for small speeds, where momentum is
  still proportional to speed at higher speeds,
  particles not in resonance with accelerating
  frequency for acceleration, need to change
  magnetic field B or accelerating frequency f or
  both

________
14
more types of Accelerators

• electron linac
• electrons reach nearly speed of light at small
  energies (at 2 MeV, electrons have 98 of speed
  of light)
  no drift tubes use travelling e.m. wave
  inside resonant cavities for acceleration.
• synchrocyclotron
• B kept constant, f decreases
• synchrotron
• B increases during acceleration, f fixed
  (electron synchrotron) or varied (proton
  synchrotron)
  radius of orbit fixed.

15
(No Transcript)
16
Fermilab aerial view
17
Fermilab accelerator chain 0 to 400 MeV
Plasma ion source H- ions,
18keV Cockroft-Walton H- ions, 18keV to
750keV
Linac H- ions, 750keV to 400 MeV
18
FNAL Cockcroft-Walton acc.

• The Cockcroft-Walton pre-accelerator provides the
  first stage of acceleration
  hydrogen gas is ionized to create negative ions,
  each consisting of two electrons and one proton.
• ions are accelerated by a positive voltage and
  reach an energy of 750,000 electron volts (750
  keV). (about 30 times the energy of the electron
  beam in a television's picture tube.)

19
FNAL Linac

• Next, the negative hydrogen ions enter a linear
  accelerator, approximately 500 feet long.
• Oscillating electric fields accelerate the
  negative hydrogen ions to 400 million electron
  volts (400 MeV).
• Before entering the third stage, the ions pass
  through a carbon foil, which removes the
  electrons, leaving only the positively charged
  protons.

20
Fermilab Linac

21
Fermilab accelerator chain 400 MeV to 980 GeV
Booster H- ions, stripped to p 400 MeV to 8
GeV
Main Injector Protons, 8GeV to 150GeV
TeVatron Protons and Antiprotons 150GeV to 980GeV
22
Main Injector and recycler

• recycler
• antiproton storage ring
• fixed momentum (8.9 GeV/c),
• permanent magnets
• Main Injector
• proton synchrotron cycle period 1.6-3 seconds
• delivers 120 GeV protons to pbar production
  target.
• Also delivers beam to a number of fixed target
  experiments.

23
Fermilab TeVatron tunnel
24
Antiproton manufacture

• 120 GeV protons from Main Injector
• extract, shoot on target (Ni)
• collect with Lithium lens
• select 8GeV antiprotons
• transfer to debuncher
• reduce beam spread by stochastic cooling
• store in accumulator (stacking)
• transfer to recycler when stack reaches 1012
  pbars

• when enough antiprotons
• extract from accumulator or recycler
• transfer to Main Injector
• accelerate to 150 GeV
• transfer to Tevatron

25
Antiprotons -- target and collection

• pbars from target have wide angular
  distribution
• Li lens focuses
• bend magnet selects 8 GeV pbars
• efficiency 8 pbars per 1 M protons hitting
  target make it into accumulator

26
Debuncher

• pbars from target are in bunches (small time
  spread), wide energy spread (4)
• debuncher performs bunch rotation to swap
  large energy spread and small time spread into
  narrow energy spread and large time spread
• low momentum pbars have shorter path ? arrive
  earlier at RF cavity ? get stronger accelerating
  kick

• after sufficient turns, energy spread reduced

27
Debuncher and accumulator

• debuncher
  accumulator

28
Accumulator

• accumulates antiprotons
• successive pulses of antiprotons from debuncher
  stacked over a day or so
• momentum stacking newly injected pbars are
  decelerated by RF cavity to edge of stack
• stack tail cooling system sweeps beam deposited
  by RF towards core of the stack
• additional core cooling systems keep antiprotons
  in core at desired energy and minimize beam size

29
Beam Cooling

• Beam cooling reduce size and energy spread of
  a particle beam circulating in a storage ring
  (without any accompanying beam loss)
• motion of individual beam particles deviate
  from motion of beam center (ideal orbit)
• transverse deviations in position and angle
  betatron oscillations
• longitudinal deviations due to energy
  (momentum) spread -- synchrotron oscillations
• motions of particles with respect to beam center
  similar to random motion of particles in a gas
• beam temperature measure of average energy
  corresponding to these relative motions
• beam cooling reduction of these motions --
  decrease of beam temperatures

30
Phase space
Transverse Phase space

• Phase Space space defined by coordinates
  describing motion wrt beam center
• Emittance region of phase space where particles
  can orbit, also its size (phase space volume)
• Liouvilles Theorem phase space volume
  constant (cannot be changed by conservative
  forces)
• L.T. only for continous particle stream (liquid)
  discrete particles ? can swap particles and
  empty phase space reduce area occupied by beam

