L Journal of Alloys and Compounds 328 (2001) 35–41 www.elsevier.com / locate / jallcom Invited lecture The essential features of synchrotron radiation: an elementary approach * G. Margaritondo ´ ´´ Institut de Physique Appliquee, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland Received 12 June 2000; received in revised form 20 August 2000; accepted 22 December 2000 Abstract Synchrotron light is usually treated with a rather complicated electrodynamics formalism. However, its basic properties can be easily understood with a simple approach based on the classical emission of electromagnetic radiation by an accelerated charge in a constant or periodic magnetic field, on a combination of relativistic phenomena (Lorentz contraction and Doppler effect) and on simple Fourier-theorem arguments.  2001 Elsevier Science B.V. All rights reserved. Keywords: Synchrotron light; Electrodynamics; Electromagnetic radiation; X-rays; Coherence; Undulators; Wigglers 1. Introduction function. Starting from this classical picture, the special properties of synchrotron light can be understood as caused Synchrotron light has become a standard tool for by the relativistic motion of the emitting electrons. Their different research fields, in different disciplines. This treatment requires the standard (Lorentz) transformation of justifies an effort to make its basic properties easily special relativity between two reference frames (Fig. 1): understandable for interested colleagues without a special- ized background. This effort was initiated in Ref. [1], • The laboratory frame, with x9 the coordinate along the which derived many properties of synchrotron sources with electron beam motion, y9 the perpendicular coordinate a simplified approach and elementary mathematics. I in the plane of the storage ring and u 9 the light emission propose here a step towards additional simplification. angle with respect to the x-axis. The specific objective is to derive three basic sets of • The electron frame with the corresponding coordinates properties: (1) spectral peak, bandwidth and the angular x, y and u. Note that the ‘electron frame’ is not the spread of an undulator; (2) spectral peak, bandwidth and frame moving with the electron (which is not an inertial the angular spread of a bending magnet and of a wiggler; frame) — but the inertial frame moving along the x-axis and (3) time and spatial coherence. I assume that the with the same instantaneous speed u as the light- reader qualitatively knows the general components of a emitting electron. synchrotron source and roughly how such a source works. 2. Background Besides the above-mentioned qualitative notions, the only required additional background is the following. The emission of electromagnetic waves is caused by the acceleration of an electric charge, and the emitted power is proportional to the square of the acceleration. The emitted angular pattern of an oscillating charge in its reference 2 frame is two-lobed and described by the angular cos u Fig. 1. Coordinate systems: x and y in the source reference frame, and x9 *Tel.: 141-21-693-4465; fax: 141-21-693-4666. and y9 in the laboratory frame. The source (electron) is moving along the E-mail address: marga@dpmail.epfl.ch (G. Margaritondo). x-axis, at the speed u in the laboratory frame. 0925-8388 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388(01)01327-5