Pomraning G C, Prinja A K
School of Engineering and Applied Science, University of California, Los Angeles 90095-1597, USA.
Med Phys. 1996 Oct;23(10):1761-74. doi: 10.1118/1.597759.
The Fermi pencil beam formula and the higher-order multiple scattering theory due to Jette are shown to result from a perturbative treatment of the linear Boltzmann equation with Fokker-Planck scattering. Using asymptotic one-dimensional solutions for the transverse integrated (spherical) fluence as well as its variance, approximate higher-order pencil beam theories are constructed. These simple and explicit formulae are shown, by comparison with benchmark Monte Carlo results, to be significantly more accurate than the Fermi and Jette equations, particularly at large distances from the beam axis.
费米笔形束公式以及由杰特提出的高阶多次散射理论，被证明是通过对具有福克 - 普朗克散射的线性玻尔兹曼方程进行微扰处理而得到的。利用横向积分（球形）注量及其方差的渐近一维解，构建了近似的高阶笔形束理论。通过与基准蒙特卡罗结果相比较，这些简单且明确的公式被证明比费米方程和杰特方程精确得多，特别是在离束轴较远的距离处。
