We will describe and perform computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a 4th order Runge-Kutta integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We will compare the resulting transfer maps with (3) the DA transfer map of COSY INFINITY's built-in electrostatic spherical deflector element ESP and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS.
In addition to the electrostatic spherical deflector, we study an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We compute the DA transfer map by the ODE integration method (1), and compare it with the transfer maps by (3) COSY INFINITY's built-in electrostatic cylindrical deflector element ECL, and (4) GIOS.
In addition to the code listings in the appendices, the codes to run the test cases are available (below).
Code ELSPHTM17.fox to compute all the test cases discussed in this report
E. Valetov, M. Berz, K. Makino, MSUHEP-171023, Michigan State University (2017)
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