  Kinetic Vlasov equation for collisional plasmas with BGK
(Bhatnagar-Gross-Krook) collision integral is used. The case of arbitrary
temperature (i.e. arbitrary degree of degeneration of electronic gas) is
considered. From kinetic Vlasov equation the distribution function in
square-law approximation on size of transversal electromagnetic field is
received. The formula for calculation electric current is deduced. This formula
contains one-dimension quadrature. It is shown, that the nonlinearity account
leads to occurrence the longitudinal electric current directed along the wave
vector. This longitudinal current is perpendicular to the known transversal
classical current, received at the linear analysis. When frequency of
collisions tends to zero, all received results for collisional plasma pass in
known corresponding formulas for collisionless plasma. The case of small values
of wave number is considered. It is shown, that the received quantity of
longitudinal current at tendency of frequency of collisions to zero also passes
in known corresponding expression of current for collisionless plasmas.
  Graphic research of dimensionless density of the current depending on wave
number, frequency of oscillations of electromagnetic field and frequency of
electron collisions with plasma particles is carried out.
