# Cyclotron Frequency

## cyclotron frequency

[′sī·klə‚trän ‚frē·kwen·sē]## Cyclotron Frequency

the orbital frequency Ω of an electron in a constant magnetic field H in the plane perpendicular to H. For a free electron, the cyclotron frequency, or gyrofrequency, is given by the equation for the Lorentz force and the centrifugal force

Ω = *e*H/m_{0}*c*

where *e* is the charge of the free electron, *m*_{0} is its mass, and *c* is the speed of light in vacuum. For a relativistic electron, Ω = *ecH*/ℰ, where ℰ is the energy of the electron.

In solids, the motion of an electron is complicated by interaction with the crystal lattice. When a current carrier, such as a conduction electron, moves in a constant magnetic field, the carrier’s energy ℰ and the projection of its quasimomentum *p* in the direction H(*p _{c}*) are conserved, so that in momentum space (p space) the carrier moves along a curve where the plane

*p*= const, intersects the isoenergetic surface ℰ(p), If the curve is closed, the motion is periodic and occurs at the cyclotron frequency

_{c}Ω = *eH/m*c*

where *m** is the effective mass of the conduction electron.