Analytical structures of electric spectrographs the fields of which are expressed in a uniform generalized form

In the article an analytical representation of the fields for electric spectrographs expressed in an uniform generalized form is developed. The potentials of such fields are of Laplace’s type and presented as φ(x, y, z) = P(x, y, z) ln R(x, y, z) + Q(x, y, z), where P, Q, R — are uniform functions in Euler’s sense with an integer multiplicity. It is built an accurate algorithm to synthesize such potential structures exploiting a complex Donkin’s potential of multiplicity. In these constructions one can use any function of complex variables. Some surfaces of equal potential of these fields are demonstrated and analyze. The different variants to use in electron spectroscopy are discussed.