Characterization of the ion energy distribution function (IEDF) of low energy high current density ion beams by conventional retarding field and deflection type energy analyzers is limited due to finite ion beam emittance and beam space charge spreading inside the analyzer. These deficiencies are, to a large extent, overcome with the recent development of the variable-focusing retarding field energy analyzer (RFEA), which has a cylindrical focusing electrode preceding the planar retarding grid. The principal concept of this analyzer is conversion of a divergent charged particle beam into a quasiparallel beam before analyzing it by the planar retarding field. This allows analysis of the beam particle total kinetic energy distribution with greatly improved energy resolution. Whereas this concept was first applied to analyze 5-10 keV pulsed electron beams, the present authors have adapted it to analyze the energy distribution of a low energy (<or=1 KeV) broad ion beam. In this paper we describe the RFEA design, which was modified from the original, mainly as required by the specifics of broad ion beam energy analysis, and the device experimental characterization and modeling results. Among the modifications, an orifice electrode placed in front of the RFEA provides better spatial resolution of the broad ion beam ion optics emission region and reduces the beam plasma density in the vicinity of analyzer entry. An electron repeller grid placed in front of the RFEA collector was found critical for suppressing secondary electrons, both those incoming to the collector and those released from its surface, and improved energy spectrum measurement repeatability and accuracy. The use of finer mesh single- and double-grid retarding structures reduces the retarding grid lens effect and improves the analyzer energy resolution and accuracy of the measured spectrum mean energy. However, additional analyzer component and configuration improvements did not further change the analyzed IEDF shape or mean energy value. This led us to conclude that the optimized analyzer construction provides an energy resolution considerably narrower than the investigated ion beam energy spectrum full width at half maximum, and the derived energy spectrum is an objective and accurate representation of the analyzed broad ion beam energy distribution characteristics. A quantitative study of the focusing voltage and retarding grid field effects based on the experimental data and modeling results have supported this conclusion.