Angular Size of a Synchrotron Light Pattern * as a Function of Wavelength

Procedures are given for estimating the two dimensions of the angular size of a synchrotron light pattern as a function of wavelength for each of two polarization components. It is found that horizontal angular sizes (measured in the orbital plane) are substantially larger than corresponding vertical angular sizes. Except for wavelengths which are considerably smaller than a critical wavelength, a relativistic electron with bending radius R emits radiation with wavelength X into a pattern which has angular dimensions of order (X/R)1'3. Submitted to Review of Scientific Instruments J; Work supported by the Department of Energy, contract DE-AC03-76SF00515. -2INTRODUdTION To predict the resolving power of an electron beam momentum spectrum monitor' which uses synchrotron light, it was desired to estimate the horizontal width of the angular distribution of the visible light observed when an electron moves in a horizontal plane through a uniform vertical magnetic field. A knowledge of the horizontal spread may also be of value to users of synchrotron light and x-rays from storage rings. This interest reflects changes in experimental apparatus since 1949 when Schwinger2 remarked that the distribution in the horizontal angle was unobservable in practice. Direct observation remains difficult, but there is an experimentally observed effect of horizontal divergence that is beneficial. Suppose the horizontal angular width were as small as l/y, the ratio of rest energy to total energy of the radiating electron, for any wavelength, X. If so, a profile monitor situated a distance L from a source could have effective horizontal aperature at most -L/y, angular resolution no better than -Ay/L, and space resolution no better than "Xy. At PEP, profile monitors have Xy = 1.8 cm, but resolution is probably finer than the minimum observed horizontal spot size, which is 20 = 4 mm (Ref. 3). To clarify the idea of horizontal angular width, imagine that a sinusoidally oscillating dipole D is moving at a constant speed near that of light in a circular path with radius R in a horizontal plane which includes a distant observer 0, as in Fig.1. Let the wavelength of the signal received at 0 have some minimum value Xm<c R for the parts of the wavetrain which originated near T. Transit time differences will cause other parts of the wavetrain to differ in phase by 4 Y 2nR(xsinx)/X, = aRx3/3Xm from