ELSPHTM17.FOX: Direct Calculation of the Transfer Map of Electrostatic Deflectors

Authors: Eremey Valetov, Kyoko Makino, and Martin Berz
Organization: Michigan State University
Creation date: 01-Nov-2017
Email: valetove@msu.edu
Note: Prepared by K. Makino based on E. Valetov's codes

Description

This COSY INFINITY code computes the differential-algebraic (DA) transfer map of electrostatic spherical and cylindrical deflectors in a laboratory coordinate system. In case of the electrostatic spherical deflector, two conventional methods are used: (1) integrating the ODEs of motion using a 4th order Runge-Kutta integrator and (2) computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. Only the former method is used for the electrostatic cylindrical deflector, as Kepler theory is inapplicable in this case.

The program contains the test cases from the following report:

E. Valetov, M. Berz, and K. Makino, Direct Calculation of the Transfer Map of Electrostatic Deflectors, and Comparison with the Codes COSY INFINITY and GIOS, MSUHEP-171023, Michigan State University (2017).

Requirements

• COSY INFINITY version 9 or later

Usage

cosy ELSPHTM17.fox

The program presents an interactive menu. First, choose the deflector type:

1. Spherical
2. Cylindrical

Then choose the computation method (available methods depend on the deflector type; see below).

Methods

1. ODE integration (RK4) — Integrates the equations of motion in laboratory polar coordinates using a 4th-order Runge-Kutta integrator with DA arithmetic. Available for both spherical and cylindrical deflectors.
2. Analytical Kepler theory — Computes the transfer map analytically using Lagrange coefficients derived from Kepler orbit theory. Available for the spherical deflector only, since the 1/r^2 force law does not apply to the cylindrical case.
3. Built-in COSY elements — Uses COSY INFINITY's built-in ESP (spherical) or ECL (cylindrical) electrostatic deflector elements.
4. GIOS result analysis — Reconstructs the transfer map from GIOS aberration coefficients for comparison.

License

This project is licensed under the MIT License. See LICENSE.md for details.

Copyright Notice

© 2017 Eremey Valetov, Kyoko Makino, and Martin Berz