The asymptotic or self-similar behavior of the one-dimensional two-stream instability previously observed in numerical simulations is investigated theoretically. The main result, the relation νd = νe, implies a principle of maximum dissipation. On the microscopic level it is shown that the quasilinear solution is inconsistent with νd = ν, and the assumption of an adiabatically growing Bernstein-Greene-Kruskal wave cannot explain the observed similarity law. It is proposed that the observed behavior is due to the instability of a Bernstein-Greene-Kruskal wave. Suitably chosen simulation computations are performed to demonstrate this concept.
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Biskamp et al. (1973) studied this question.
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