We present and analyze characteristics of the runaway electron flow in a high-voltage (the voltage rise rate of up to 1.5 MV/ns) air-filled electrode gap with a strongly nonuniform electric field. It is demonstrated that such a flow contains a high-energy electron component of duration not more than 10 ps. According to numerical simulations, runaway electron generation/termination is governed by impact ionization of the gas near the cathode and switching on/off a critical (sufficient for electrons to run away) electric field at the boundary of the expanding cathode plasma. The corresponding characteristic time estimated to be 2–3 ps is defined by the ionization rate at a critical field.

The conditions under which runaway electrons are generated in a gas diode with a strongly nonuniform electric field created by electrodes of specific geometry have been investigated. For an edge cathode, the equation of motion for electrons has been solved analytically. According to the solutions, for electrons to run away at the periphery, in the low field region, it is necessary that the applied potential difference be greater than a certain threshold determined by the electrode gap spacing and by the parameters of the gas. This condition supplements the classical electron runaway condition according to which the field strength near the emitting edge of the cathode should exceed some value depending only on gas parameters. It turned out that for a sharp-edged cathode, the new condition imposes more stringent requirements on the field strength compared with the classical one. Our calculations are supported by experiments in which electron runaway conditions were determined for a set of cathodes with different edge radii.

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence of a vertical electric field is studied. We consider the limit of a strong external electric field where electrostatic forces dominate over gravitational and capillary forces. The nonlinear integrodifferential equations for the interface motion are derived under the assumption of small interfacial slopes. It is shown in the framework of these equations that, in the generic case, the instability development leads to the formation of root singularities at the interface in a finite time. The interfacial curvature becomes infinite at singular points, while the slope angles remain relatively small. The curvature is negative in the vicinity of singularities if the ratio of the permittivities of the fluids exceeds the inverse ratio of their densities, and it is positive in the opposite case (we consider that the lower fluid is heavier than the upper one). In the intermediate case, the interface evolution equations describe the formation and sharpening of dimples at the interface. The results obtained are applicable for the description of the instability of the interface between two magnetic fluids in a vertical magnetic field.

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Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.