Ring Waves on the Surface of a Liquid in a Coulomb Field

Abstract

The realization laws of instability of ring waves on the surface of an electroconductive liquid in a Coulomb field are studied. The relation is derived, which links the frequency of ring capillary gravitational waves on the surface of a conductive liquid in an inhomogeneous electrostatic field of point charge with physical parameters of the problem and with the wave number analog. Similar to the Tonks–Frenkel field parameter, a field parameter is determined, which characterizes the surface stability of a conductive liquid in an inhomogeneous Coulomb field. It is established that the critical conditions of instability of ring waves on the surface of electroconductive liquid in a Coulomb field are less strict than the conditions of Tonks–Frenkel instability.