<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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. </p><p>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.</p></abstract>

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.

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

Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava, Advanced Technologies Research Institute, Bottova 25, 917 24 Trnava, Slovakia

Research Papers Faculty of Materials Science and Technology Slovak University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper offers a theoretical study of special type of electrostatic quadrupole deflection system (EQDS) intended for ion beam optics. We deal with EQDS...

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

Published Online: Sep 30, 2015

Page range: 61 - 70

DOI: https://doi.org/10.1515/rput-2015-0028

Keywords
ion beam, quadrupole, Laplace equation, Bessel`s differential equation, Bessel`s functions

© by Stanislav Minárik

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 30, 2015

Page range: 61 - 70

DOI: https://doi.org/10.1515/rput-2015-0028

Keywordsion beam, quadrupole, Laplace equation, Bessel`s differential equation, Bessel`s functions

© by Stanislav Minárik

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
ion beam, quadrupole, Laplace equation, Bessel`s differential equation, Bessel`s functions