Penetration of Electron Beams into Water below the Critical Energy

The "moments technique" has been applied to the calculation of the spatial distribution of the energy dissipation in water by electron beams of energies 10-25 Mev. A continuous energy loss is assumed and the energy-range relationships are obtained taking into account the ionization and radiation losses. These relationships are introduced in the proper Boltzmann transport equation to approximate the scattering term by a simple function of residual range. The stopping power is approximated by a sum of powers of residual range. This leads to expressing the spatial moments of the energy dissipation as a combination of triple moments of the electron distribution function. These triple moments are the angular, spatial, and residual range moments, which are connected by a recursion system. The first three moments are calculated together with the boundary condition and the asymptotic trend. With this information, the distribution is constructed by using a simple analytical function. The agreement with experimental results is satisfactory.