Hyperbolic electron mirror as the charged particles reflector

As it is known, that the motion equation for charged particles with hyperbolic electric field has exact solution. In the present paper the solution for trajectory equation is shown with help the central particles method, which allows to study of any electron-optical systems in particular the mirror one. The electric field is presented as the Laplace equation solution in the r,ψ,z cylindric coordinates system through φ(r,z) potential in the form: φ(r,z)=a(z2-r2/2)+bz+c, where ψ - cyclic coordinate, a, b, c - constants, which are determining from boundary conditions. From variation problem the trajectory equation foe charged particle one can to obtain using the variable exchange. In the paper the solution of trajectory equation in polarimetric form is discussed. The results of the work could be useful in electron microscopy, mass-spectroscopy, as well as in the shf-technique electronics