beam is much smaller than the characteristic impact parameter) the formulas are simplified essentially (Sec.5). The experimental studies of effect were performed with flat beams (the beam vertical size is much smaller than horizontal one). This specific case is analyzed in Sec.6, while comparison with data is given in Sec.7. In Sec.8 the possible application to the linear $e^+e^-$ collider tuning is discussed.

General analysis of probability of incoherent radiation
=======================================================

In this section we discuss in detail the conditions under which we consider the incoherent radiation. One can calculate the photon emission probability in the target rest frame, since the entering combinations $\omega/\varepsilon$ and $\gamma\vartheta$ ($\gamma$ is the Lorentz factor $\gamma=\varepsilon/m$, $\vartheta$ is the angle of photon emission) are invariant (within a relativistic accuracy) and a transfer to any frame is elementary. We use the operator quasiclassical method [@BK2], [@BKS3]. Within this method the photon formation length (time) is $$\begin{aligned}
&& l_f=\frac{\varepsilon'}{\varepsilon
kv}=\frac{\varepsilon'}{\varepsilon \omega(1-\bf{n v})}\simeq
\frac{l_{f0}}{\zeta};
\nonumber \\
&& l_{f0}=\frac{1}{q_{min}}=\frac{2\varepsilon
\varepsilon'}{\omega m^2} = \frac{4\varepsilon' \gamma_c
\varepsilon_r}{\omega m^2};
\nonumber \\
&& \zeta = 1+\gamma^2 \vartheta^2, \quad \varepsilon'=\varepsilon
-\omega,
\label{2.1}\end{aligned}$$ where $p_{\mu}= \varepsilon v_{\mu}~(v_{\mu}=(1, {\bf v}))$ is the 4-momentum of radiating particle, $\gamma_c=\varepsilon_c/m_c$, $\varepsilon_c$ is the energy of target particle in 