Editing Bremsstrahlung (section)

== Sources ==

=== X-ray tube ===
[[File:TubeSpectrum-en.svg|thumb|Spectrum of the X-rays emitted by an [[X-ray tube]] with a [[rhodium]] target, operated at 60 [[kilovolt|kV]]. The continuous curve is due to bremsstrahlung, and the spikes are [[energy-dispersive X-ray spectroscopy|characteristic K lines]] for rhodium. The curve goes to zero at 21 [[picometer|pm]] in agreement with the [[Duane–Hunt law]], as described in the text.]]
{{main|X-ray tube}}
In an [[X-ray tube]], electrons are accelerated in a vacuum by an [[electric field]] towards a piece of material called the "target". X-rays are emitted as the electrons hit the target.

Already in the early 20th century physicists found out that X-rays consist of two components, one independent of the target material and another with characteristics of [[fluorescence]].<ref name=":0">{{Cite book |last=Eckert |first=Michael |url=https://books.google.com/books?id=kzMPEAAAQBAJ&pg=PA28 |title=Establishing Quantum Physics in Munich: Emergence of Arnold Sommerfeld’s Quantum School |date=2020-12-15 |publisher=Springer Nature |isbn=978-3-030-62034-9 |language=en}}</ref> Now we say that the output spectrum consists of a continuous spectrum of X-rays with additional sharp peaks at certain energies. The former is due to bremsstrahlung, while the latter are [[characteristic x-ray|characteristic X-rays]] associated with the atoms in the target. For this reason, bremsstrahlung in this context is also called '''continuous X-rays'''.<ref>{{cite book|author=S. J. B. Reed|title=Electron Microprobe Analysis and Scanning Electron Microscopy in Geology| url=https://books.google.com/books?id=9-_v4YgpoVMC&pg=PA12|year=2005|publisher=Cambridge University Press|isbn=978-1-139-44638-9|page=12}}</ref> The German term itself was introduced in 1909 by [[Arnold Sommerfeld]] in order to explain the nature of the first variety of X-rays.<ref name=":0" />

The shape of this continuum spectrum is approximately described by [[Kramers' law]].

The formula for Kramers' law is usually given as the distribution of intensity (photon count) <math>I</math> against the [[wavelength]] <math>\lambda</math> of the emitted radiation:<ref name="laguitton">{{cite journal| doi=10.1002/xrs.1300060409| last=Laguitton| first=Daniel| author2=William Parrish | date=1977| title=Experimental Spectral Distribution versus Kramers' Law for Quantitative X-ray Fluorescence by the Fundamental Parameters Method| journal=X-Ray Spectrometry| volume=6| issue=4| pages=201| bibcode=1977XRS.....6..201L}}</ref>
<math display="block"> I(\lambda) \, d\lambda = K \left( \frac{\lambda}{\lambda_{\min}} - 1 \right)\frac{d\lambda}{\lambda^2} </math>

The constant {{math|''K''}} is proportional to the [[atomic number]] of the target element, and <math>\lambda_{\min}</math> is the minimum wavelength given by the [[Duane–Hunt law]].

The spectrum has a sharp cutoff at {{nowrap|<math>\lambda_{\min}</math>,}} which is due to the limited energy of the incoming electrons. For example, if an electron in the tube is accelerated through 60 [[kilovolt|kV]], then it will acquire a kinetic energy of 60 [[electronvolt|keV]], and when it strikes the target it can create X-rays with energy of at most 60 keV, by [[conservation of energy]]. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray [[photon]]. Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of at most 60&nbsp;keV has wavelength of at least {{val|21|ul=pm}}, so the continuous X-ray spectrum has exactly that cutoff, as seen in the graph. More generally the formula for the low-wavelength cutoff, the Duane–Hunt law, is:<ref>{{cite book|author1=Rene Van Grieken| author2=Andrzej Markowicz|title=Handbook of X-Ray Spectrometry|url=https://books.google.com/books?id=i_iDRTp75AsC&pg=PA3| year=2001| publisher=CRC Press| isbn=978-0-203-90870-9|page=3}}</ref>
<math display="block">\lambda_\min = \frac{h c}{e V} \approx \frac{1239.8}{V}\,\mathrm{pm/kV}</math>
where {{math|''h''}} is the [[Planck constant]], {{math|''c''}} is the [[speed of light]], {{mvar|V}} is the [[voltage]] that the electrons are accelerated through, {{math|''e''}} is the [[elementary charge]], and {{math|pm}} is [[picometre]]s.

=== Beta decay ===
{{main|Beta decay}}
Beta particle-emitting substances sometimes exhibit a weak radiation with continuous spectrum that is due to bremsstrahlung (see the "outer bremsstrahlung" below). In this context, bremsstrahlung is a type of "secondary radiation", in that it is produced as a result of stopping (or slowing) the primary radiation ([[beta particle]]s). It is very similar to X-rays produced by bombarding metal targets with electrons in [[X-ray generator]]s (as above) except that it is produced by high-speed electrons from beta radiation.

