Cyclotron resonance frequency

The Cyclotron Resonance Frequency calculator compute the resonance frequency (ƒ) of a particle based on the mass of the particle (m), the charge (q) and the magnetic field (B).

INSTRUCTIONS: Choose units and enter the following:

• (q) Charge of the Particle
• (m) Mass of the Particle
• (B) Magnetic Field strength

Cyclotron Frequency(ƒ): The calculator returns the frequency in hertz.  However, this can be automatically converted to compatible units via the pull-down menu.

Related Calculators

• Centripetal Force Formula

The Math / Science

The formula for the Cyclotron Frequency is:

             `ƒ = (q·B) / (2·π·m)`

where:

• ƒ is the cyclotron resonance frequency (aka gyrofrequency)
• q is the charge of the particle
• m is the mass of the particle
• B is the magnetic field strength

A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field. 

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