Space Charge Influence on the Angle of Conical Spikes Developing on a Liquid-Metal Anode

Abstract

The influence of the space charge of ions emitted from the surface of a conical spike on its shape has been studied. The problem of the calculation of the spatial distributions of the electric field, ion velocity field, and the space charge density near the cone tip has been reduced to the analysis of a system of ordinary differential equations. As a result of numerical solution of these equations, the criterion of the balance of the capillary and electrostatic forces on the conic surface of a liquid-metal anode has been determined. It has allowed us to relate the electrical current flowing through the system, the applied potential difference and the cone angle. We have compared the results of our calculations with available experimental data concerning emission from the surface of pure liquid gallium (Ga), indium (In), tin (Sn), and some liquid alloys, such as Au+Si, Co+Ge, and Au+Ge. On the basis of the proposed model, explanations have been given for a number of specific features of the emissive behavior of different systems.