The slow positron beam facility Hong Kong submillimeter electron annihilator (HOSEA) at the University of Hong Kong has now been in operation for 6 years with a beam diameter of similar to6 mm and intensity similar to10(4) e(+) s(-1). It is now planned to improve the facility by narrowing the beam diameter to less than I mm, while increasing the intensity to similar to5 x 10(-5)e(+) s(-1). The motivation behind the submillimeter beam is to make it a more effective tool in the study of MOS and MS systems that are hard to fabricate in larger than millimeter dimensions. In particular the development of positron deep level transient (thermal) spectroscopy (PDLTS) could also benefit from a beam of submillimeter dimensions. While consisting of a hybrid electric/magnetic lens structure close to the moderator to produce low canonical momentum phase space, the guidance to the target is purely magnetic. The beam structure is however unusual, consisting as it does of a recurrent re-focusing of the first primary positron focus produced by the hybrid focusing lens close to the moderator. The simulation program, SIMION, is employed to simulate the trajectories of positrons through possible hybrid lens structures and optimize the working parameters of the facility. The simulations show that an outstanding focusing diameter and a repetitive focusing can be obtained all the way to the target above beam energies of 1 keV (C) 2002 Elsevier Science B.V. All rights reserved.