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Multiple Scattering of Electrons Used in Medical Radiation Therapy

出版	University of Alberta, 1984
URL	http://books.google.com.hk/books?id=IJ260AEACAAJ&hl=&source=gbs_api

註釋Since the initiation of electron radiation therapy, most of the experimental efforts to understand the transport of electrons in a medium have been concentrated on the investigation of dose deposition by electrons. Because the dose distribution of an electron beam is only the end result of the transport of electrons, it has not been possible to predict the dose distribution in a complex medium. In addition, the prediction of a dose distribution even for a simple medium, such as, an all water "phantom", cannot be made generally because of the the degradation of the accelerated beam caused by the method of shaping a broad beam(e.g., scattering foil and collimator). In this study of electron transport in a homogeneous semi-infinite medium, the linearized Boltzmann transport equation is used with the boundary condition of an individual pencil beam is used. To facilitate the mathematical treatment of the problem, the medium is divided into two regions. The first region is where the path-length of an electron is still far shorter than the "diffusion length" of the medium. By applying the "Fokker-Plank" approximation we obtain the angular distribution of electrons and the average lateral, and longitudinal displacements. The second region is where the orientations of electrons has become very diffuse. In order to take care of the energy dependence of the scattering cross-section, we use the "continuous slowing down approximation". The angular density function is expanded in terms of spherical harmonics and the scattering cross-section is also expanded by the Legendre polynomial. The series is truncated at m=l and n=l. The spatial distribution of electrons is obtained by solving the resulting coupled equations. Results are compared to those obtained by Fermi and discrepancies are found in angular distributions of electrons. Furthermore, it is pointed out that Fermi's solution has a serious drawback because the depth of the medium is used as an energy indicator instead of the actual path-length of eletrons. Its application to the radiation transport problem is thus inappropriate, despite its popularity in applications to medical physics problems.