Electrostatic waves in periodic inhomogeneous plasma

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Abstract
In periodic, inhomogeneous plasma, the dispertion relation w(k) can begeneralized to a relation w(k, K), where K is the wave-number of the periodic steady state. Two models are studied: the ‘water-bag’ model and the ‘two-stream’ model. The solution for these models is obtained easily by the introduction of a Lagrangian formulation. Results are presented. It is shown that, in the water-bag case, the appearance of narrow bands of allowed frequencies practically discretizes the lower part of the spectrum. In the two-stream case, while the long wavelengths have a smaller growth rate, an increased instability is found for k/K = ½