Production of Higgs with Z--boson by an electron in external fields

The rate of associative production of Higgs and $Z$--bosons by charged leptons in the field of a plane electromagnetic wave of arbitrary intensity and in the constant crossed field is obtained. The cross section is examined as a function of particle energies and external field intensities for various values of the Higgs boson mass. It is shown, that the photoproduction cross section increases logarithmically at super high energies up to the values, that essentially exceed the cross section of the reaction $e^+e^-\to ZH,$ which, at present, is considered as the most probable channel of Higgs boson production.