Analytical solutions for helium bubble and critical radius parameters using a hard sphere equation of state

Considerable theoretical and experimental work has verified the role of helium-stabilized bubbles as the precursor to void formation in fast neutron irradiated stainless steels. The concept of the critical bubble radius or critical helium number for bubble-to-void conversion has received particular attention. A hard sphere equation of state is used to compute these parameters for a variety of irradiation conditions and the results are compared with those computed using the ideal gas law. Simplified analytical solutions are developed which permit the calculation of the bubble radius and the critical bubble parameters without resorting to iterative techniques and yet retain the accuracy of the hard sphere equation of state. The use of these solutions is illustrated using a rate theory model of void swelling which has been calibrated using fast reactor swelling data. (orig.)