accelerator physics Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams ...

, 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 The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by :r_ ...

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. 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 In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

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''.

References

Accelerator physics {{accelerator-stub