Rigidity (electromagnetism)

In accelerator physics, rigidity is the effect of particular magnetic fields on the motion of the charged particles. It is a measure of the momentum of the particle, and it refers to the fact that a higher momentum particle will have a higher resistance to deflection by a magnetic field. It is defined as R = Bρ = p/q, where B is the magnetic field, ρ is the gyroradius of the particle due to this field, p is the particle momentum, and q is its charge. It is frequently referred to as simply "Bρ". The unit of the rigidity R is tesla-metres (N·s/C).[1]

The rigidity is defined by the action of a static magnetic field, whose direction is perpendicular to the velocity vector of the particle. This will cause a force perpendicular both to the velocity vector, and to the field, defining a plane through which the particle moves. The definition of the Lorentz force implies that the particle's motion will be circular in a uniform field, thus giving a constant radius of curvature.

If the particle momentum, p, is given in GeV/c, then the rigidity, in tesla-metres, can be conveniently computed as Bρ = 3.3356pc/q, where 3.3356 (which has units of s/m) is nothing but 10^9/c, where c is the speed of light in m/s.

## References

1. ↑ Lee, S.Y. (2004). Accelerator Physics (Second ed.). World Scientific. p. 576. ISBN 978-981-256-200-5. Bibcode: 2004acph.book.....L.

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