Episode 518: Particle accelerators
Lesson for 16-19
- Activity time 150 minutes
- Level Advanced
This episode requires students to apply their knowledge of charged particles and fields.
- Discussion and worked example: Acceleration in an electric field (15 minutes)
- Student activity: Researching accelerators (30 minutes)
- Demonstration: Electrical breakdown (15 minutes)
- Discussion: How a linear accelerator works (15 minutes)
- Discussion: Particles in a magnetic field (10 minutes)
- Demonstration: Fine beam tube (20 minutes)
- Student questions: Calculations (30 minutes)
- Discussion (optional): Relativistic effects and Bertozzi’s experiment (15 minutes)
- Visit (optional): Take a trip to CERN (A long weekend)
Discussion and worked example: Acceleration in an electric field
Why accelerate particles? Following Rutherford’s alpha-scattering experiment, physicists wanted to probe matter with beams of particles that were more energetic, more intense and
How can particles be speeded up? (use an electric field.) Won’t a magnetic field do? (particles are accelerated, but the force is centripetal, so their speed does not increase.)
Calculate the speed of an electron (or proton) accelerated through 10 kV. What equation to use?
12 × m × v 2 = e × V
e = 1.6 × 10-19 C
m = 9.1 × 10-31 kg
v = 2qV m approximately equal to 6 × 107 m s-1
Take care! This is approaching speeds where relativistic effects need to be taken into account.
Will a proton travel faster or slower than this? (slower, because charge is the same but mass is greater.)
In the largest research accelerators, energies are so great that they recreate the conditions minuscule fractions of a second after the Big Bang (typically ~ 10-10 s for LEP and a planned ~ 10-12 s for the Large Hadron Collider (LHC) opening in 2007).
Student activity: Researching accelerators
Find out about the development of linear and circular accelerators. Identify important spin-offs (e.g. the development of www, computer graphics, body scanner magnets, isotope production for medicine and industry, material processing etc.)
Demonstration: Electrical breakdown
In linear accelerators, the approach is to get as large a voltage as possible, and to apply it to the particles several times. A practical limit to voltage difference is set by the ability of materials to withstand the electric fields involved. You can demonstrate electrical breakdown.
Discussion: How a linear accelerator works
Explain the construction of the linear accelerator. The drift tubes get longer as the particles move faster. But at the highest speeds approaching that of light, increase in energy makes very little difference to the speed, so the drift tubes are the same length.
Discussion: Particles in a magnetic field
There is an advantage in making the particles travel around in a circular path – they can be accelerated time and again. Discuss how the particles trajectories are bent into a circular path with a magnetic field to bring them back to the accelerating electrical field many times. Compare with an electric field.
Recap the equation for this
mv 2r = Bqv.
Demonstration: Fine beam tube
Do this if you haven’t previously done so in
Show the fine beam tube with Helmholtz coils to provide a magnetic field.
Student questions: Calculations
Your students now know the equations needed to solve many problems relating to accelerators. You may have covered these questions in Episode 413, if not students should try them now.
Discussion (optional):Relativistic effects and Bertozzi’s experiment
Your students should be aware that, at relativistic speeds, things become more complicated. One way to present this is to discuss Bertozzi’s experiment.
Accelerators such as the synchrotron are designed to compensate for the effective increase in m by controlling the frequency of the accelerating voltage as the particles speed up.
Visit (optional): Take a trip to CERN (a long weekend)
You can organise a trip to CERN.