Angular Distribution of Betatron Target Radiation

An attempt is made to combine the bremsstrahlung intrinsic energy-angle distribution for radiated photons with Moli\`ere's multiple-scattering theory for the incident electrons.The angular distribution of betatron radiation is essentially characterized by a function I(θ), which is given as a series in inverse powers of Moli\`ere's parameter B. The first term of this expansion, which is dominant for small angles, is equivalent to a combination theory developed on the basis of a Gaussian approximation for multiple scattering. This term is worked out exactly and its final expression may be compared with previous theories which depend upon mathematical approximations. The term of order B^-1 becomes important for larger angles and gives the transition to the contribution of single-scattered electrons. Expressions for the forward radiation and energy-angle distribution are given. The angular distribution predicted by these results was found to be in good agreement with an experiment performed by Lanzl and Hanson.