Calculation of the ion extraction boundary of a plasma ion source

The hypothesis that an unmagnetized plasma will form a meniscus sheath above an ion extraction aperture on the electric field magnitude contour, |E|=E_p=T_e/λ_D, is tested. The hypothesis is assumed to be true, that the ion extraction surface of a single aperture ion extraction optic is given by the vacuum Laplace electric field magnitude contour equal to E_p. The ion current extracted from this surface for a single aperture is calculated analytically. The analytically calculated current is compared to a particle-in-cell simulation of ion extraction from a single aperture, for densities ranging from 1.49·10¹⁴ to 1.49·10²⁰ m^-3 and electron temperatures of 1.35-2.7 eV. The simulated extraction current and extraction area agree with the calculated current and area very well, with deviations of only 0.1%-8% relative to the simulated value.