To facilitate calibration of the Rice ALSEP/SIDE instrument a low energy (thermal to 4.0 kev) positive ion beam of variable current density (10-12 to 10-8 amp/cm2) has been developed. A high perveance electron beam of 0.15 to 0.40 kev is formed using electrostatic lenses alone, without recourse to the customary confining axial magnetic field. The electron beam is introduced into a region where ionization occurs by electron collisions with any of several species of gas introduced into the vacuum system for this purpose. Ions are then extracted by an asymmetric electric field designed to produce a minimal increase in the width of their initial Maxwellian energy distribution. An investigation of the spreading of the ion energy distribution due to dispersion of the electron beam and inherent lens defects is carried out using arguments taken primarily from statistical mechanics and electrostatic field theory. Once removed from the ionization region, ions are focused into a beam and accelerated or decelerated to the desired energy by conventional ion optics.