31
Beam cooling -- 2

• beam cooling beats constraints of Liouville
  theorem (phase space volume is constant) because
  phase space volume is not reduced, only occupancy
  (distribution of particles) within phase space
  volume is changed
• Cooling is, by definition, not a conservative
  process. The cooling electronics act on the beam
  through a feedback loop to alter the beam's
  momentum or transverse oscillations.
• Two types of beam cooling have been demonstrated
  and used at various laboratories electron
  cooling which was pioneered by G. I. Budker, et.
  al., at Novosibirsk, and stochastic cooling,
  developed by Simon van der Meer of CERN.

32
Stochastic cooling -- 1

• Stochastic cooling
• pick-up electrode detects excursions of a
  particle from its central orbit
• sends signal to a kicker downstream
• kicker applies a correction field to reduce this
  amplitude.

Short cut, (n¼)??
33
Stochastic cooling - 2

• by suitable choice of gain, overall cooling can
  be achieved

• The cooling process can be looked at as a
  competition between two terms
• (a) the coherent term which is generated by the
  single particle,
• (b) the incoherent term which results from
  disturbances to the single particle.
• (a)linear with gain (b)quadratic

34
Stochastic Cooling - 3

• Particle beams are not just a single particle,
  but rather, a distribution of particles around
  the circumference of the storage ring. Each
  particle oscillates with a unique amplitude and
  random initial phase. The cooling system acts on
  a sample of particles within the beam rather than
  on a single particle.
• Since stochastic cooling systems cannot resolve
  the motion of a single antiproton, only a
  phenomenon called mixing makes cooling possible.
  Mixing arises because particles with different
  momenta take different times to travel around the
  ring, and get spread out over the beam. After a
  few turns around the ring, the noise averages to
  zero for accumulating antiprotons.

35
Stochastic Cooling in the Pbar Source

• Standard Debuncher operation
• 108 pbars, uniformly distributed
• 600 kHz revolution frequency
• To individually sample particles
• to resolve 10-14 seconds, would need 100 THz
  bandwidth
• Dont have good pickups, kickers, amplifiers in
  the 100 THz range
• Sample Ns particles -gt Stochastic process
• Ns N/2TW where T is revolution time and W
  bandwidth
• Measure ltxgt deviations for Ns particles
• The higher the bandwidth the better the cooling

36
Betatron Cooling

• With correction gltxgt, where g is gain of system
• New position x - gltxgt
• Emittance Reduction RMS of kth particle(W
  bandwidth and N number of circulating
  particles),
• Must also consider noise (characterized by U
  Noise/Signal)
• Mixing
• Randomization effects M number of turns to
  completely randomize sample
• Net cooling effect if g sufficiently small

37
Momentum cooling

• Momentum cooling systems reduce the
  longitudinal energy spread of a beam by
  accelerating or decelerating particles in the
  beam distribution towards a central momentum.
• The sum signal is used for longitudinal cooling
  and the difference for betatron cooling.

38
AntiProton Source
39
Electron cooling

• invented by G.I. Budker (INP, Novosibirsk) in
  1966 as a way to increase luminosity of p-p and
  p-pbar colliders.
• first tested in 1974 with 68 MeV protons in the
  NAP-M ring at INP.
• cooling of ion beams by a co-moving low
  emittance electron beam is a well-established
  technique for energies up to hundreds of MeV per
  nucleon
• at higher energy, expect slower cooling, but may
  still give enhancement in the performance of
  high energy colliders as well.
• is now used for cooling of 8 GeV antiprotons in
  the Fermilab recycler ring
• GSI project for cooling antiprotons

40
How does electron cooling work?

• velocity of electrons made equal to velocity of
  ions (antiprotons)
• ions undergo Coulomb scattering in the electron
  gas and lose energy which is transferred from
  the ions to the co-streaming electrons until
  thermal equilibrium is attained

41
Electron cooling
42
Summary

• many different types of accelerators have been
  developed for nuclear and particle physics
  research
• different acceleration techniques suitable for
  different particles and energy regimes
• most accelerators in large research laboratories
  use several of these techniques in a chain of
  accelerators
• beam cooling has become important tool in
  improving beam quality and luminosity
• active research going on to develop new
  accelerating techniques for future applications
• many types of accelerators have found
  applications in fields other than nuclear and
  particle physics (e.g. medicine, ion implantation
  for electronics chips, condensed matter research,
  biology,.)