  Usually, the emission of low-energy photons in electron-positron (or
electron-ion) bunch collisions is calculated with the same approach as for
synchrotron radiation (beamstrahlung). However, for soft photons (E_gamma < E_c
where E_c is a critical photon energy), when the coherence length of the
radiation becomes comparable to the bunch length, the beamstrahlung
approximation becomes invalid. In this paper, we present results of our
calculation for this region based on approximation of classical currents. We
consider several colliders with dense bunches. The number of low-energy photons
dN_gamma emitted by N_e electrons per bunch crossing in the energy interval
dE_gamma is dN_gamma = alpha g N_e dE_gamma/E_gamma, where alpha is the
fine-structure constant, and the function g, which depends on the bunch
parameters, typically is of order unity for modern colliders. In particular,
for the ILC, we find that E_c = 83 keV and g=5.5 at a vanishing beam axis
displacement, and g=0.88, E_c=0.24 keV for KEKB. We also calculate the specific
dependence of dN_gamma on the impact parameter between the two beam axes. In
principle, the latter aspect allows for online monitoring of the beam axis
displacement.
