Charged Particle Dynamics Inside Electrostatic Quadrupole Deflection System with Circular Electrodes and Rotationally Symmetric Design

This paper offers a theoretical study of special type of electrostatic quadrupole deflection system (EQDS) intended for ion beam optics. We deal with EQDS consisting of electrode pairs with rotational symmetry design. This systems was pre-designed for an ion beam modification and trajectory controlling. Basic assumptions for determination of transfer characteristics of such systems are analysed on the basic of charged particle dynamics.

We are especially interested in the electrostatic field distribution among electrodes inside the mentioned type of EQDS. Typical case of the Sturm-Liouville boundary value problem called Bessel`s differential equation arises in calculation of the electrostatic scalar potential with rotational symmetry. Bessel`s functions are particular solution of Laplace equation in this case. The scalar potential equations of motion for ions in this electrostatic field are found. The path of charge-particles in this field could be determined by solving the trajectory equation of motion in Cartesian coordinates.