==== Inner and outer bremsstrahlung ====
The "inner" bremsstrahlung (also known as "internal bremsstrahlung") arises from the creation of the electron and its loss of energy (due to the strong [[electric field]] in the region of the nucleus undergoing decay) as it leaves the nucleus. Such radiation is a feature of beta decay in nuclei, but it is occasionally (less commonly) seen in the beta decay of free neutrons to protons, where it is created as the beta electron leaves the proton.

In electron and [[positron]] emission by beta decay the photon's energy comes from the electron-[[nucleon]] pair, with the spectrum of the bremsstrahlung decreasing continuously with increasing energy of the beta particle. In electron capture, the energy comes at the expense of the [[neutrino]], and the spectrum is greatest at about one third of the normal neutrino energy, decreasing to zero electromagnetic energy at normal neutrino energy. Note that in the case of electron capture, bremsstrahlung is emitted even though no charged particle is emitted. Instead, the bremsstrahlung radiation may be thought of as being created as the captured electron is accelerated toward being absorbed. Such radiation may be at frequencies that are the same as soft [[gamma radiation]], but it exhibits none of the sharp spectral lines of [[gamma decay]], and thus is not technically gamma radiation.

The internal process is to be contrasted with the "outer" bremsstrahlung due to the impingement on the nucleus of electrons coming from the outside (i.e., emitted by another nucleus), as discussed above.<ref>{{Cite journal |doi= 10.1016/S0031-8914(36)80008-1 |issn= 0031-8914 |volume= 3 |issue= 6 |pages= 425–439 |last= Knipp |first= J.K. |author2= G.E. Uhlenbeck |title= Emission of gamma radiation during the beta decay of nuclei |journal= Physica |date= June 1936 |bibcode= 1936Phy.....3..425K }}</ref>

==== Radiation safety ====
In some cases, such as the decay of {{chem|link=Phosphorus-32|32|P}}, the bremsstrahlung produced by [[radiation shield|shielding]] the beta radiation with the normally used dense materials (e.g. [[lead]]) is itself dangerous; in such cases, shielding must be accomplished with low density materials, such as  [[Plexiglas]] ([[Lucite]]), [[plastic]], [[wood]], or [[water]];<ref>{{Cite web | url=https://ehs.umich.edu/wp-content/uploads/sites/37/2016/04/Phosphorus-32.pdf | title=Environment, Health & Safety | access-date=2018-03-14 | archive-url = https://web.archive.org/web/20170701033144/http://ehs.umich.edu/wp-content/uploads/sites/37/2016/04/Phosphorus-32.pdf | archive-date = 2017-07-01 | url-status=dead }}</ref> as the atomic number is lower for these materials, the intensity of bremsstrahlung is significantly reduced, but a larger thickness of shielding is required to stop the electrons (beta radiation).

=== In astrophysics ===
The dominant luminous component in a cluster of galaxies is the 10<sup>7</sup> to 10<sup>8</sup> kelvin [[intracluster medium]]. The emission from the intracluster medium is characterized by thermal bremsstrahlung. This radiation is in the energy range of X-rays and can be easily observed with space-based telescopes such as [[Chandra X-ray Observatory]], [[XMM-Newton]], [[ROSAT]], [[Advanced Satellite for Cosmology and Astrophysics|ASCA]], [[EXOSAT]], [[Suzaku (satellite)|Suzaku]], [[Reuven Ramaty High Energy Solar Spectroscopic Imager|RHESSI]] and future missions like [[International X-ray Observatory|IXO]] [https://web.archive.org/web/20080303062108/http://constellation.gsfc.nasa.gov/] and Astro-H [https://web.archive.org/web/20071112015825/http://www.astro.isas.ac.jp/future/NeXT/].

Bremsstrahlung is also the dominant emission mechanism for [[H II region]]s at radio wavelengths.

=== In electric discharges ===
In electric discharges, for example as laboratory discharges between two electrodes or as lightning discharges between cloud and ground or within clouds, electrons produce Bremsstrahlung photons while scattering off air molecules. These photons become manifest in [[terrestrial gamma-ray flashes]] and are the source for beams of electrons, positrons, neutrons and protons.<ref>{{cite journal |last1=Köhn |first1=C. |last2=Ebert |first2=U.|author2-link= Ute Ebert |title=Calculation of beams of positrons, neutrons, and protons associated with terrestrial gamma ray flashes |journal= Journal of Geophysical Research: Atmospheres|year=2015 |volume=120 |issue=4 |pages=1620–1635 |doi=10.1002/2014JD022229 |bibcode=2015JGRD..120.1620K |url=https://ir.cwi.nl/pub/23845 |doi-access=free }}</ref> The appearance of Bremsstrahlung photons also influences the propagation and morphology of discharges in nitrogen–oxygen mixtures with low percentages of oxygen.<ref>{{cite journal |last1=Köhn |first1=C. |last2=Chanrion |first2=O. |last3=Neubert |first3=T. |title=The influence of bremsstrahlung on electric discharge streamers in N<sub>2</sub>, O<sub>2</sub> gas mixtures |journal= Plasma Sources Science and Technology|year=2017 |volume=26 |issue= 1|pages=015006 |doi=10.1088/0963-0252/26/1/015006 |bibcode=2017PSST...26a5006K |doi-access=free }}</ref>