Abstract
Electrostatic instabilities in electron plasmas have been studied by analyzing initial value problems. The self-electric field of a non-neutral plasma produces a flow that brings about non-Hermitian property into the generating operator. Because of the nonorthogonality of eigenmodes, the evolution of the system is rather complex. Secular behavior is a typical appearance of unresolvable mode couplings that may be cast in a representation of Jordan block. The coupling of the perpendicular (with respect to the magnetic field) electrostatic modes (Kelvin–Helmholtz or diocotron modes) and parallel plasma oscillations causes a more complex phenomena.
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