Abstract: A new theoretical line of attack to solve the self-coordinated problem in charge particle optics isdeveloped basing on the aberration theory and$tau@-variation technique. The self-coordinated problemis treated as initial-value problem for the evolutionintegro-differential equation which directly followsfrom the Lorentz equation with taking into account thespace charge effects. The Coulomb potential of a beamis presented in the form of integral taken over theinitial parameters domain, and the induced potential(the `mirror image' potential) is presented in theconvolution form with a Green function satisfying theadjacent Fredholm integral equation of the first kind.Some considerations to numerical solution of theevolution equation obtained are applied.!4
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机译：摘要：基于像差理论和$ tau @-变差技术，发展了解决电荷粒子光学中自协调问题的新的理论攻坚线。考虑到空间电荷效应，将自协调问题视为演化积分微分方程的初值问题，该方程直接遵循洛伦兹方程。束的库仑势以积分形式呈现在初始参数域上，感应势（“镜像”势）以卷积形式呈现，其中格林函数满足第一类弗雷德霍尔姆积分方程。 4对所获得的演化方程的数值解进行了考虑。！4
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