De-bremsstrahlung.ogg (Media help·De-bremsstrahlung.ogg), (from the German bremsen, to brake and Strahlung, radiation, thus, "braking radiation"), is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum. The phenomenon was discovered by Nikola Tesla 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 (acceleration) that causes the emission. Strictly speaking, bremsstrahlung refers to any radiation due to the acceleration of a charged particle, which includes synchrotron radiation; however, it is frequently used (even when not speaking German) in the more literal and narrow sense of radiation from electrons stopping in matter.

Outer

"Outer bremsstrahlung" is the term applied in cases where the energy loss by radiation greatly exceeds that by ionization as a stopping mechanism in matter. This is seen clearly for electrons with energies above 50 keV.

Inner

"Inner bremsstrahlung" is the term applied to the less frequent case of radiation emission during beta decay, resulting in the emission of a photon 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 field in the region of the nucleus of the atom undergoing decay, in a manner similar to that which causes outer bremsstrahlung. In electron and positron emission the photon's energy comes from the electron/neutron 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, 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 the primary radiation (beta particles). In some cases, e.g. ³²P, the Bremsstrahlung produced by shielding this radiation with the normally used dense materials (i.e. lead) is itself dangerous; in such cases, shielding must be accomplished with low density materials, e.g. Plexiglas, acrylic, Lucite, plastic, wood, or water ^*; because the rate of deceleration of the electron is slower, the radiation given off has a longer wavelength and is therefore less penetrating.

The case where acceleration is parallel to velocity

If a particle of charge $q$ experiences an acceleration $\backslash vec\{a\}$ which is collinear with its velocity $\backslash vec\{v\}$, the angular distribution of the bremsstrahlung is

$\backslash frac\{dP\}\{d\backslash Omega\}\; =\; \backslash frac\{\backslash mu\_0\; q^2\; a^2\}\{16\; \backslash pi^2\; c\}\backslash frac\}\{(1\; -\; \backslash beta\; \backslash cos\{\backslash theta\})^5\}$,

where $\backslash beta\; =\; \backslash frac\{v\}\{c\}$ and $\backslash theta$ is the angle from $\backslash vec\{a\}$.

Integration by parts then gives the total power emitted as

$P\; =\; \backslash frac\{\backslash mu\_0\; q^2\; a^2\; \backslash gamma^6\}\{6\; \backslash pi\; c\}$,

where $\backslash gamma\; =\; \backslash frac\{1\}\{\backslash sqrt\{1\; -\; \backslash frac\{v^2\}\{c^2\}\}\}$ is the Lorentz factor.

Note that, since $\backslash gamma\; =\; \backslash frac\{E\}\{m\; c^2\}$, for a given energy E, $P\; \backslash propto\; \backslash frac\{1\}\{m^6\}$. So, if an electron and muon have the same energy E, the electron will emit $207^6\; =\; 7.87\; \backslash times\; 10^\{13\}$ times more radiation than the muon. This is why muons have such high penetrating power - they lose very little energy via bremsstrahlung.
Reference: "Introduction to Electrodynamics", 3rd edition, David J. Griffiths, pages 463 - 464.

From a plasma

In a plasma the free electrons are constantly producing Bremsstrahlung in collisions with the ions. The power density of the Bremsstrahlung radiated is given by

$P\_\{Br\}=\backslash frac\{16\backslash alpha^3\backslash hbar^2\}\{m\_e^\{3/2\}\backslash sqrt\{3\}\}n\_e^2T\_e^\{1/2\}Z\_\{eff\}$

T_e is the electron temperature, α is the fine structure constant, and the "effective" ion charge state Z_eff is given by an average over the charge states of the ions:

Z_eff = Σ (Z²n_Z) / n_e

This formula is derived in "Basic Principles of Plasmas Physics: A Statistical Approach" by S. Ichimaru, p. 228. It applies for high enough T_e that the electron deBroglie wavelength is longer than the classical Coulomb distance of closest approach. In practical units, this formula gives

{| P_Br = (1.69×10^-32 W cm^-3) (n_e/cm^-3)² (T_e/eV)^1/2 Z_eff   = (5.34×10^-37 W m^-3) (n_e/m^-3)² (T_e/keV)^1/2 Z_eff

For very high temperatures there are relativistic corrections to this formula, that is, additional terms of order T_e/m_ec².^*

See also

• synchrotron light or cyclotron radiation
• Section on Bremsstrahlung losses in the article on nuclear fusion
• Section on History in the article on X-rays

External links