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- W42740270 abstract "The transport of charged particles in media characterized by highly forward-peaked scatter, which results in slow spatial and angular relaxation with increasing depth, is an old and difficult problem. The most significant early advance was due to Fermi, who obtained an approximate but accurate solution to the Fokker-Planck equation describing the transport of cosmic rays.This solution, and a generalized one that incorporated energy dependence, was subsequently adopted in electron transport studies and to this day forms the centerpiece of dose calculations in radiation therapy applications. Recently, there has been renewed interest in the subject of highly forward-peaked transport from the point of view of asymptotic theory, in particular in an attempt to improve on Fermi`s solution. While Fermi`s solution for the spatial spreading of an initially collimated pencil beam in a purely scattering medium is known to be accurate, as given by the scalar flux {phi} (x, y, z), the transverse integrated solution {phi}(x), however, is not so accurate. Fermi`s solution is a constant function of depth, when in fact it is easily argued that {phi}(x) should increase with depth. The first attempts at improving this solution used an asymptotic development that neglected backscattering and assumed the angular distribution remainedmore » peaked about the original beam direction, thereby restricting solution to small depths, i.e., to {sigma}{sub tr}T {much_gt} 1, where a, is the transport cross section (neglecting absorption) and T the lateral dimension. The asymptotic expansion in Ref. 5 was able to predict only the O({sigma}{sub tr}x) correction to the (constant) Fermi solution, while a slightly different scaling in Ref. 6 also gave the quadratic correction. Subsequently, Borgers and Larsen used a different method to generate an asymptotic expansion for {phi}(x) and showed that the scalar flux is given by.« less" @default.
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- W42740270 date "1995-12-31" @default.
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- W42740270 title "Forward-peaked beam transport in media with randomly fluctuating properties" @default.
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