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However the solution of a task of Pierce assumes that the anode has no opening. Therefore as soon as the opening in the anode is entered into consideration, situation sharply changes: near the anode distribution of potential and the course of electronic trajectories become at all not what are put in calculation. There is a so-called anode lens which changes distribution of potential in a down.

where  - the function describing an extreme trajectory of an electron beam in cylindrical system of coordinates; r - radial coordinate of cylindrical system of coordinates; Z - longitudinal coordinate of cylindrical system of coordinates; F0 - a unit of measure of the radial sizes of a bunch; l - unit of measure of the longitudinal sizes of a bunch; q2 – curvilinear orthogonal coordinate.

At calculation of a trajectory of electrons in EOS, the method of consecutive approximations consisting in the following was widely used. As fields of the first approach fields without own fields of a stream of particles undertake. This field is used for calculation of trajectories of the first approach. Fields and trajectories of the second approach pay off taking into account (approximate) own fields of a bunch. Process of consecutive approximations proceeds until results of the subsequent – approximations are not rather close to results previous (n – l) – go approximations. Coordinates and tilt angles of trajectories of particles in some chosen plane of the analyzed system can serve as criterion of convergence of process, for example. When process of consecutive approximations meets, receiving the end result with an accuracy, necessary for practice, usually requires 5 – 10 approximations.

At design of multibeam EOS with reversny magnetic focusing the task becomes complicated that it is necessary to provide lack of saturation magnetosoft polar tips in crossing points between the neighboring flying canals. It is necessary not to allow violation of axial symmetry of a magnetic field in each opening of a polar tip of multibeam system.

Thus, according to a formula (at a transmission of a direct current through a sample in it there is a potential difference which will be proportional to intensity of a magnetic field. At sensors.. . The hall proportionality between U and N is observed with an accuracy of several percent for fields about 2  104.

The effect of the Hall consists that on lateral sides of a sample. Through which the direct current is passed, in the presence of an external magnetic field there is a cross potential difference. For the sample made of the semiconductor in the form of a parallelepiped it is a potential difference is defined by the equation