Semi-Empirical Models of Electron Beam Control for Radiation Sterilization

To carry out radiation sterilization, one needs to determine the permissible irradiation modes, which is carried out using computer dosimetry methods. Nowadays, the choice of optimal irradiation modes can be based on the models of the depth-dose curve at different incidence angles of the electron beam on the layer of matter. In the present paper, the distribution of transferred energy in the volume of the target initiated by the normal incidence of a point beam of radiation on the surface of a semi-infinite medium (Dose-Map object) is used to develop such models. Semi-empirical models of the Dose-Map object are designed based on two assumptions. One is that the target has axial symmetry relative to the direction of the radiation particle incidence on the target. The second is that the dose spatial distribution is uniform or normal (Gaussian distribution) in the cross-sections of the Dose-Map object at all depths. For a two-parameter approximation of the Dose-Map object, three-dimensional geometric figures are suggested, which surfaces are formed by rotating the plots of power functions around the abscissa axis. Semi-empirical models are developed based on the assumption that the parameters of the Dose-Map object in its eigen coordinate system do not change when the beam incidence angle changes. Expressions are obtained for calculating the depth-dose curves from radiation incident on the target at an angle θ in the form of an integral transformation of the depth-dose curve for normal incidence of the radiation beam on the target. Software has been developed for calculating depth-dose curves in a semi-infinite medium under uniform irradiation by an electron beam. The implemented algorithms for calculating the depth-dose curves from an electron beam incident on the target at the angle θ are tested. Satisfactory agreement is established between the results obtained using the developed semi-empirical models and the results of Monte Carlo modeling of the depth-dose curves at different incidence angles of the electron beam on the target. Good agreement is established between the results obtained using the semi-empirical model "Cone" and the results obtained using the developed two-parameter semi-empirical models SEM2U and SEM2N. The capabilities of the developed two-parameter models for a more complete description of the technological characteristics of the radiation sterilization process are investigated using the numerical methods. Examples are provided where the developed two-parameter models allow for the simultaneous description of two technological characteristics of the two-sided irradiation process: the optimal target thickness and the dose uniformity ratio (DUR) in the target. Consistent data on these characteristics allow choosing optimal modes of electron beam irradiation during radiation sterilization in a reasonable manner. The possibilities of using the approach suggested in the present paper for developing a set of semi-empirical models of computer dosimetry of irradiation processes in radiation technologies are noted.