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Particle Accelerators. An accelerators is a device which is used to impart kinetic energy to the charged particles. Linear Accelerator.

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particle accelerators

Particle Accelerators

An accelerators is a device which is used to impart kinetic energy to the charged particles

linear accelerator
Linear Accelerator
  • An linear accelerator is a device which accelerates particles in a straight line by mean of oscillating electric field which provides either a series of boosting kicks in correct phase at a series of electrodes gaps
drift tube accelerator
Drift tube Accelerator

Principle – An oscillator electric field is applied across the electrodes joined in series. The charged particle when passed through them is accelerated if the frequency of the applied field is in resonance with the motion of the particle.


It consists of a series metallic hollow cylinders called electrodes (E) or drift tubes of successively increasing lengths arranged co-axially within tube (G). Alternate electrodes are connected to the terminals of high frequency oscillator i.e. the even numbered electrodes are connected to one terminal while the odd number electrodes are connected to the second terminal of the oscillator.

expression for energy acquired by ions
Expression for Energy acquired by ions

The average potential difference between the gap of any two electrodes = V

The energy acquired by ions in passing one gap = ZqVo

The total number of gaps = n

Total energy of ions E = ZqnVo =1/2mv

Tn =Vn /2v=(2ZqnV/m)1/2 1/2v

  • Requirements of generating very high voltages ~ million volts ranges is avoided in these accelerators.
  • They are economical for obtaining very high – energy particle beams.
  • They provides well- collimated beam of accelerated ions.

1-They are inconveniently long in size.

2- They require extremely high frequency and high – voltage oscillator.

wave guide accelerators

Accelerate electrons beyonds ~ 2 MeV, alternate version of linear accelerator was based on wave – guides. These accelerators are known as wave guide accelerators. In such accelerators drift tubes are completely eliminated. These accelerators consist of a circular wave – guide loaded with metallic annular disc.


Device used to accelerate heavy charged particles like proton, deutron, alpha particles etc. by passing them again and again in radio frequency electric field along a closed path


It is based on the principle that charged particles can acquire high energy when they are repeatedly passed through an alternating electric field


  • An evacuated chamber is divided into two D shaped sections D1 and D2 having small gap b\w them
  • “dees” are connected to terminals of a high frequency oscillator of the order 107 Hz and potential of 10,000 V
  • Chamber is placed b\w pieces of huge electromagnet
  • Electromagnet produces strong magnetic field perpendicular to the plane of dees
  • Positive ions are produced in the gap b\w the two dees by ionising the gas

The charged particle (say a positively charged proton) is released near mid point of the face of one of the Dees. Being in the electric field from one Dee to another, it is accelerated by the electric force in the direction of electric field. As the particle enters the adjoining Dee, the magnetic force, being perpendicular to it, renders the charged particle to move along a semicircular path within the Dee. By the time, it emerges again in the narrow gap separating the two Dees, the electrical polarity of Dees changes so that the particle is again accelerated again with an increase in speed.

The frequency of the oscillator is so chosen

that the time required to describe this semi-circle

corresponds to one half cycle. It is essential that

the resonance condition is maintained throughout,

otherwise the ions will not reach the gap in proper

phase to be accelerated. The ions go on travelling

until they reach the dees periphery and extracted

out through window.

magnetic focussing in cyclotron


Need:-To prevent the deviation of ion from ideal condition.

Focussing:-Essential thing in operation of cyclotron is resonance condition. To prevent the deviation of ion from ideal condition, restoring forces are applied in such a way that the ions are brought back to median plane. These forces are provided by shaping the pole pieces of main magnet such as to reduce the magnetic field from centre outwards. The central field is little more than ideal condition and peripheral field is little less. The component of M.F. toward centre of Dees keeps the particle in a circular orbit and component toward median plane helps in median plane focussing. Larger the deviations from the median plane, larger will be the vertical restoring forces.



  • Cyclotrons can be used in particle therapy to treat cancer.
  • Cyclotrons have a single electrical driver, which saves both money and power.
  • cyclotrons are able to produce a continuous stream of particles at the target, so the average power passed from a particle beam into a target is relatively high.

Betatronis a device for speeding up electrons to very high energy by expanding magnetic field. It is perfect example of reality of induced electric fields.


Based on principle of electromagnetic induction an alternating current applied to ‘primary coil’ induces a similar current in the ‘secondary coil’ windings. The primary current produces an ‘oscillatory magnetic field’. This field, in turn, induces an ‘oscillatory potential’ in the secondary coil.

