Statistical signal processing

2013-09-26T12:51:53Z

158.132.148.35: /* Further reading */

'''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}}

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Statistical signal processing