Generalization of the Zhukovsky function to the electric field of gratings formed by tilted metallic strips

Analytic expressions describing the electrostatic field of a shutter grating are obtained by conformal mapping of a domain containing the shutter grating onto a domain containing a grating of cylindrical rods. These expressions are applicable for optimizing devices used for determining the parameters of charged particle flows and for analyzing the effects associated with focusing of particles to some thermonuclear targets and with the grid confinement of the plasma.