A Monte Carlo simulation model for radiation-induced plasmas with nonlinear properties due to recombination has been developed employing a piecewise-linearized predict-correct technique. Several variance reduction techniques are used, including antithetic variates. The resulting code is applied to the determination of the electron energy distribution for a noble-gas plasma created by alpha-particle irradiation. Results are presented for helium with an electron source rate from 1014 to 1018 electrons/(cm3 sec), initial energies from 70 to 1500 eV, pressures from 10 to 760 Torr, and electric-field-to-pressure ratios from 0 to 10 V/(cm Torr). The low-energy portion of the distribution function approaches a Maxwellian for zero field and Druyvesteyn’s distribution with an applied electric field. However, above the ionization potential and extending to the source energy, a parabolic-shaped distribution (tail) occurs.