Europhys. Lett., 76 (1), pp. 36-41 (2006)
DOI: 10.1209/epl/i2006-10241-3

Influence of the space charge on the configuration of conical spikes on a liquid-metal surface

G. Sh. Boltachev and N. M. Zubarev

Institute of Electrophysics, UD, RAS - 106 Amundsen St., 620016 Ekaterinburg, Russia

grey@iep.uran.ru
nick@ami.uran.ru

received 2 June 2006; accepted in final form 11 August 2006
published online 6 September 2006

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.

PACS
41.20.Cv - Electrostatics; Poisson and Laplace equations, boundary-value problems.
79.70.+q - Field emission, ionization, evaporation, and desorption.
61.25.Mv - Liquid metals and alloys.

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