Cyclotron resonance

Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus moving on a circular path.

Since the motion in an orthogonal and constant magnetic field is always circular,[1] the cyclotron frequency is given by equality of centripetal force and magnetic Lorentz force with the particle mass m, its charge q, velocity v, and the circular path radius r, also called gyroradius.

This is only true in the non-relativistic limit, and underpins the principle of operation of the cyclotron.

When the charged particle begins to approach relativistic speeds, the centripetal force should be multiplied by the Lorentz factor, yielding a corresponding factor in the angular frequency: The above is for SI units.

[2] In Gaussian units, the Lorentz force differs by a factor of 1/c, the speed of light, which leads to: For materials with little or no magnetism (i.e.

, so we can use the easily measured magnetic field intensity H instead of B:[3] Note that converting this expression to SI units introduces a factor of the vacuum permeability.

For some materials, the motion of electrons follows loops that depend on the applied magnetic field, but not exactly the same way.