Plasma dynamics and a significant error of macroscopic averaging
  The methods of macroscopic averaging used to derive the macroscopic Maxwell equations from electron theory are methodologically incorrect and lead in some cases to a substantial error. For instance, these methods do not take into account the existence of a macroscopic electromagnetic field EB, HB generated by carriers of electric charge moving in a thin layer adjacent to the boundary of the physical region containing these carriers. If this boundary is impenetrable for charged particles, then in its immediate vicinity all carriers are accelerated towards the inside of the region. The existence of the privileged direction of acceleration results in the generation of the macroscopic field EB, HB. The contributions to this field from individual accelerated particles are described with a sufficient accuracy by the Lienard-Wiechert formulas. In some cases the intensity of the field EB, HB is significant not only for deuteron plasma prepared for a controlled thermonuclear fusion reaction but also for electron plasma in conductors at room temperatures. The corrected procedures of macroscopic averaging will induce some changes in the present form of plasma dynamics equations. The modified equations will help to design improved systems of plasma confinement. 
Marek A. Szalek