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本文介绍了一种计算电场分布的计算方法,即不变嵌入法。此方法依据拉普拉斯方程的有限差分方程,利用矩阵表示法及运算,最后将边值问题化为简单、稳定的初值问题,用递推公式算出场中电位分布。这是计算场分布的一种直接方法。本文还导出了含轴上点的不变嵌入法计算场分布的公式,并用此公式计算了同心球场,将其结果和超松弛法以及解析法做了比较。此方法简单,容易掌握,效率比较高,计算精度和迭代法一样。这种方法适合于象管的近轴计算和电子枪的电子光学系统计算。这方法也很容易编成程序。这方法的缺点是要事先给出边界电位分布值。所以就产生了高效率的混合法,即由面电荷法给出需求解场的边界值,再用不变嵌入法计算这个缩小区域内的电位分布。
This article describes a calculation method for calculating the electric field distribution, namely invariant embedding. Based on the finite difference equation of Laplace equation, matrix method and operation are used in this method. Finally, the boundary value problem is transformed into a simple and stable initial value problem, and the field potential distribution is calculated by recursion formula. This is a direct way of calculating the field distribution. In this paper, we also derive a formula for calculating the field distribution of invariable inlaying points with points on the axis, and use this formula to calculate the concentric ball fields. The results are compared with the over-relaxation method and the analytic method. This method is simple, easy to grasp, high efficiency, the same precision and iterative method. This method is suitable for the paraxial calculation of the tube and the electron optical system of the electron gun. This method is also easy to program. The disadvantage of this method is that the boundary potential distribution is given in advance. Therefore, a high efficiency hybrid method is produced, in which the boundary value of the demanded field is given by the surface charge method, and then the potential distribution in the narrowed area is calculated by the invariant embedding method.