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# Gyrofrequency

## Description

If the magnetic field is uniform and all other forces are absent, then the Lorentz force will cause a particle to undergo a constant acceleration perpendicular to both the particle velocity and the magnetic field. This does not affect particle motion parallel to the magnetic field, but results in circular motion at constant speed in the plane perpendicular to the magnetic field. This circular motion is known as the gyromotion.

The gyrofrequency (also known as cyclotron frequency) is the angular frequency of the circular motion of a charged particle moving perpendicular to the direction of a uniform magnetic field B (constant magnitude and direction). In SI units, the gyrofrequency is given by the shown formula.

The cyclotron frequency is independent of the radius and velocity and therefore independent of the particle’s kinetic energy – all particles with the same charge-to-mass ratio rotate around magnetic field lines with the same frequency.

The cyclotron frequency is also useful in non-uniform magnetic fields, in which (assuming slow variation of magnitude of the magnetic field) the movement is approximately helical – in the direction parallel to the magnetic field, the motion is uniform, whereas in the plane perpendicular to the magnetic field the movement is, as previously circular. The sum of these two motions gives a trajectory in the shape helix.

Related formulas

## Variables

 ωg gyrofrequency (rad/s) (dimensionless) q particle charge (dimensionless) B magnetic field (dimensionless) m mass of the particle (dimensionless)