Bremsstrahlung , is
electromagnetic radiationElectromagnetic radiation is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation...
produced by the
accelerationIn physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...
of a charged particle, such as an
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
, when deflected by another charged particle, such as an
atomic nucleusThe nucleus is the very dense region consisting of nucleons at the center of an atom. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus, with a very small contribution from the orbiting electrons....
. The term is also used to refer to the process of producing the radiation.
Bremsstrahlung has a
continuousThe electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
spectrumSpectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength . In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g. by a prism. Later the concept was expanded greatly to comprise...
. The phenomenon was discovered by
Nikola TeslaNikola Tesla was an inventor and a mechanical and electrical engineer. He is frequently cited as one of the most important contributors to the birth of commercial electricity and is best known for his many revolutionary developments in the field of electromagnetism in the late 19th and early 20th...
during high frequency research he conducted between 1888 and 1897.
Bremsstrahlung may also be referred to as free-free radiation. This refers to the radiation that arises as a result of a charged particle that is free both before and after the deflection (
accelerationIn physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...
) that causes the emission. Strictly speaking,
bremsstrahlung refers to any radiation due to the acceleration of a charged particle, which includes
synchrotron radiationSynchrotron radiation is electromagnetic radiation, similar to cyclotron radiation, but generated by the acceleration of ultrarelativistic charged particles through magnetic fields....
; however, it is frequently used (even when not speaking German) in the more narrow sense of radiation from electrons stopping in matter.
The word
Bremsstrahlung is retained from the original German to describe the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the X-ray region of the electromagnetic spectrum. It is characterized by a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons is increased.
Outer Bremsstrahlung
"Outer
bremsstrahlung" is the term applied in cases where the energy loss by radiation greatly exceeds that by
ionizationIonization is the physical process of converting an atom or molecule into an ion by adding or removing charged particles such as electrons or other ions. This is often confused with dissociation ....
as a stopping mechanism in matter. This is seen clearly for electrons with energies above 50 keV.
Inner Bremsstrahlung
"Inner
bremsstrahlung" is the term applied to the less frequent case of radiation emission during
beta decayIn nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted. In the case of electron emission, it is referred to as beta minus , while in the case of a positron emission as beta plus...
, resulting in the emission of a
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic field and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
of energy less than or equal to the maximum energy available in the nuclear transition. Inner
bremsstrahlung is caused by the abrupt change in the
electric fieldIn physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. This electric field exerts a force on other electrically charged objects...
in the region of the nucleus of the atom undergoing decay, in a manner similar to that which causes outer bremsstrahlung. In electron and
positronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1, a spin of , and the same mass as an electron. When a low-energy positron collides with a low-energy electron, annihilation occurs, resulting in the production...
emission the photon's energy comes from the electron/
nucleonIn physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles. In those days their interactions defined strong interactions. Now they are known to be composite...
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
neutrinoNeutrinos are elementary particles that often travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect. Neutrinos have a minuscule, but nonzero mass...
, and the spectrum is greatest at about one third of the normal neutrino energy, reaching zero at zero energy and at normal neutrino energy.
Beta particle-emitting substances sometimes exhibit a weak radiation with continuous spectrum that is due to both outer and inner
bremsstrahlung, or to one of them alone.
Secondary radiation
Bremsstrahlung is a type of "secondary radiation", in that it is produced as a result of stopping (or slowing) the primary radiation (beta particles). In some cases,
e.g. 32P, the
Bremsstrahlung produced by shielding this radiation with the normally used dense materials (
e.g. leadLead is a main-group element with symbol Pb and atomic number 82. Lead is a soft, malleable poor metal, also considered to be one of the heavy metals. Lead has a bluish-white color when freshly cut, but tarnishes to a dull grayish color when exposed to air...
) is itself dangerous; in such cases, shielding must be accomplished with low density materials,
e.g. Plexiglass (lucite),
plasticPlastic is the general common term for a wide range of synthetic or semisynthetic organic amorphous solid materials suitable for the manufacture of industrial products...
,
woodWood is an organic material; in the strict sense wood is produced as secondary xylem in the stems of trees . In a living tree it transfers water and nutrients to the leaves and other growing tissues, and has a support function, enabling woody plants to reach large sizes or to stand up for themselves...
