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On radiation by electrons in a betatron

Julian Schwinger produced this paper in preprint form in 1945 and, apparently, distributed it only to a few selected colleagues at the time. He later presented the results as a 15-minute invited paper in 1946, at an American Physical Society meeting, under the title "Electron Radiation in High Energy Accelerators" (the abstract is published in Phys. Rev. 70, 798 (1946)). Although he published this work four years later in revised form ("On the Classical Radiation of Accelerated Electrons," Phys. Rev. 75, 1912 (1949)), this original version seems fresher and, in some respects, superior to the published one, hence my motivation to make it widely available. For example, the discussion of coherent radiation (shielded and unshielded) included in this version was wholly omitted in the published paper. In addition, this version exhibits many explicit calculations that are of pedagogical value even today for students of synchrotron radiation. But perhaps the most interesting aspect of this paper is that it shows so well the author's superb dexterity in manipulating mathematical expressions to obtain physical conclusions with clarity and efficiency.