Accelerators of Particles

ACCELERATORS OF PARTICLES

In the beginning of our century scientists conducted many experiments on charged particles. The first sources of the particles were radioactive materials. They send f.e. alpha particles of energies up to 6 Me V. That kind of particles was used in first controlled nuclear reactions. But those sources were very expensive and hard to control. And foremost produced particles had not enough energy to make many of the experiments possible to conduct. Scientists needed some better ways of achieving high-energetic particles. Some of the constructions (these systems are called generally accelerators) are described above:

Cockcroft-Walton generator

In 1932 two scientists - J.D. Cockcroft and E.T. Walton - built a system thanks to which they could accelerate charged particles. The system consisted of a container filled with gaseous helium. Helium was shot with electrons, and they caused ionization of that helium. Free protons were created. They were accelerated by the potential difference (0,15 MV). Accelerated protons incidence at a thin foil caused some emission of alpha particles as the formula shows below:

(1)

Each alpha particle achieved energy of 8,6 MeV.

Van de Graffa generator (belt-type generator)

The section of the Van de Graffa generator

That generator consisted of a source of high voltage and a belt hanging on two rolls. The electric charge caused by the source was transferred to the belt thank to some special blades. Another blades situated in the sphere were collecting the charge and transferring it to the external surface of the sphere increasing its potential. The ions created inside the sphere were accelerated thanks to the potential difference between the sphere and earth. The ions were moving inside the vacuum tube.

Cyclotron

- Computer programm - experiment simalation

In the beginning of the thirties at the Californian University in Berkeley two scientists E.O. Lawerence and M.S. Livingstone constructed a new type of ions' accelerator. It consists of the two empty, semicircular chambers- duants. There is a narrow, empty slot between the chambers. The chambers are supplied with the voltage of the radio frequency. The duants are placed in the vacuum chamber, between the poles of the mighty electromagnet. The creation of ions proceeds in the source placed in the middle, between the duants. After leaving the source the ions' path is curved in the strong magnetic field. That is because they are bound by the magnetic force. In this case, when the vector of induction is perpendicular with the respect to the vector of velocity, the magnetic force is given by the formula shown below:

(2)

According to the Newton's law for the circular motion it is:

(3)

Having those two formulas we can calculate the radius of the trajectory of the ion leaving the source:

(4)

When passing through the slot between the duants each ion undergoes acceleration thanks to the electric field. That electric field between the duants is caused by the source of the radio frequency. So the ion moves a bit faster. That is why in the second duant the radius of the ion's movement is longer. The source of the variable current (the current is of the radio frequency) is synchronized, so every time when the ion passes through the space between duants it is "pushed". That means that each time it moves faster and the radius of the movement grows longer. The final velocity of the ion is its mas, the magnetic field intensity (B) and the duants' radiuses depended. The final kinetic energy of the particle is given with the formula:

Ek = 1/2*m*v^2MAX = 1*(q^2*B2*r^2MAX)/(m)

(5)

Betatron

In the beginning of the forties D.W. Kerst of the Illinois University constructed a new machine accelerating ions - the betatron. It consists of the torus shaped vacuum chamber placed between the overpoles of a very strong electromagnet. In the chamber there is a source of electrons. The variable current fed coils induce a variable electromagnetic field between the poles of the electromagnet. The field accelerates electrons ant keeps them on a circular orbit. That is why there is no such limit as in the cyclotron - the radius of the particle's movement doesn't get longer.

Linear accelerators

Simplified version of the Loius Alvarez linear accelerator

These are one of the most simple accelerators of particles. Charged particles (the protons, the electrons) are firstly accelerated in some other machines (i.e. in a van de Graff generator) and then shot in a long vacuum tube. The beam of the particles goes through the many of empty, metallic cylinders and that are connected alternate (positive - negative) with a radio frequency generator. So the particles are accelerated by the electric field of the electromagnetic wave moving along the accelerator. Every next cylinder has to be longer than the preceding one because of the increasing velocity of the particle.

Synchrotron

It is a kind of circle accelerator for charged particles. The particles circulate at stable orbits, where they are held by the magnetic field increasing with the increasing velocity of the particles. The particles are accelerated each time they pass through the place in the synchrotron called the resonator slot. The slot is fed by a high frequency generator.

Some of the first accelerators constructed from the thirties to seventies are listed below:

ACCELERATOR	PARTICLE	ENERGY	YEAR
Lawrence's-Livingstone's cyclotron	The proton	1,2 MeV	1932
Kerst's Betatron Stanford University	The electron	20 MeV	1942
Linear accelerato Stanford University	The elektron	35 MeV	1950
Synchrotron Brookhaven National Laboratory	The proton	2,2 GeV	1952
Synchrotron CERN, Szwajcaria	The proton	28 GeV	1959
SLAC - linear accelerator Stanford University	The electron	20 GeV	1966
Synchrotron Sierpuchow, ZSRR	The proton	76 GeV	1967
Synchrotron National Accelerator Laboratory Weston, Illinois	The proton	500 GeV	1971