Analytical electric potentials for simulation of the multipole radiofrequency ion funnels with nonlinear profiles

The article considers analytical expressions for electric field potentials that correspond to radio frequency funnels with quadratic, cubic and biquadratic profiles. The funnel electrodes are a sequence of diaphragms with a circular or multipole structure and apertures of variable size. The latter varies along the transport channel according to the desired law. The resulting expressions can be useful for fast, high-quality simulation of radiofrequency devices designed to convey ion beams with simultaneous focusing.