the laboratory frame, $m_c$ is its mass, $\varepsilon_r$ is the energy of radiating particle in the laboratory frame;  $k_{\mu}=(\omega,~\omega {\bf n}))$ is the photon 4-momentum, $\vartheta$  is the angle between vectors [**n**]{} and [**v**]{}.

In the case when the transverse dimension of beam $\sigma$ is $\sigma \gg l_{f0}$ the impact parameters $\varrho \leq
\varrho_{max}=l_{f0}$ contribute. One can put that the particle density in the target beam is a constant, so that the standard QED formulas are valid. Note that the value $\varrho_{max}$ is the relativistic invariant which is defined by the minimal value of square of the invariant mass of the intermediate photon $|q^2|$. In the case when the characteristic size of beams is smaller the value $\varrho_{max}$ the lower value of $|q^2|$ is defined by this size.

In the target rest frame the scattering length of emitting particle is of order of the impact parameter $\varrho$. This length is much smaller than the longitudinal dimension of the target $\gamma_c l$ ($l$ is the length of target beam in the laboratory frame). So one can neglect a variation of configuration of the beam during the scattering time. A possible variation of particle configuration in the beam during a long time 