Penetration of Electron Beams into Water below the Critical Energy

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Abstract
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.

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