Аңдатпа
This work is devoted to the adjustment of the existing methods of research and design of charged particle sources, which are the most important components of most analytical electron-optical devices and ion-beam technological installations, widely used in various scientific and technical complexes and systems. Therefore, many scientific papers are devoted to the problems of the theory of cathode lenses. In these works, it is indicated that the development of the theory of cathode lenses is associated with noticeable difficulties of a mathematical nature, due to the specificity of the initial conditions of the differential equations to be solved. One of the most promising ways to overcome these difficulties was proposed in the works that used the method of analyzing arbitrary motion relative to the motion of the central particle. However, in these works there are inaccuracies associated with the inconsistent use of initial conditions in solving the equations of motion of charged particles. These inaccuracies did not allow in these works to achieve sufficient adequacy of the mathematical model to the physical process under study. In this paper, the inaccuracies of the existing theories of cathode lenses are eliminated and a theory for the study and design of cathode lenses with constant axisymmetric electric and magnetic fields is developed. The method proposed in this paper can be used to construct theories of charged particle sources with other types of focusing field symmetry.