Cyclotron resonance

The cyclotron frequency (also gyration ) is the rotational frequency of charged particles (mostly electrons) in a homogeneous magnetic field. An alternating electric field with a frequency equal to the cyclotron frequency is used in particle physics in cyclotrons.

General

Is the cyclotron frequency matches the rotational frequency of the wave vector of the charged particle on the cyclotron.

It is proportional to the magnetic flux density and is dependent upon the mass and the charge of the particle as follows:

The cyclotron frequency is independent of the path radius, and therefore, leads to a characteristic absorption of electromagnetic waves (see cyclotron resonance ) by located in a magnetic field, charged particles. Is twice as large as the Larmor frequency.

The name comes from the cyclotron particle accelerator cyclotron. Here, the constancy of the rotational frequency of charged particles is utilized in a magnetic field, in order to speed up an alternating electric field.

Derivation

In the magnetic field, the Lorentz force acts as a centripetal force and deflects charged particles into a circular path from. Your overall rate is not changed, thus the magnitude of the Lorentz force remains the same. The result is a uniform circular motion:

Relativistic effects

The above relationship is valid only if is negligibly small compared to the speed of light. The relativistic formula is valid for all speeds

Where the Lorentz factor.

More

As cyclotron energy is referred to

With - Planck's constant and

.

Essays that use the Gaussian CGS system with the flux density B in the unit Gaussian, the charge q in units of Franklin and the mass m in units of grams, the cyclotron frequency is usually defined as

Is the magnetic length Landau'sche

In this way are often equations in which the magnetic field is expressed by and, formally identical to the corresponding equations in the SI system.