Mathematical Modeling of the Operation of a Directed Bremsstrahlung Formation Line

Abstract

Accelerator-based bremsstrahlung generators are of particular interest for use in solving scientific and applied problems, the most important ones being remote radiation monitoring, production of tomographic images of hidden objects, viz., in medical diagnostics and customs control, activation analysis in metallurgy, agriculture, ecology, crime detection and flaw analysis [1]. Remote monitoring systems based on charged-particle accelerators have a large advantage due to their controllability, radiation safety in the off state and possibility of generating penetrating radiation in a wide range of intensity and energy over isotopic sources. Aside from the accelerator, one of the main elements of a bremsstrahlung generator is the unit where the radiation with the required parameters is formed and which for this reason we shall call the formation line. It is comprised of individual cells, each of which consists of a converter, which transforms the electron-beam energy into bremsstrahlung, a drift section and a lens which restores the divergence of the beam after the converter and at the entrance into the next cell. The computational method and mathematical modeling are based on the synthesis of cells which makes it possible to determine the main parameters of the formation line at the first stage of the calculations based on the prescribed output characteristics of the bremsstrahlung. The numerical modeling of the operation for checking and refining the parameters obtained at the first stage is done at the second stage. Synthesis of the Cells of the Formation Line. Let d denote the length of a cell’s drift section, where a lens with focal length f is located. In what follows, dimensionless quantities are used everywhere. The linear dimensions are represented in units of the quantity chosen on the basis of computational convenience. The matrix F of the drift section and focusing lens (in the thin-lens approximation) has the form