  From kinetic Vlasov equation for collisional plasmas distribution function in
square-law approximation on sizes of intensivities of electric fields is
received. The known integral of collisions of relaxation type, so-called BGK
(Bhatnagar, Gross, Krook) integral of collisions is considered. The formula for
calculation electric current at any temperature (any degree of degeneration of
electronic gas) is deduced. This formula contains an one-dimensional
quadrature. It is shown, that the nonlinearity account leads to occurrence the
longitudinal electric current directed along a wave vector. This longitudinal
current is orthogonal to a known transversal classical current, received at the
linear analysis. When frequency of collisions tends to the zero, all received
results for collisional plasmas pass in corresponding formulas for
collisionless plasmas. The case of small values of wave number is considered.
It is shown, that the received quantity of longitudinal current at aspiration
of frequency of collisions to zero also passes in corresponding expression of
current for collisionless plasmas. Graphic comparison of dimensionless quantity
of current depending on wave number, frequency of oscillations of
electromagnetic field and frequencies of electron collisions with plasma
particles is carry out.
