From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current orthogonal to known transversal classical current, received at the linear analysis. From the kinetic equation with Wigner integral for collisionless quantum plasma distribution function is received in square-law on vector potential approximation. Formulas for calculation electric current at any temperature are deduced. The case of small values of wave number is considered. It is shown, that size of a longitudinal current at small values of wave number and for classical plasma and for quantum plasma coincide. Graphic comparison of dimensionless size of a current quantum and classical plasma is made.
Longitudinal electric current in classical collisional Maxwellian plasma, inducted by transversal electromagnetic wave
采用麦克斯韦等离子体碰撞动力学方程。碰撞积分采用BGK（Bhatnagar，Gross and Krook）型。从弗拉索夫方程出发，得到了电子在横向电场大小平方律近似下的分布函数。推导了电流计算公式。这个公式包含一个一维求积。它示出，非线性导致揭示的纵向电流沿波矢量。该纵向电流垂直于已知的所谓横向经典电流。经典电流在线性分析中出现。计算了小波数情况下的纵向流。当碰撞频率趋于零时，碰撞等离子体的所有公式都通过了已知的无碰撞等离子体的相应结果。对无因次电流密度进行了图解研究。
