Cyclotron frequency

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The cyclotron frequency (also gyration frequency ) is the frequency of rotation 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

The cyclotron frequency corresponds to the orbital frequency of the wave vector of the charged particle on the cyclotron orbit .

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

.

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

The name cyclotron frequency comes from the cyclotron particle accelerator . Here, the constancy of the orbital frequency of charged particles in the magnetic field is used to accelerate them with an alternating electric field.

Derivation

In the magnetic field, the Lorentz force acts as a centripetal force and deflects charged particles onto a circular path. Your overall speed is not changed, so the amount of the Lorentz force also remains the same. A uniform circular motion is created:

Relativistic Effects

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

,

where is the Lorentz factor .

additional

One calls cyclotron energy

with - Planck's quantum of action and

.

Papers using the Gaussian CGS system with flux density in units of Gauss , charge in units of Franklin, and mass m in units of grams commonly define the cyclotron frequency as

Landau's magnetic length is

In this way, equations in which the magnetic field is expressed by and often become  formally identical to the corresponding equations in the International System of Units (SI) .

Individual evidence

  1. Harry Pfeifer, Herbert Schmiedel, Ralf Stannarius: Compact physics course: With virtual experiments and exercises . Springer DE, 2004, p. 246 ( limited preview in Google Book search).
  2. ^ Charles Kittel, Walter D. Knight, Malvin A. Ruderman, A Carl Helmholz, Burton J Moyer: Mechanics, Berkeley Physics Course 1 . Springer, 2001 ( limited preview in Google Book Search).