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Magnet and beam
The beam moves on a circle of radius rho = p / (qB). In practical units B rho [T m] = 3.33564 p [GeV/c], so stiffer beams need stronger fields or longer arcs.
Model checks
The science
What is modelled
A charged particle crossing a region of uniform magnetic field. The Lorentz force bends it onto an arc whose radius sets the bend angle for a given magnet length; enough identical dipoles in sequence turn the beam through 360 degrees.
Equations
- Rigidity
B rho = p / q = 3.33564 p(T m, p in GeV/c). - Bend angle
theta = L / rho; sagittarho (1 - cos theta). - Turning rate
omega = q B c2 / Efrom the Lorentz force. - Field energy in a bore of radius a:
B2 / (2 mu0) x pi a2 L.
Checks run in the page
- Rigidity from SI units.
- Bend angle by integrating the Lorentz force along the magnet.
- Path geometry of the traced arc.
- Field energy and its B2 scaling.
Honest simplifications
A uniform field with sharp edges: no fringe fields, focusing, beam size, synchrotron radiation, coil or yoke energy, or magnet saturation. Not a magnet design tool.
What to try
- Press Strong field and see the radius shrink.
- Press High momentum: the beam barely bends in one magnet.
- Change the magnet count until the ring closes at 360 degrees.