A-level Physics (Advancing Physics)/Particle Accelerators

Modern experimental particle physics requires particles to be accelerated to very high energies. This is accomplished by passing them through an electric field multiple times, in a similar fashion to an electron gun. Types of particle accelerator include linear accelerators and cyclotrons.

Linear Accelerators

In a linear accelerator, particles pass through a series of tubes. At either end of each tube are electrodes. An alternating current is used. This means that, when particles pass an electrode to which they are being attracted, the electrode switches charge, and starts to repel the particle. The distances between electrodes increase as you go along the accelerator, since, as the particles accelerate, they travel further per. oscillation of the current.

Aerial photo of the Stanford Linear Accelerator Center, with detector complex at the right (east) side

The original patent for a cyclotron.

Cyclotrons

A cyclotron is like a linear accelerator, except that, instead of using lots of different electrodes, it uses the same two over and over again. The particles move around in a circle due to a magnetic field. The radius of this circle depends on the velocity of the particles. The orbits of the particles are enclosed by two semi-cylindrical electrodes. An alternating current is used to accelerate the particles. When the particles enter one half of the cyclotron, they are pulled back to the other half. When they reach the other half, the current switches over, and they are pulled back to the first half. All the time, the magnetic field keeps them moving in circles. As they gain energy from the electric field, the radii of their orbits increase, and their velocities increase, until the radius is as large as the cyclotron.

Questions

1. Use the formula for centripetal force to show that the radius of motion depends on the speed of the moving object.

2. A cyclotron with a diameter of 1.5m is used to accelerate electrons (mass 9.11 x 10⁻³¹kg). The maximum force exerted on an electron is 2.4 x 10⁻¹⁸N. What is the maximum velocity of the electrons?

3. What are the problems involved in constructing a large cyclotron?

4. Why don't particles stick to the electrodes when passing through them?

Worked Solutions