![]() Synchrotron radiation from a bending magnet Synchrotron radiation from an undulator Synchrotron from an astronomical source History When the source follows a circular geodesic around the black hole, the synchrotron radiation occurs for orbits close to the photosphere where the motion is in the ultra-relativistic regime. In astrophysics, synchrotron emission occurs, for instance, due to ultra-relativistic motion of a charged particle around a black hole. For particles in the mildly relativistic range (≈85% of the speed of light), the emission is termed gyro-synchrotron radiation. Radiation emitted by charged particles moving non-relativistically in a magnetic field is called cyclotron emission. The general term for radiation emitted by particles in a magnetic field is gyromagnetic radiation, for which synchrotron radiation is the ultra-relativistic special case. Synchrotron radiation is similar to bremsstrahlung radiation, which is emitted by a charged particle when the acceleration is parallel to the direction of motion. Pictorial representation of the radiation emission process by a source moving around a Schwarzschild black hole in a de Sitter universe. The radiation produced in this way has a characteristic polarization, and the frequencies generated can range over a large portion of the electromagnetic spectrum. It is produced artificially in some types of particle accelerators or naturally by fast electrons moving through magnetic fields. Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity ( a ⊥ v). For details on the production of this radiation and applications in laboratories, see Synchrotron light source. It is obviously of great importance, in both reading and writing on the subject of stellar atmospheres, to be very clear as to the meaning intended by such terms as "intensity".This article is about physical phenomenon of synchrotron radiation. The use of the adjective "specific" does little to help, since in most contexts in physics, the adjective "specific" is understood to mean "per unit mass". This is clearly a quite different usage of the word intensity and the symbol \(I\) that we have used hitherto. In the literature of stellar atmospheres, however, the term used for radiance is often "specific intensity" or even just "intensity" and the symbol used is \(I\). Radio astronomers usually use the term "surface brightness". Thus \(L = B\), and we see that the two definitions, namely surface brightness and radiance, are equivalent, and will henceforth be called just radiance. But the radiance \(L\) of a point on the right hand surface is the irradiance of the point in the left hand surface from unit solid angle of the former. But \(dA \cos \theta/r^2 = d\omega\), the solid angle subtended by \(dA\). The irradiance of a surface at a distance \(r\) away is \(dE = dI/r^2 =BdA \cos \theta / r^2\). ![]() The intensity radiated in that direction by an element of area \(dA\) is \(dI = BdA\cos \theta\). In the figure the surface brightness at some point on a surface in a direction that makes an angle \(\theta\) with the normal is \(B\). Henceforth we can use the one term radiance and the one symbol \(L\) for either, and either definition will suffice to define radiance. We see, then, that radiance \(L\) and surface brightness \(B\) are one and the same thing. Therefore, by definition, \(\delta E / \delta \omega\) is \(L\), the radiance. But \(\delta A \ \cos \theta/r^2\) is the solid angle \(\delta \omega\) subtended by the elemental area at the observer. The irradiance of an observer at a distance \(r\) from the elemental area is \(\delta E = \delta I/r^2 = B \delta A \ \cos \theta / r^2\). We suppose the surface brightness to be \(B\), and, since surface brightness is defined to be intensity per unit projected area, the intensity in the direction of interest is \(B \delta A \ \cos \theta\). \), the area projected on a plane at right angles to that direction is \(\delta A \ \cos \theta\).
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