[MUSIC] Hello, and welcome to this third module of our introductory course, where we'll touch upon the basics of particle acceleration and detection methods. In this video, we will explain the physical principles of linear and circular accelerators. Afterwards, you will be able to answer the following questions. What are the principles of particle acceleration by electromagnetic fields? How does an electrostatic accelerator work? And how do cyclotrons and synchrotrons work? The force acting on a particle of charge e, in an electric field E, and a magnetic field B, is given by the Lorentz force that is quoted in blue. Electric fields are used to accelerate particles by increasing their momentum. Magnetic fields serve to deflect them from their original direction, to store them in a ring, or to focus a beam of particles. The simplest accelerator for electrons is the cathode ray tube, that you may remember from your grandfather's TV set. An electron emerging from a heated filament is accelerated by a potential V. The energy of the outgoing electron is then obviously V electron volts. Electrostatic accelerators chain together stages of this type as shown in this photograph. Their energy is limited by the stability of the high voltage insulation. Thus, it does not exceed a few million electron volts. To reach a higher energy requires that the projectile passes several times by an accelerating potential. The simplest circular accelerator is the cyclotron. In a uniform and constant magnetic field B, a particle of charge e moves on a circle of radius rho equal to p divided by eB where p is its moment. The angular frequency of this movement is called cyclotron frequency omega_c. It is proportion to the ratio e over m of the particle charge and mass and proportional to the magnetic field intensity B. The particle is accelerated by the electric field present between the two D shaped cavities. This field is provided by a radio frequency generator such that its frequency is equal to the cyclotron frequency. In the non relativistic domain, this frequency is constant because the circumference of the orbit increases proportional to the velocity of the particle. Thus, we can inject particles in a quasi continuous manner, if the accelerating RF frequency's high and an even multiple of the cyclotron frequency. You can find a calculation of the cyclotron frequency in video 3.1a. The cyclotron has its limits in that the velocity of the particle does not remain proportional to the momentum, but approaches the speed of light in an asymptotic process. In the relativistic limit, the velocity barely increases despite a steady increase in energy. Acceleration radio frequency and particle revolution frequency dephase thus quickly at an energy of some tens of MeV for protons. One must thus adjust the radio frequency to the relativistic velocity. For example, the proton cyclotron at the Paul Scherrer Institute in Villigen, Switzerland accelerates protons to nearly 80% of the speed of light. And you can see a picture of this accelerator in this photograph. The asymptotic saturation of the speed of the particle to the speed of light is, on the contrary, very useful, provided that the radius of curvature is held constant. In this case, the rotational frequency, again, is independent of energy. This is the principle of the synchrotron. By increasing the magnetic field proportional to the momentum of the particle, the radius of curvature remains constant. One does not have to fill a large volume with a magnetic field, but can concentrate it inside a vacuum chamber, whose shape approximates a ring. The synchrotron frequency becomes constant at high energies if the field B is kept proportional to the momentum. We can then work with a constant accelerating radio frequency. The RF field is transmitted to the beam by resonant cavities. The synchrotron principle requires a certain initial velocity sufficiently close to the speed of light. The beam is thus usually pre-accelerated before injection by say, a linear accelerator. The acceleration process must stop when one reaches the maximum field of the dipole magnets. One then either extracts the beam or converts the accelerator into a storage ring. In this latter operational mode, it provides at each turn just the energy lost by the beam via bremsstrahlung. This loss of energy will be introduced in the next section of the module, video 3.2. The separation of functions and the concentration of the components around the ring, allows to combine two rings to construct what is called a collider. A historical example is the Princeton- Stanford storage ring, an early example of a particle collider. It worked with electrons in the two rings which interact in the middle, where the two storage rings touch. The detector was rather primitive, a spark chamber, but it did allow to determine the scattering angle. Obviously, one can also fold the two accelerators on top of each other, or even combine them if you want to collide particles and antiparticles. Examples of the latter type of colliders are the Tevatron at the Fermi National Laboratory close to Chicago in the US, which collided protons and antiprotons until 2011. And also the Large Electron Positron collider, LEP at CERN, which collided electrons and positrons. It was in operation between 1989 and 2000 in the tunnel which now houses the Large Hadron Collider, LHC at CERN. We will return to the LHC in the next video of this module. [MUSIC]
