Cyclotron resonance

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

The cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicular to the direction of a uniform magnetic field B (constant magnitude and direction). Since that motion is always circular, the cyclotron frequency is given by equality of centripetal force and magnetic Lorentz force

$\frac{mv^2}{r} = qBv$

with the particle mass m, its charge q, velocity v, and the circular path radius r, also called gyroradius.

By substitution for the circulation frequency $f = \frac{v}{2 \pi r}$ which defines the cyclotron frequency, this leads to

$f = \frac{q B}{2\pi m}$.

See also

• Gyroradius
• Cyclotron
• Ion cyclotron resonance
• Electron cyclotron resonance
• Calculate Cyclotron frequency with Wolfram Alpha