We present a set of 1-D transport models for solid cylinders of material irradiated with particles on the axial ends. The models are based on 1-D models originally developed for evacuated ducts with reflecting walls. The goal of this work is to show that 1-D models can be used for time-dependent transport in solid cylinders. A future use of this approach will apply these models to the high-energy density physics problem of a Marshak wave propagating down a cylindrical foam or other experiments. The models we present use a Galerkin procedure to project the radial dependence of the 3-D transport equation onto an expansion in terms of polynomials. Results demonstrate that for steady state problems with low scattering ratios, a three-basis function expansion can adequately capture the 3-D solution as computed via Monte Carlo. Smaller number of basis functions did not result in adequate solutions. As the radius of the cylinder increases, the 1-D model is more effective. Results from time dependent problems indicate that the 1-D models move particles too fast down the cylinder at early times, but are accurate on the order of 10 or more mean-free times. Our results indicate that 1-D models may be effective in modeling 2-D Marshak waves, but further work is necessary to answer this question.

我们为固体圆柱体的轴向端上的粒子辐照提供了一套一维传输模型。这些模型基于最初为具有反射壁的真空管道开发的一维模型。这项工作的目的是证明一维模型可以用于实心圆柱体中随时间变化的运输。这种方法的未来使用将把这些模型应用于沿着圆柱泡沫或其他实验传播的Marshak波的高能量密度物理问题。我们目前的模型使用Galerkin程序将3-D传输方程的径向相关性投影到多项式展开式上。结果表明，对于具有低散射比的稳态问题，三基函数展开可以充分捕获通过Monte Carlo计算的3-D解。基本函数数量较少，无法提供适当的解决方案。随着圆柱体半径的增加，一维模型更加有效。时间相关问题的结果表明，一维模型在早期将粒子沿圆柱体移动得过快，但精确度约为10次或更多次平均时间。我们的结果表明，一维模型可能对二维Marshak波建模有效，但需要进一步的工作来回答这个问题。