An electron optical system that yields a calculated beam edge resolution of 21 nm at a beam voltage of 100 kV and a current density of 50 A/cm(2) was developed for the EB-X3 x-ray mask writer. Based on the system, we investigated a way to increase the current density. The introduction of a zoom lens into the system provided a calculated beam edge resolution of 35 nm at 100 A/cm(2). Problems arising from the high beam voltage and high current density, such as the melting of the first shaping aperture and microdischarges in the electron gun, were also examined. Optimization of the aperture and its holder through thermal simulations reduced the temperature of the first shaping aperture to 753 degrees C at 100 A/cm(2). Through electron trajectory calculations, an electron gun was designed in which reflected electrons are prevented from charging the insulators; and this enabled us to completely eliminate microdischarges,