Abstract
The stationary states of a one-dimensional system formed by a double Water-Bag electron distribution and a fixed homogeneous ion background are discussed. Conditions for the existence of periodic and aperiodic equilibria are calculated. The stability of aperiodic solutions is investigated by a perturbative technique already used for a similar gravitational problem. A sufficient condition for stability is found to be tau 1> tau 2 ( tau 1 and tau 2 being the periods of rotation of electrons on the inner and outer contour respectively). A sufficient condition for instability, derived from a thermodynamic theory, is found to be in agreement with the results of the perturbative analysis.
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