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Its nonrelativistic reduction reduces to Larmor's original formula. For high-energies, it appears that the power radiated for acceleration parallel to the velocity is a factor larger than that for perpendicular acceleration. However, writing the Liénard formula in terms of the velocity gives a misleading implication.
The power radiated by a charged particle is given by a generalization of the Larmor formula derived by Liénard in 1898 [1] [2]
Bremsstrahlung produced by a high-energy electron deflected in the electric field of an atomic nucleus. In particle physics, bremsstrahlung / ˈ b r ɛ m ʃ t r ɑː l ə ŋ / [1] (German pronunciation: [ˈbʁɛms.ʃtʁaːlʊŋ] ⓘ; from German bremsen 'to brake' and Strahlung 'radiation') is electromagnetic radiation produced by the deceleration of a charged particle when deflected by ...
Electromagnetic field (arbitrary unit) of a positive point charge moving at constant speed. When =, the electromagnetic field reduces to electrostatic field (in blue).Due to its insignificance at large distance, this field is ignored in high energy physics when computing electromagnetic radiation power.
Classically, the radiated power P from an accelerated electron is: = this comes from the Larmor formula; where ε 0 is the vacuum permittivity, e is elementary charge, c is the speed of light, and a is the acceleration. Within a circular orbit such as a storage ring, the non-relativistic case is simply the centripetal acceleration.
Using this fact in the classical limit, the radiated power according to the relativistic generalization of the Larmor formula becomes: [13] = As a result, emission is improved by higher values of and, therefore, some considerations can be done on which are the conditions for prolific emission, further evaluating the definition .
According to the Larmor formula in classical electromagnetism, a single point charge under acceleration will emit electromagnetic radiation. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted. [ 1 ]
Bremsstrahlung#Dipole approximation discusses the power radiated from an accelerated charge, but the formulas are different from this article. I don't see how to reconcile them. At the very least I expect the two articles to cross-reference each other and explain the different assumptions that lead to the different formulas.