Numerical study of divergence half angle reduction with preserved ion-beam transmission in a converging-grid electrospray thruster

Abstract Ionic-liquid electrospray thrusters are promising micropropulsion devices for small spacecraft; however, excessive ion-beam divergence reduces useful axial momentum and increases particle interception by downstream electrodes. This study investigates a compact converging-grid configuration designed to reduce the maximum beam-divergence half-angle while preserving high ion-transmission efficiency. Unlike architectures employing a dedicated focusing electrode or a separate focus grid, the proposed configuration uses the downstream biased accelerator extractor itself as an ion-optical field-shaping element. A three-dimensional bidirectionally coupled electrostatic–particle model was used to account for particle-induced space-charge effects. Following preliminary screening of the rational Bezier emitter-tip geometry, a multidimensional all-combinations study comprising 15,625 configurations was performed for six geometrical and electrical variables, followed by targeted one-dimensional analyses and numerical mesh- and particle-number sensitivity assessments. The configurations were evaluated using the maximum divergence half-angle and ion-transmission efficiency as the principal beamtransport metrics, together with the trajectory-based mean effective axial specific impulse and maximum emitter-tip electric-field magnitude as complementary indicators. The selected configuration, defined by ( w = 0.56),( C 1 = 0.04 mm),( C 2 = 0.05 mm),( r 3 = 0.23 mm),( r 4 =0.28 mm),( V emi = 3500 V),and ( V acc = 2800 V), reduced the maximum divergence half-angle from approximately (44°) for the reference single-extractor configuration to approximately (~25°), corresponding to an approximately (43%) reduction, while maintaining an ion-transmission efficiency of approximately (89.3%).Under the investigated numerical conditions, these results indicate that the converging downstream accelerator extractor can substantially reduce the outer divergence envelope of the transmitted ion beam while preserving high ion transmission without requiring a separate focusing grid.