  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.
