SYNCHROTRON LIGHT IN A NUTSHELL
Surface review and letters
I present an extremely simple derivation of the underlying physics and basic equations of the five most important properties of synchrotron light sources. The use of synchrotron sources is widespread in different disciplines, and in a state of explosive growth. Paradoxically, many users do not understand the simple physical causes of their amazing properties. In a recent article, I demonstrated 1 that such properties can be derived with a very simple approach -and no integrals at all.. I now
... s at all.. I now present an even simpler derivation for a subset of the synchrotron light properties. This allows the underlying physics to stand up clearly, not cluttered by mathematical formalism. The treated propertied are (1) the spectrum (peak and bandwidth) and the angular spread of an undulator; (2) the spectrum (peak and bandwidth) and the angular spread of a bending magnet and of a wiggler; (3) flux and brightness; (4) polarization (5) coherence. I will assume that the reader is already qualitatively and generally familiar with the components of a synchrotron source, i.e., the storage ring with its bending magnets and insertion devices (wigglers and undulators). Before going into the detailed discussion, we need a minimum of background. The most important physical point underlying the discussion is that synchrotron light production is always achieved by exploiting the combination of two relativistic effects, for example Lorentz contraction and the Doppler shift. Thus, we must recall the simple relativistic rules for changing the reference frame. As shown in Fig. 1 , in the laboratory frame we call x' the coordinate along the electron beam motion, y' the perpendicular coordinate in the plane of the storage ring and θ' the light emission angle with respect to the x-axis. The corresponding coordinates in the source frame (electron frame) are: x, y and θ.