Abstract

The first application of the U_N (Chebyshev polynomials of the second kind) method with higher order approximations is performed to solve the neutron diffusion problem in a slab reactor. The moments of equations are carried out by solving neutron transport equation using first the conventional spherical harmonics (P_N) and then the U_N method. These differential equations with constant coefficients are then solved together to obtain the diffusion equation corresponding to related approximation. The roots of the diffusion equation are estimated to calculate the diffusion lengths of the neutrons for various values of c, the number of secondary neutrons per collision. Numerical results obtained by the present method with its easily executable equations are tabulated with the ones already existing in literature. A good accordance is observed between them. Better results are also obtained than the conventional P_N method for certain values of c.

摘要

执行具有更高阶近似的UN（第二类切比雪夫多项式）方法的首次应用以解决板式反应器中的中子扩散_问题。方程的矩是通过首先使用常规球谐函数 ( P _N ) 然后使用U _N方法求解中子输运方程来执行的。然后将这些具有常数系数的微分方程一起求解，以获得对应于相关近似的扩散方程。估计扩散方程的根，以计算各种c值的中子扩散长度，每次碰撞的次级中子数。通过本方法获得的数值结果及其易于执行的方程与文献中已经存在的方程一起列出。在它们之间观察到良好的一致性。对于某些c值，也可以获得比传统P _N方法更好的结果。