Editing Cyclotron radiation (section)

==Properties==
The [[Power (physics)|power]] (energy per unit time) of the emission of each electron can be calculated:<ref>{{cite book|last1=Longair|first1=Malcolm S.|title=High Energy Astrophysics: Volume 2, Stars, the Galaxy and the Interstellar Medium|date=1994|publisher=[[Cambridge University Press]]|isbn=9780521435840|page=232|url=https://books.google.com/books?id=x1TMSMpzD2UC&pg=PA232|language=en}}</ref>

: <math>{-dE \over dt}={\sigma_t B^2 v^2 \over c \mu_0} </math>

where ''E'' is energy, ''t'' is time, <math> \sigma_t </math> is the [[Thomson cross section]] (total, not differential), ''B'' is the magnetic field strength, ''v'' is the velocity perpendicular to the magnetic field, ''c'' is the speed of light and <math> \mu_0 </math> is the [[permeability of free space]].{{verify source|date=December 2023}}

Cyclotron radiation has a spectrum with its main spike at the same fundamental frequency as the particle's orbit, and [[harmonic]]s at higher integral factors. Harmonics are the result of imperfections in the actual emission environment, which also create a broadening of the [[spectral line]]s.<ref>{{cite book|last1=Hilditch|first1=R. W.|title=An Introduction to Close Binary Stars|date=2001|publisher=Cambridge University Press|isbn=9780521798006|page=327|url=https://books.google.com/books?id=hJSADIxyheoC&pg=PA327|language=en}}</ref> The most obvious source of line broadening is non-uniformities in the magnetic field;<ref>{{cite book|last1=Cairns|first1=R. A.|title=Plasma Physics|date=2012|publisher=Springer|isbn=9789401096553|page=SA7–PA8|url=https://books.google.com/books?id=-3agBwAAQBAJ&pg=SA7-PA8|language=en}}</ref> as an electron passes from one area of the field to another, its emission frequency will change with the strength of the field. Other sources of broadening include collisional broadening<ref>{{cite conference |url=http://www-naweb.iaea.org/napc/physics/2ndgenconf/data/Proceedings%201958/papers%20Vol32/Paper47_Vol32.pdf |title=Cyclotron Radiation from a Magnetized Plasma |last1=Hayakawa |first1=S |last2=Hokkyō|first2=N |last3=Terashima |first3=Y |last4=Tsuneto |first4=T. |date=1958 |conference=2nd Geneva Conference on Peaceful Uses of Atomic Energy }}</ref> as the electron will invariably fail to follow a perfect orbit, distortions of the emission caused by interactions with the surrounding plasma, and [[special relativity|relativistic]] effects if the charged particles are sufficiently energetic.  When the electrons are moving at relativistic speeds, cyclotron radiation is known as [[synchrotron radiation]].

The recoil experienced by a particle emitting cyclotron radiation is called [[radiation reaction]]. Radiation reaction acts as a resistance to motion in a cyclotron; and the work necessary to overcome it is the main energetic cost of accelerating a particle in a cyclotron. Cyclotrons are prime examples of systems which experience radiation reaction.