CERN brochures:

Information booklet for teachers (students aged 16-19 years)

WG Leader: Antonella del Rosso

ACCELERATORS

Marinela Bitu

Particle accelerators are used to investigate the structure of subatomic particles.

The motivation to strive for higher energy came from quantum mechanics, which describes particles as waves whose length is related to the momentum of particle by de Broglie’s expression:

Higher momentum brings shorter wavelengths and the capability to reveal the structure of matter with more details.

Discovery of smaller particles reveals more massive particles, which require, according to Einstein’s , more and more energy to produce them.As particles are accelerated to energies many times their rest mass, momentum and energy will be calculated in terms of the special relativity. Although velocity saturates asymptotically – always below the speed of light-, momentum and energy continue to increase as particles are accelerated.

CERN’s accelerator complex, one of the world’s complex scientific instruments, includes particle accelerators and colliders and handles beams of electrons, positrons, protons, antiprotons and ions. The achieved energies are about 100GeV in the Large Electron-Positron Collider LEP2, and will increase up to 7TeV in the future Large Hadron Collider LHC.

Fig.1 CERN’s accelerators complex

As a basic principle, accelerators use powerful electric fields to push energy into a beam of charged particle. According to Lorentz force:

one can see that particles gain energy only due to the electric field. Particles acquire an energy which is just their charge multiplied by the electric potential difference.

But, building up high-voltage electrostatic generators creates many difficulties because of the electrical breakdown, which becomes a serious problem above a few tens of KV.

The idea of overcoming the voltage breakdown problem of a single stage of acceleration was to place a series of cylindrical electrodes one after another in a straight line to form linear accelerators, called LINACs, and use an alternative field.

Fig. 2 LINAC’s basic scheme

Charged particles enter on the left and are accelerated towards the first drift tube by an electric field. Once inside the drift tube, they are shielded from the field and drift through a constant velocity. When they arrive, at the next gap, the field accelerates them again until they reach the next drift tube. This continues with the particles picking up more and more energy in each gap, until they shoot out of the accelerator on the right. The drift tubes shield the particles for the length of time that the field would be decelerating.

But, to reach high energy, it would require extremely long linear accelerators.

The following step was the cyclotron invention (1929), based on making a particle follow a circular path in a magnetic field through the same accelerating gap.

The balance between centripetal acceleration of motion in a circle and Lorentz’s force is:

The radius of the orbit in cyclotron is proportional to the velocity and the frequency of revolution:

A radio frequency generator excites particles with an electric alternating field of constant frequency. The electric field oscillates at the particle’s circulation frequency.

For low energy particles, the revolution frequency of cyclotron is constant as far as the particle mass remains into the classic limit.

But, as momentum and energy increase and the velocity of a particle approaches that of light, then the velocity begins to increase less rapidly than the particle mass, so the revolution frequency drops so that particles are no longer synchronous with the accelerating potential.

The discovery of the synchrotron principle opened the way to the series of circular accelerators, which are used up, to the present day.

A short pulse of particles is injected at low magnetic field, the field rises in proportion to the momentum of particles as they are accelerated and this ensures that the radius of the orbit remains constant.

The accelerated particles take less and less time to complete their orbit so the frequency of the accelerating alternative current must increase as well.

Fig.3 Synchrotron basic scheme

Charged particles receive the energy needed to reach a speed close to that of light from accelerating cavities, which store up electric energy, transferring a small amount to the particles each time they pass. They act like a short section of linear accelerator. Several radio-frequency (rf) cavities are positioned around the ring. These contain the alternating electric field synchronized with the beam’s orbital period, and accelerate the charges.

Dipole magnets keep the particles moving in a circle. Whenever a charged particle is swung in a circle it radiates energy. The greater its centripetal acceleration the greater the rate of radiation, so high-energy electrons in circular accelerators lose a lot of energy as synchrotron radiation.

Fig. 4 Synchrotron radiation emitted by an accelerated charged particle

The opening angle depends on 1/g, where g is the gamma factor , so the higher energetic are particles, the smaller will be this angle. The radiated power depends on  and curvature of the path. This must be pumped into the beam through the rf cavities. The LEP radius of about 3,1km is designed to ensure a smooth bending of particle beam to avoid energetic losses.

The radiation losses in electron-positron accelerators are much bigger than in proton-antiproton accelerators. The mass of electron is roughly 2000 times smaller than that of the proton, and therefore, for the same energy it has a g, that is 2000 times larger. The radiated power depends on , so there are necessary powerful rf systems and much of the voltage per turn, U, to keep the beam from decelerating.

Table 1. Comparison between the colliders’ parameters. The particle energies, collider’s radius, number of particles per bunch, the necessary voltage per turn and radiated power are given in the column for each type of collider 

So, each time more energy is pumped into the particles, the magnetic field has to be increased to prevent them for skidding of the ring.

Focusing quadrupole magnets are used to keep the particles tightly packed within the beam. They work in much the same way as lenses do with light. Effective focusing is very important as it enhances the beam intensity and reduces the beam cross-section.

The particle beam travels inside a pipe, from which the air has been removed in order that particles collisions with molecules of air to be avoided. Beam stability depends on the vacuum chamber geometry.

Large particle colliders are used to accelerate particles to very high energies. If the incoming particles are simply slammed into a stationary target, much of the projectile energy is taken up by the target’s recoil and not exploitable. Much more energy is available for the production of new particles if two beams traveling in opposite directions are collided together.

The energy of interest to produce new particles in different collisions is E_cm, the enrgy in the center-of-mass frame. In the case of colliders, E_cm=2E_p, where E_b means the energy of one incident particle.

The electron-positron accelerator LEP is a collider. Electrons and positron circulated in opposite directions in the same guide field, being equal in mass but opposite charge, appeared to the magnetic bending and focusing fields as identical currents, one bent to the left, the other to the right. Another CERN collider, the Super Proton Synchrotron (SPS) uses the same technique to circulate protons in one direction and anti-proton in the opposite direction.

Fig.4 Basic scheme of LEP collider

Bunches of particles are focused down to the thickness of a hair and made to collide. Each bunch contains more than 10¹¹ (see Table 1), but on average only one in about 40000 collisions between the bunches produces the desired effect-a head-on electron-positron collision. To increase the probability of these events, bunches are made to circulate several hours into the ring.

The LEP2 collider at CERN was until 1999 the largest particle collider in the world, accelerating bunches of electrons and positrons to the energies needed to produce pairs of charged carriers of the weak force W⁺ and W^- particles. Detection of Z⁰s and Ws, allowed the LEP experiments to make precise tests of the Standard Model of particles and their interactions.

The Large Hadron Collider LHC is designed to accelerate hadrons in experiments probing beyond the Standard Model, more precisely, addressing the following topics: the origin of the particle masses, unification of strong, weak, electromagnetic gauge interaction, and the quarks flavour. LHC machine will share the 27-kilometre LEP tunnel, and will use the most advanced superconducting magnets and accelerators technologies. The magnitude of the magnetic field will be B=8,4T, at a current of 11700 A and temperature of T=1,9K.

References:

1.E.J.N. Wilson, “An Introduction to Particle Accelerators”, Oxford University Press, 2001

2. O. Bruning, Accelerators, In: Summer Student Lecture Program, CERN, Geneva, Switzerland, 2002