Abstract
Because of the existence of perturbations on the equilibrium velocity distribution of an electron plasma that are entire functions and yet do not give the damping predicted by Landau, the Landau calculation is re-examined critically, for the source of these solutions. It is shown that certain tacit assumptions go into the Landau calculation which were not proved there, but are demonstrated to be true. A broad class of initial perturbations is constructed that satisfies all the Landau criteria but does not yield Landau damping. These results derived for a Maxwell equilibrium distribution are generalized to a broader class of equilibrium distributions. Newcomb’s result that an increasing electric potential cannot be monotonic is quite simply proved as a by-product of the integral equation for the plasma.
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