, or
waterWater is an ubiquitous chemical substance that is composed of hydrogen and oxygen and is essential for all known forms of life.In typical usage, water refers only to its liquid form or state, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam. Water covers 71%...
http://www.oseh.umich.edu/TrainP32.pdf; because the rate of deceleration of the electron is slower, the radiation given off has a longer
wavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
and is therefore less penetrating.
Dipole Radiation
Suppose that a particle of charge experiences an acceleration which is collinear with its velocity (this is the relevant case for
linear acceleratorsA linear particle accelerator is a type of particle accelerator that greatly increases the velocity of charged subatomic particles or ions by subjecting the charged particles to a series of oscillating electric potentials along a linear beamline; this method of particle acceleration was invented...
). Then, the relativistic expression for the angular distribution of the
bremsstrahlung (considering only the dominant dipole radiation contribution), is
-
- ,
- where and is the angle between and the point of observation.
IntegratingIn calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into other, hopefully simpler, integrals...
over all angles then gives the total power emitted as
where is the
Lorentz factorThe Lorentz factor or Lorentz term appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula. Because of its ubiquity, physicists generally represent it with the shorthand symbol γ. It gets its name from its earlier...
.
The general expression for the total radiated power is
where signifies a time derivative of . Note, this general expression for total radiated power simplifies to the above expression for the specific case of acceleration parallel to velocity , by noting that and . For the case of acceleration perpendicular to the velocity (a case that arises in circular particle accelerators known as
synchrotronA synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronized with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
s), the total power radiated reduces to
The total power radiated in the two limiting cases is proportional to or . Since , we see that the total radiated power goes as or , which accounts for why electrons lose energy to
bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed
International Linear ColliderThe International Linear Collider is a proposed linear particle accelerator. It is planned to have a collision energy of 500 GeV initially, and, if approved after the project has published its Technical Design Report, planned for 2012, could be completed in the late 2010s. A later upgrade to 1000...
) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the
Large Hadron ColliderThe Large Hadron Collider is the world's largest and highest-energy particle accelerator intended to collide opposing particle beams of either protons at an energy of 7 TeV per particle or lead nuclei at an energy of 574 TeV per nucleus...
) can utilize a circular tunnel. The electrons lose energy due to
bremsstrahlung at a rate quicker than protons do.
From plasma (thermal Bremsstrahlung)
In a plasma the free electrons are constantly producing
Bremsstrahlung in collisions with the ions. In a uniform plasma, with thermal electrons (distributed according to the
Maxwell–Boltzmann distributionThe Maxwell–Boltzmann distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions. It describes the probability of a particle's speed being near a given value as a function of the temperature of the...
with the temperature ), the power spectral density (power per angular frequency interval per volume, integrated over the whole solid angle) of the
Bremsstrahlung radiated, is calculated to be
where is the number density of electrons, is the
classical radius of electronThe classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical relativistic model of the electron...
, is its mass, is the
Boltzmann constantThe Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant N
A:...
, and is the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
. Note that the first bracketed factor has units of 1/volume and the second factor has units of energy, giving the correct total units of energy/volume. The "effective" ion charge state is given by an average over the charge states of the ions:
,
where is the number density of ions with charge .
The special function is defined in the
exponential integralIn mathematics, the exponential integral is a special function defined on the complex plane given the symbol -Definitions:For real, nonzero values of , the exponential integral can be defined as...
article, and the unitless quantity is
( is a maximum or cutoff wavenumber). when 27.2 eV (for a single ion species; 27.2 eV is twice the ionization energy of hydrogen) where K is a pure number and is a thermal electron de Broglie wavelength. Otherwise, where is the classical Coulomb distance of closest approach.
For the case , we find
.
is infinite at , and decreases rapidly with . The resulting power density, integrated over all frequencies, is finite and equals
.
The first bracketed factor has units of 1/volume, while the second has units of power. Note the appearance of the fine structure constant due to the quantum nature of . In practical units, a commonly used version of this formula is
.
This formula agrees with the theoretical estimate if we set K=3.17; the value K=3 is suggested by Ichimaru.
