A cryogenic pumping system capable of pumping 300, 000 1/sec of nitrogen is proposed for the Bevatron to decrease the base pressure from ~2x10-6 to ~2 x 10-7 torr. The Bevatron consists of approximately 10,000 ft3 of free volume with approximately 15,000 ft2 of free outgassing area. The magnet pole tips, which consists of 1/2-in. laminations, add a potential 80,000 ft2 of outgassing area. The design calls for an approximately 360-ft-long, 20??K surface shielded by an 80??K surface strung along the inside perimeter of the Bevatron. Initial design considerations indicate that radiant heat flux from the 80??K surface is a prime design factor which could greatly affect the operating and installation costs of 80??K refrigeration. A two-dimensional Monte Carlo type program was devised and used to optimize designs with maximum nitrogen pumping speed and minimum 80??K shield area to reduce the refrigeration costs.