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Related to Brehmsstrahlung: characteristic radiation, inverse bremsstrahlung, Bremsstrahlung effect


(brĕm`shträ'ləng): see X rayX ray,
invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10−8 m to about 10−11
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In a narrow sense, the electromagnetic radiation emitted by electrons when they pass through matter. Charged particles radiate when accelerated, and in this case the electric fields of the atomic nuclei provide the force which accelerates the electrons. The continuous spectrum of x-rays from an x-ray tube is that of the bremsstrahlung; in addition, there is a characteristic x-ray spectrum due to excitation of the target atoms by the incident electron beam. The major energy loss of high-energy (relativistic) electrons (energy greater than about 10 MeV, depending somewhat upon material) occurs from the emission of bremsstrahlung, and this is the major source of gamma rays in a high-energy cosmic-ray shower. See Electromagnetic radiation

In a broader sense, bremsstrahlung is the radiation emitted when any charged particle is accelerated by any force. To a great extent, as a source of photons in the ultraviolet and soft x-ray region for the investigation of atomic structure (particularly in solids), bremsstrahlung from x-ray tubes has been replaced by synchrotron radiation. Synchrotron radiation is an analog to bremsstrahlung, differing in that the force which accelerates the electron is a macroscopic (large-scale) magnetic field.


(brem -shtrah-lûng) (literally: ‘braking radiation’) Electromagnetic radiation arising from the rapid deceleration of electrons in the vicinity of an atom or ion. It has a continuous spectrum. See synchrotron emission; thermal emission.



(or braking radiation), the electromagnetic radiation emitted by a charged particle when it is deflected or retarded in an electric field. The related term “magnetobrak-ing radiation” is sometimes applied to the radiation emitted by relativistic charged particles moving in macroscopic magnetic fields in, for example, accelerators or outer space; a more common term for such radiation, however, is “synchrotron radiation.”

According to classical electrodynamics, which describes the basic regularities of bremsstrahlung rather accurately, the intensity of bremsstrahlung is proportional to the square of the acceleration of the charged particle (seeRADIATION, ELECTRO MAGNETIC). Since the acceleration is inversely proportional to the mass m of the particle, the bremsstrahlung emitted by the lightest

Figure 1. Theoretical energy spectra of bremsstrahlung photons, screening being taken into account, In lead (four upper curves) and in aluminum (lowest curve): (Eδ) photon energy, (I) intensity in arbitrary units, (TC) initial kinetic energy of electron; the numbers on the curves indicate Tr in units of the rest energy of the electron mtC2 ≈ 0.511 MeV

charged particle, that is, an electron, will be millions of times more intense than the bremsstrahlung emitted by a proton in the same field. For this reason, the bremsstrahlung most often observed and most frequently used in practical applications is that resulting from the deflection of electrons by the electrostatic fields of atomic nuclei and electrons. In particular, the X rays generated in X-ray tubes and the gamma radiation emitted by fast electrons during their passage through a substance are of this nature.

The spectrum of the bremsstrahlung photons is continuous; it breaks off at the maximum possible energy, which is equal to the initial energy of the electron. The intensity of bremsstrahlung is proportional to the square of the atomic number Z of the nucleus in whose field the electron is retarded. This circumstance can be explained by reference to Coulomb’s law and Newton’s second law: according to Coulomb’s law, the force f of interaction between the electron and nucleus is proportional to the charge of the nucleus Ze, where e is the elementary electric charge; according to Newton’s second law, the acceleration is a = f/m. When an electron with energy greater than some critical energy E0 moves in a substance, the electron is slowed primarily through the generation of bremsstrahlung. For example, E0 = 10 million electron volts (MeV) for lead and E0 ≈ 200 MeV for air. At lower energies, energy losses as a result of excitation and ionization of atoms predominate.

The deflection of an electron in the electric field of a nucleus and atomic electrons is a purely electromagnetic process and is most accurately described by quantum electrodynamics (seeQUANTUM FIELD THEORY). For electron energies that are not extremely high, good agreement between theory and experiment can be obtained by considering only the Coulomb field of the nucleus. According to quantum electrodynamics, within the field of the nucleus there is a definite probability of the quantum transition of the electron to a state of lower energy with the emission of, generally, a single photon (the probability of the emission of a greater number of photons is low). Since the photon’s energy E is equal to the difference between the initial and final energies of the electron, the spectrum of bremsstrahlung (Figure 1) has a sharp boundary at the photon energy that is equal to the initial kinetic energy of the electron Te. The probability of radiation during the elementary deflection event is proportional to Z2; consequently, targets made of materials with a high Z, such as lead and platinum, are used to increase the yield of bremsstrahlung photons from electron beams.

The angular distribution of bremsstrahlung depends strongly on Te. In the nonrelativistic case (Temec2, where me is the mass of the electron and c is the speed of light), bremsstrahlung is similar to the radiation of an electric dipole that is perpendicular to the plane of the electron trajectory. At high energies (Te >> mec2), bremsstrahlung has the direction of the forward motion of the electron and is concentrated within a cone with an angle of opening of the order of θ = mec2/Te radians (Figure 2). This property

Figure 2. Angular distribution of bremsstrahlung at high initial electron energies (Tr >> mec2)

is made use of to obtain intense high-energy photon beams in electron accelerators. Bremsstrahlung is partially polarized.

The theory of bremsstrahlung can be further refined by taking into account the screening of the Coulomb field of a nucleus by the atomic electrons. Corrections for screening are substantial at Te >> Mec2 and Er << Te. These corrections decrease the probability of bremsstrahlung, since the effective field is weaker than the Coulomb field of the nucleus.

The properties of the bremsstrahlung produced in the passage of electrons through a substance are affected by phenomena associated with the structure of the medium and with the multiple scattering of the electrons. If Te >> 100 MeV, multiple scattering shows up in another way: during the time required to emit a photon, the electron travels a considerable distance and may experience collisions with other atoms. Generally speaking, in amorphous substances multiple scattering at high energies results in a decrease in intensity and a widening of the bremsstrahlung beam. The passage of high-energy electrons through crystals results in interference phenomena: sharp maxima appear in the bremsstrahlung spectrum, and the degree of polarization increases (Figure 3).

Figure 3. Polarization (upper curve) and energy spectrum (lower curve) of bremsstrahlung photons as a function of Eδ in units of the total initial energy of the electron Ee = Tr + mec2 for Ee = 1 gigaelectron volt: (P) polarization, (I) intensity in arbitrary units

Thermal motion in a hot rarefied plasma (with a temperature of 1050 – 1060 or higher) can produce substantial bremsstrahlung, which is sometimes called thermal bremsstrahlung. The elementary bremsstrahlung events are due to collisions of the charged particles making up the plasma. Cosmic X rays, which became observable with the advent of artificial earth satellites, apparently are, to some extent, thermal bremsstrahlung. Indeed, the radiation of some discrete X-ray sources may consist entirely of such bremsstrahlung.

Bremsstrahlung in the X-and gamma-ray regions is widely used in technology, in medicine, and in biological, chemical, and physical research.


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Sokolov, A. A., and I. M. Ternov. Reliativistskii elektron. Moscow, 1974.



Radiation that is emitted by an electron accelerated in its collision with the nucleus of an atom.