No abstract

Nonlinear dynamics of the interface of dielectric liquids under the conditions of suppression of the Kelvin–Helmholz instability by a tangential electric field has been investigated. Two broad classes of exact analytical solutions to the equations of motion describing the evolution of spatially localized and periodic interface perturbations have been found. Both classes of solutions tend to the formation of strong singularities: interface discontinuities with formally infinite amplitudes. The discontinuity sign is determined by the sign of liquid velocity jump at the interface.

Conical singularities (spikes) appearing on the surface of a liquid with ionic conduction in the electric field have been studied with allowance for the influence of bulk and surface charges. It is established that the problem of field distribution admits an exact analytical solution that corresponds to the regime of charge-limited current. Dependences of the saturation current passing via a stationary conical surface singularity on the cone angle, dielectric permittivity of liquid, and mobility of positive and negative ions are determined.

The conditions of electron runaway in a gas diode with a cathode in the form of a needle are studied theoretically. It is shown that the runaway conditions are qualitatively different for needles with relatively large and small tip radii, i.e., in fact, for different degrees of electric field inhomogeneity. In a weakly inhomogeneous field, the transition of electrons to the runaway regime is determined by the local distribution of the field near the place of their start – the tip of the needle. In a strongly inhomogeneous field, the runaway condition has a nonlocal character: it is determined by the behavior of electrons in the near-anode region. This difference leads to a nonmonotonic dependence of the threshold runaway voltage on the tip radius.