Abstract
The radiation at collision of high-energy particles is formed over a rather long distances and therefore is sensitive to an environment. In particular the smallness of the transverse dimensions of the colliding beams leads to suppression of bremsstrahlung cross section for soft photons. This beam-size effect was discovered and investigated at INP, Novosibirsk around 1980. At that time an incomplete expression for the bremsstrahlung spectrum was calculated and used because a subtraction associated with the extraction of pure fluctuation process was not performed. Here this procedure is done. The complete expression for the spectral-angular distribution of incoherent bremsstrahlung probability is obtained. The case of Gaussian colliding beams is investigated in details. In the case of flat beams the expressions for the bremsstrahlung spectrum are simplified essentially. Comparison of theory with VEPP4 and HERA data is performed. Possible application of the effect to linear $e^+e^-$ collider tuning is discussed.
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