ABSTRACT
The first and simplest approximation including the effects of kinetic theory in equation (2.84) is to neglect any effects due to correlations. This zero order equation (in 1/ND) along with the Maxwell equations are called the Vlasov equations, although frequently this collisionless Boltzmann equation alone is referred to as the Vlasov equation. In the singular, we prefer to refer to this fundamental equation either as the collisionless Boltzmann equation or as the kinetic equation, and refer to the system of equations as the Vlasov-Maxwell equations or simply as the Vlasov equations (plural).
