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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* = *pc*/*q*, where *B* is the magnetic field, *ρ* is the gyroradius of the particle due to this field, *p* is the particle momentum, *c* is the speed of light and *q* is its charge. It is frequently referred to as simply "*Bρ*".

The unit of the rigidity *R* is volts(N·m/C), a convenient unit is GV (*10^9* V). In this case, unit of *B* is T(N·s/C·m), *ρ* is in the unit rad/s, *p* is in the unit kg· m/s, *c* is in the unit m/s, *q* is in the unit C.

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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, is *Bρ* = 3.3356*pc*/*q*.