Nonstationary process of ion bunch acceleration in flat diode was investigated. Accurate self-consistent solution for Vlasov equation was obtained. Current dependence from longitudinal emittance, ion sound velocity and rate of anode potential value growth was found, and current density value is shown to exceed Child-Langmuir limit current.

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Mixed Pierce-two-stream instability may occur in an extraction system of a negative ion source based on a volume-produced plasma. The reasons for instability development are discussed. Analytically the conditions of unstable beam propagation are determined. The instability threshold is shown to be increased compared with the pure Pierce instability. The influence of inclined perturbations on the instability behavior is investigated. The numerical calculations are performed in COMSOL Multiphysics. The simulation results confirm the existence of such a mixed instability appearance that develops due to both the electrons of the external circuit and the background positive ions.

The behavior of a uniform charged particle bunch is studied. External and own bunch fields are taken into account. Two-dimensional and three-dimensional self-consistent problems are considered. The equations for bunch radii are obtained in the case of the bunch formed as a rotation ellipsoid. The model is proposed for the bunch with zero longitudinal emittance.

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