Analytical quadrature formulae for electric fields of the RF straight-axis ion funnels of a general type

The article presents analytical quadrature expressions for electric field potentials that correspond to radio-frequency straight-axis ion funnels of a general type, specifically, the funnels with a curved channel profile, with multipole diaphragms, and with unequally spaced electrodes. When determining electric fields, the distribution of electric potential over the axis of the device was taken as a basis. The resulting formulae would be appropriate for use in quick, high-quality simulating of radio-frequency devices designed for isolation, conveying and focusing ions, as well as in solving some problems of mathematical physics.