## Details

Proposed by A.A. Vlasov in 1938, the kinetic equation with a self-consistent electromagnetic field led to a fundamentally new perspective in plasma physics. This equation represents the most profound approach to the description of plasma because it operates directly with plasma particles using the distribution function. Plasma is found everywhere in space; that is why this equation has an extensive application. A large number of works where the study of plasma properties based on the solution of the Vlasov equation have appeared.

However, the results based on the solution of the Vlasov equation should be assumed with caution. As noted in the manuscript, the Vlasov equation has a set of formal solutions. The researcher must have the ability to select the correct solutions, correct in the sense of their adequacy to the processes under investigation.

Some aspects of the polarization of a magnetoactive plasma are investigated. It is shown that neglecting the electric field in problems of such sharply inhomogeneous structures as a boundary or current layers leads to an inadequate model. Thus, the successive solution of the kinetic equation taking into account the electric polarization field indicates that the equations describing the equilibrium of these sharply inhomogeneous structures become nonlinear and exhibit the property of structural instability.

Natural science over time included the expansion of the field of numbers from natural to real. Now, physics is in the stage of semi-recognition of complex numbers. On the one hand, when solving the differential equation, the physicist finds the value of the roots of the characteristic equation in a complex field. However, at the final stage, all imaginary parts are discarded, and only real values of physical quantities are passed in response. In this case, the complex field has a fundamental feature that distinguishes it: it is algebraically closed. The restriction of physical quantities only to the field of real numbers seems logically unsatisfactory since often mathematical operations derive them from the field of the original definition. In this manuscript, some problems of the complexification of physics are investigated.