Abstract
The influence of the space charge of ions evaporated from the surface of a conical spike that develops on a liquid-metal anode on the spike shape has been studied theoretically. A possibility of the self-similar reduction of the equations that govern the space distributions of the electric field, ion velocity field, and space charge density to a system of ordinary differential equations has been revealed. Its solution, which is compatible with the balance condition for the capillary and electrostatic forces at a free liquid surface, has allowed us to obtain the current-voltage characteristic for a liquid-metal ion source and the current dependence of the cone angle. An increase in emission current leads to a monotonic decrease of the cone angle, which agrees with the available experimental data.