Properties and Possible Use of Beam-Beam Synchrotron Radiation

In large electron-positron colliding beam facilities the fields created by one beam in the crossing point are quite large and cause the particles in the other beam to radiate synchrotron radiation. The total power emitted in the form of this beam-beam synchrotron radiation is calculated for beams with a bi-Gaussian cross-section colliding head-on, and its dependence on beam separation is estimated. The radiation emitted in the forward direction is quite hard and has a complicated spectrum. However the radiation emitted at angles much larger than both 1/γ and the deflecting angle, is softer and has the properties of "short magnet" radiation. Its spectrum observed at a fixed angle is directly given by the Fourier transform of the longitudinal dependence of the deflecting field, i. e. of the longitudinal distribution of the particles in the other beam. The polarization has a simple azimuthal dependence. This radiation can be used for beam diagnostics, i. e. centring the two beams suffering a natural separation, optimizing the luminosity, measuring the bunch length.