ACCELERATORS

= 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)

• 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.

• 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 = 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 change of mass'')

• 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)

• 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.

• ``relativistic effects'':
  • the theory of 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 becomes

    

    = ``rest mass''

  • i.e. mass is replaced by (rest mass times ) - ``relativistic growth of mass''
  • factor often called ``Lorentz factor''; is ubiquitous in relations from special relativity;
  • energy:

    

  • 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;
• synchrocyclotron: B kept constant, f decreases;
• synchrotron :
  B increases during acceleration,
  f fixed (electron s.) or varied (proton s.)
  radius of orbit fixed.

PARTICLE DETECTORS

• when passing through matter, particles interact with the electrons and/or nuclei of the medium; this interaction can be e.m. or strong interaction, depending on the kind of particle; its effects can be used to detect the particles;
• possible interactions and effects in passage of particles through matter:
  • excitation of atoms or molecules (e.m. int.):
    charged particles can excite an atom or molecule (i.e. lift electron to higher energy state); subsequent de-excitation leads to emission of photons;
  • ionization (e.m. int.):
    electrons liberated from atom or molecule, can be collected, and charge is detected
  • Cherenkov radiation (e.m. int.):
    if particle's speed is higher than speed of light in the medium, e.m. radiation is emitted -- ``Cherenkov light'' or Cherenkov radiation, which can be detected;
    amount of light and angle of emission depend on particle velocity;
  • transition radiation (e.m. int.):
    when a charged particle crosses the boundary between two media with different speeds of light (different ``refractive index''), e.m. radiation is emitted -- ``transition radiation'':
    amount of radiation grows with (energy/mass) ;
  • bremsstrahlung (= braking radiation) (e.m. int.):
    when charged particle's velocity changes, e.m. radiation is emitted;
    due to interaction with nuclei, particles deflected and slowed down emit bremsstrahlung;
    effect stronger, the bigger = (energy/mass) electrons with high energy most strongly affected;
  • pair production (e.m. int.):
    by interaction with e.m. field of nucleus, photons can convert into electron-positron pairs
  • electromagnetic shower (e.m. int.):
    high energy electrons and photons can cause electromagnetic shower'' by successive bremsstrahlung and pair production
  • hadron production (strong int.):
    strongly interacting particles can produce new particles by strong interaction, which in turn can produce particles,... ``hadronic shower''

• photomultiplier:
  photomultiplier tubes convert small light signal (even single photon) into detectable charge (current pulse)
  photons liberate electrons from photocathode, electrons ``multiplied'' in several (6 to 14) stages by ionization and acceleration in high electric field between ``dynodes'', with gain
  photocathode and dynodes made from material with low ionization energy;
  photocathodes: thin layer of semiconductor made from Sb (antimony) plus one or more alkali metals, deposited on glass or quartz;
  dynodes: alkali or alkaline earth metal oxide deposited on metal, e.g. BeO on Cu (gives high secondary emission);

• scintillator:
  energy liberated in de-excitation and capture of ionization electrons emitted as light - ``scintillation light''
  light channeled to photomultiplier in light guide (e.g. optical fibers);
  scintillating materials: certain crystals (e.g. NaI), transparent plastics with doping (fluors and wavelength shifters)
• proportional tube:
  metallic tube with thin wire in center, filled with gas, HV between wall (-, ``cathode'') and central wire (+,``anode'') strong electric field near wire;
  charged particle in gas ionization electrons liberated;
  electrons accelerated in electric field can liberate other electrons by ionization which in turn are accelerated and ionize ``avalanche of electrons'' moves to wire current pulse;
  current pulse amplified electronic signal:
  gas is usually noble gas (e.g. argon), with some additives e.g. carbon dioxide, methane, isobutane,..) as ``quenchers'';
• Geiger-Müller counter:
  similar to proportional tube, but operated at higher voltage and lower pressure higher gas gain avalanche becomes so big that all of gas ionized plasma electric discharge
• multi wire proportional chamber:
  contains many parallel anode wires between two cathode planes (array of prop.tubes with separating walls taken out)
  operation similar to proportional tube;
  cathodes can be metal strips or wires get additional position information from cathode signals.

• drift chamber:
  field shaping wires and electrodes on wall to create very uniform electric field, and divide chamber volume into ``drift cells'', each containing one anode wire;
  within drift cell, electrons liberated by passage of particle move to anode wire, with avalanche multiplication near anode wire;
  arrival time of pulse gives information about distance of particle from anode wire;
  ratio of pulses at two ends of anode wire gives position along anode wire;
• Cherenkov detector:
  measure Cherenkov light (amount and/or angle) emitted by particle going through counter volume filled with transparent gas, liquid, aerogel, or solid get information about speed of particle.
• calorimeter:
  ``destructive'' method of measuring a particle's energy: put enough material into particle's way to force formation of hadronic or electromagnetic shower (depending on kind of particle),
  eventually particle loses all of its energy in calorimeter;
  energy deposit gives measure of original particle energy.

• Note:
  many of the detectors and techniques developed for particle and nuclear physics are now being used in medicine, mostly diagnosis, but also for therapy.