Conditions for Explosive Growth of Free Surface Perturbations for a Dielectric Liquid in a Normal Electric Field in Confined Axisymmetric Geometry

We consider the behavior of the free surface of an ideal dielectric liquid in an applied normal electric field for the case of confined axisymmetric geometry of the system. The quadratic nonlinear amplitude equation which describes the evolution of the boundary is derived in the framework of the Hamiltonian formalism. According to this equation, the hard regime of excitation of electrohydrodynamic instability is always realized. Also, it is shown that the part of the potential energy functional which is responsible for the higher-order nonlinearities is negatively defined if the dielectric constant of the liquid is sufficiently large, ε > 2.78. Under this condition, the growth of surface perturbations has an explosive character.