Bremsstrahlung in magnetic field and in matter

Bremsstrahlung of the ultrarelativistic electron and pair production by the photon moving through a flat layer of the magnetic field is considered. The case of an infinitely thin layer whose role (if the reflected wave is neglected) reduces to rotation of the electron momentum through a given angle is studied in detail. The simplicity of the obtained formulas for the probabilities allows to study qualitatively a system of many thin layers which imitate either a constant electromagnetic field or an ondulator system. At sufficiently high energies the total probabilities of the radiative processes per a unit length for the constant field essentially exceed those for the equal-value field alternating its direction. Probability formulas concerning the constant magnetic field are used to make semiquantitative estimates for a crystal