Statistical signal processing: Difference between revisions
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'''Cyclotron resonance''' describes the interaction of external forces with charged particles experiencing a [[magnetic field]], thus already moving on a circular path. It is named after the [[cyclotron]], a cyclic [[particle accelerator]] using this resonance to add kinetic energy to charged particles. | |||
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,<ref name="Physics">Physics by M. Alonso & E. Finn, Addison Wesley 1996.</ref> the cyclotron frequency is given by equality of [[centripetal force]] and magnetic [[Lorentz force]] | |||
:<math>\frac{mv^2}{r} = qBv</math> | |||
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 <math>f = \frac{v}{2 \pi r}</math> which defines the cyclotron frequency, this leads to | |||
:<math>f = \frac{q B}{2\pi m}</math>. | |||
== See also == | |||
* [[Gyroradius]] | |||
* [[Cyclotron]] | |||
* [[Ion cyclotron resonance]] | |||
* [[Electron cyclotron resonance]] | |||
* [http://www.wolframalpha.com/input/?i=cyclotron+frequency| Calculate Cyclotron frequency with Wolfram Alpha] | |||
== References == | |||
<references /> | |||
[[Category:Condensed matter physics]] | |||
[[Category:Electric and magnetic fields in matter]] | |||
[[Category:Accelerator physics]] | |||
[[Category:Scientific techniques]] | |||
{{accelerator-stub}} | |||
Revision as of 14:51, 26 September 2013
Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator using this resonance to add kinetic energy to charged particles.
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,[1] the cyclotron frequency is given by equality of centripetal force and magnetic Lorentz force
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 which defines the cyclotron frequency, this leads to
- .
See also
- Gyroradius
- Cyclotron
- Ion cyclotron resonance
- Electron cyclotron resonance
- Calculate Cyclotron frequency with Wolfram Alpha
References
- ↑ Physics by M. Alonso & E. Finn, Addison Wesley 1996.