Magnet Types in Particle Accelerators

Major components of circular particle accelerators (for example LHC in CERN) are its magnets. In this Demonstration, you can study the forces on moving charged particles in a magnetic field.
The locator represents a particle moving perpendicularly to the screen. If the particle is positively charged, it moves in the direction into the screen, away from you; if the particle is negative, it moves in the direction out of the screen, toward you.
Magnetic dipoles are used to deflect the particle beam into a circular orbit. Magnetic quadrupole magnets, in addition, focus the beam in a transverse plane (vertically by focusing or horizontally by defocusing). Magnetic sextupoles are used to focus the beam in a longitudinal direction (changing the so-called chromaticity of the beam).



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The magnetic force (Lorentz force) on a particle with charge in a magnetic field of strength B moving with velocity v is:
F= v × B.
This force is centripetal, directing the particle into a circular path. This is the role of the main dipole magnets.
Quadrupole magnets can focus the beam of particles, but only in one direction. They focus the charged particles in the vertical direction, but unfortunately also defocus them in the horizontal direction. It is possible to focus particles back into the horizontal direction with a quadrupole magnet rotated by 90 degrees. The optimal result is obtained by alternating these two orientations.
The strength of the magnetic field along the focusing axis of a quadrupole grows linearly from the center of the field, where it is zero. There are many pairs of focusing-defocusing magnets (so called FODO cells) in circular accelerators.
Sextupoles can be used in combination with quadrupoles to align the particle momentum of particles as the radial positions of the circulating particles change with momentum. The strength of the field of sextupoles along the horizontal axis grows quadratically from the center, where it is zero.
[1] N. Marks, "Conventional Magnets for Accelerators," The Cockcroft Institute.
[2] S. Baird, "Accelerators for Pedestrians," European Organization for Nuclear Research.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+