In ion optics, there is a concept called Magnetic Rigidity. When an charged ion passing through a magnetic field, it will bend and rotate. The magnetic rigidity is the , where is the magnetic field strength in Tesla, and is the rotation radius.

using basics physics, we have the centripetal force equals to the Lorentz force,

Simplify,

The above is non-relativistic, and I always assume the can be replaced by relativistic momentum . Now I give a prove.

The relativistic centripetal force is

Thus,

where is speed of light. In the last equation, the unit of is MeV/c, mm/ns, and in meter.

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