that the main contribution to the bremsstrahlung cross section give emitted by the recoil particle virtual photons with very low energy $$q_0 \sim \frac{m^2\omega}{\varepsilon (\varepsilon-\omega)},
\label{1.1}$$ so that the formation length of virtual photon is $$L_v(\omega)=l_f(q_0)= \frac{4\varepsilon^3
(\varepsilon-\omega)}{m^4\omega}. \label{1.2}$$ This means that the effect for the recoil particles appears much earlier than for the radiating particles. For example, the Landau-Pomeranchuk effect distorted the whole bremsstrahlung spectrum in a TeV range (for heavy elements) while it turns out that the action on the recoil particle can be important for contemporary colliding beam facilities in GeV range [@BK1].

There are a few factors which could act on the recoil electron. One of them is the presence of an external magnetic field in the region of collision of particles [@BK1]-[@KS2]. If the formation length of virtual photon $L_v$ turns out to be larger than the formation length $l_H(\omega)$ of a photon with energy $\omega$ in a magnetic field $H$ than the magnetic field will limit the region of minimal momentum transfers, which will lead to a decrease of the bremsstrahlung cross section and a change of its spectrum. Another effect can appear due to the smallness of the linear interval $l$ where the 