Accelerators

Resolution It is clear that if we wish to produce particle of large mass, then very large amounts of kinetic energy are needed. We also know that in order to ‘see’ something very small, the object ‘thrown’ at it, must have a wavelength of a comparable size. Otherwise, the wave is not deflected; it just continues along its original path. Since the constituents of the particles are assumed to be very small, the wavelength used must be very small. For example, if a photon is used to detect a particle that has a radius of ~10-15m, it must have a energy of Visible Light has E ~ 10’s eV Gamma Radiation: E ~ MeV

Accelerators To get high energetic particles, particle accelerators are used. 1) In the linear accelerator, particles are accelerated along a straight path by electric fields. The linear accelerator The cyclotron The synchrotron The Betatron 2) The cyclotron accelerates particles through a potential difference. Magnets are used to curve the path of the particles back to the gap. The path of the particles’ gets bigger and bigger. 4) The Betatron accelerates electron and they follow a constant radius. 3) The synchrotron accelerates the particles like the cyclotron but they follow a path of constant radius.

Linacs Linear Accelerators, or linacs, consist of a series of evacuated tubes. An alternating voltage is applied across the gaps between consecutive tubes. The charged particles accelerate every time they move from one tube to another. The length of the tubes increases so that the particles spend an equal time in each tube. The beam can be accelerated to hit a fixed target or two beams can be accelerated along the same straight line from opposite ends and made to collide with each other.

Cyclotron The cyclotron consists of two D shapes, with a gap between them, placed in a uniform magnetic field. A charged particle is accelerated from the center. A magnetic field pushes the particle back toward the gap. When the particle reaches the gap, the polarity of the voltage is switched so that the particle accelerates through the potential difference. Remember that the period of the particle’s rotation is constant. The radius increases but the velocity also increases proportionally. Where v = 2πr/T qvB = mv2/r Cyclotron frequency: f = qB/(2πm) T = 2πm/(qB)

The Synchrotron Protons move along a circular path of fixed radius. Accelerating region electromagnet _ + A B Electric field B Acceleration takes place here A

The positive particles will accelerate across the gap The positive particles will accelerate across the gap. The electric potentials in the gaps must be carefully established by carefully timing the arrival of the beam at every gap. The period of the electric field must be synchronous with the beam. Fc = Fm Mv2/R = qvB R = mv/qB As the particles move closer to the speed of light, their energy becomes E2 = (pc)2 +(mc2)2 R = _E_ qBc E2 = (pc)2 E = pc (When the momentum is very large, we may ignore its rest energy) The magnetic field must be constantly increasing as the particle’s energy increases (that’s why they’re electromagnets).

BETATRON Betatron helps to accelerate electrons to its highest speed. Fast moving electrons are also known as beta particles so the device is called Betatron. It can accelerate electron upto 300 MeV. It works on the principle of Lenz’s law. We provide non uniform magnetic field to it and It helps electron in two ways: . It keeps electron in a constant radius . Due to non uniform magnetic field EMF induces in it that creates electric field and help electron to accelerates much faster. The accelerated electron then focussed to the target which is used to perform various experiments like to generate the beam of X-ray. The electron is accelerated in dough nut shaped chamber having injector, tungsten filament coated with Barium oxide. €=(2πr)^2B Betatron condition Where € is magnetic flux