  • Betatron consists of highly evacuated angular tube D known as doughnut chamber.
  • The chamber is placed b/w poles of an electromagnet excited by an alternating current.
  • Electrons are produced by electron gun and are injected into doughnut at the beginning of each cycle of alternating current.
  • The increasing magnetic flux give rise to a electric field around the doughnut which accelerates orbiting electrons.

Electrons from the electron gun are injected into doughnut shaped vacuum chamber when the magnetic field is just rising from its zero value into the first quarter cycle.

The electrons now make several thousands revolutions and gain energy

When magnetic field has reached its max.value,the electrons are pulled out from their orbit.

Either they strike a target and produce x rays or emerge from the apparatus through a window.



  • Good sharpness of the image due to small focal point.
  • Stable radiation output
  • Highly reliable and easy to use
  • Portable, quick and easy to setup
  • More affordable
  • Used as a source of x-rays
  • Used in cancer therapies


The maximum energy that a betatron can impart is limited by the strength of magnetic field due to saturation of iron and practical size of the magnet core.

  • It is an accelerator in which the frequency of the radio frequency is kept constant while magnetic field is varied for resonance.
  • In a synchrotron ,the particles are accelerated to high energies in an orbit of essentially constant radius.

There are two types of synchrotrons

  • Electron synchrotron
  • Proton synchrotron


It is a device used to accelerate electrons.


It consist of an electromagnet having annular pole pieces and a doughnut (ring) shaped vacuum chamber which is usually made of glass or ceramic.

The doughnut is placed be tween the pole pieces. The interior part of doughnut is coated with silver or copper to give a resonance cavity .

A very small gap in cavity divided it into two parts and very high frequency electric field is applied across the gap at the proper time in the magnetic cycle. When accelerator is on the electron is accelerated each time it crosses through the resonator.

Electron orbit



Flux pass

x ray


r.f. oscillator

  • The electrons are injected into orbit by means of an electron gun at about 50-100 Kev energy but the electrons are first accelerated to 1 or 2 Mev .
  • This is achieved by operating the accelerator first as betatron .The betatron start is achieved by means of small but high permeability flux bars located inside the orbit attach to the poles of guide magnet .
  • These bars get magnetically saturated and are no longer able to induce an e.m.f. This saturation cause the betatron mechanism to stop and there is smooth transition from betatron action to synchrotron action.

Now if the potential applied to the resonator at the proper frequency, the electrons are all kept in phase and receive increment of energy at each revolution as they pass through the cavity.

  • when the electrons acquire maximum desired energy ,the r.f. electric field is switched off.
  • At this stage ,magnetic flux condition for stable orbit is destroyed and electron changes the radius of orbit and strike the target projecting from the inner edge of the doughnut which give off x-rays of short wavelength.
proton synchrotron
Proton synchrotron
  • Proton synchrotron does not mean that the synchrotron can accelerate only proton but is equally applicable for deutrons,alpha particles or other ions ,but the name is given because protons being elementary particles are preferred for investigations in elementary particles sometimes also called Bevatron or Cosmotron.
  • Its principle is similar to electron synchrotron and gives proton upto 10Gev energy.

It consists of ring shaped magnet having four quadrants produces normal magnetic field to the doughnut shaped vacuum chamber the orbit radius is held constant by means of a magnetic field that increases with time.

The doughnut chamber is made up of steel or plastic. The doughnut chamber is supported in the gap of annular ring. The magnetic field is applied over four quadrants only and straight sectrons are kept free from magnetic field to be used for injection, acceleration and ejection of particles.


The proton initially is accelerated upto 10Mev in a linear accelerator and is then injected into the doughnut tube, when the magnetic field is small.

The pressure in the doughnut tube is about 1/10⁶ mm of Hg to reduce the loss of proton beam by gas scattering.

The proton recevies an impulse of about 1KV per turn through r.f. supply.

The magnetic field is increase in proportion to the momentum to keep the protons in the synchrotron moving in an orbit of constant radius.

Due to the protons gain energy, its frequency increases gradually.

Since protons are heavier mass particles, their energies for a relativistic velocity will be very high say 5Bev .

In proton synchrotron, the protons could be accelerated to energies of the order of multi Bev.

When protons reach their maximum energy, the oscillator frequency is distorted so that the orbit expands or contracts and the protons strike the target.