For very high temperatures there are relativistic corrections to this formula, that is, additional terms of order
kBTe/
mec
2.
http://theses.mit.edu/Dienst/UI/2.0/Page/0018.mit.theses/1995-130/25?npages=306
If the plasma is optically thin, the
Bremsstrahlung radiation leaves the plasma, carrying part of the internal plasma energy. This effect is known as the
Bremsstrahlung cooling.
In astrophysics
The dominant luminous component in a cluster of galaxies is the 10
7 to 10
8 Kelvin intracluster medium. The emission from the intracluster medium is characterized by thermal
Bremsstrahlung. Thermal
Bremsstrahlung radiation occurs when the particles populating the emitting plasma are at a uniform temperature and are distributed according to the
Maxwell–Boltzmann distributionThe Maxwell–Boltzmann distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions. It describes the probability of a particle's speed being near a given value as a function of the temperature of the...
where speed,
v, is defined as
The bulk emission from this gas is thermal
Bremsstrahlung. The power emitted per cubic centimeter per second can be written in the compact form
with cgs units [erg cm
−3 s
−1] and where 'ff' stands for free-free, 1.4x10
−27 is the condensed form of the physical constants and geometrical constants associated with integrating over the power per unit area per unit frequency,
ne and
ni are the electron and ion densities, respectively,
Z is the number of protons of the bending charge,
gB is the frequency averaged Gaunt factor and is of order unity, and
T is the global x-ray temperature determined from the spectral cut-off frequency
above which exponentially small amount of photons are created because the energy required for creation of such a photon is available only for electrons in the tail of the Maxwell distribution.
This process is also known as
Bremsstrahlung cooling since the plasma is optically thin to photons at these energies and the energy radiated is emitted freely into the universe.
This radiation is in the energy range of X-rays and can be easily observed with space-based telescopes such as
Chandra X-ray ObservatoryThe Chandra X-ray Observatory is a satellite launched on STS-93 by NASA on July 23, 1999. It was named in honor of Indian-American physicist Subrahmanyan Chandrasekhar who is known for determining the mass limit for white dwarf stars to become neutron stars. "Chandra" also means "moon" or...
,
XMM-NewtonThe XMM-Newton is an orbiting X-ray observatory, named in honor of Sir Isaac Newton.Originally known as the High Throughput X-ray Spectroscopy Mission, it was launched by the European Space Agency from the Guiana Space Centre at Kourou on 10 December 1999 by an Ariane 5 rocket...
,
ROSATROSAT was a German X-ray satellite telescope. It was named in honour of Wilhelm Röntgen. It was launched on June 1 1990 with a Delta II rocket from Cape Canaveral, and operated until February 12 1999.- Overview :...
,
ASCAASCA can refer to:* ASCA * Advanced Satellite for Cosmology and Astrophysics* Australian Shepherd Club of America* Amsterdam School for Cultural Analysis* American School Counseling Association* American Swimming Coaches Association...
,
EXOSATThe Exosat satellite, originally named HELOS, was operational from May 1983 until April 1986 and in that time made 1780 observations in the X-ray band of most classes of astronomical object including active galactic nuclei, stellar coronae, cataclysmic variables, white dwarfs, X-ray binaries,...
, Astro-E2,
RHESSIReuven Ramaty High Energy Solar Spectroscopic Imager is the sixth mission in the line of NASA Small Explorer missions...
and future missions like Con-X
http://constellation.gsfc.nasa.gov/ and NeXT
http://www.astro.isas.ac.jp/future/NeXT.
See also
- Cyclotron radiation
Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that...
- Free electron laser
A free-electron laser, or FEL, is a laser that shares the same optical properties as conventional lasers such as emitting a beam consisting of coherent electromagnetic radiation which can reach high power, but which uses some very different operating principles to form the beam...
- Nuclear fusion: Bremsstrahlung losses
- Radiation length
In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic-interacting particles with it.-Definition:High-energy electrons predominantly lose energy in matter...
characterising energy loss by Bremsstrahlung by high energy electrons in matter
- Synchrotron light
A synchrotron light source is a source of electromagnetic radiation produced by synchrotron radiation, which is artificially produced for scientific and technical purposes by specialized particle accelerators, typically accelerating electrons....
- X-rays: History
External links