On adiabatic plasma motion

The nearly periodic motion of a charged particle in the presence of a growing or slightly damped electrostatic wave is considered. Adiabatic plasma motion in one dimension with less than three slowly varying field parameters violates the conservation laws (unless the parameters do not vary). It is conjectured that there are not more than two independent relations between the slowly varying parameters, because from the Vlasov equations and the two conservation laws it is possible to derive the Maxwell equations. When the spatial dependence of both the field and the distributions are known, e.g., periodic with given wavenumber.