Title :
Runge-kutta da integrator in mathematica language
Author :
Kaltchev, D. ; Baartman, R.
Author_Institution :
TRIUMF, Vancouver
Abstract :
The method of truncated power series algebra is applied in a Mathematica code to compute the transfer map for arbitrary equations of motion describing a charged particle optical system. The code is a non-symplectic integrator - a combination between differential algebra module and a numerical solver of the equations of motion. Using the symbolic system offers some advantages, especially in the case of non-autonomous equations of motion (element with fringe-fields). An example is given - a soft-fringe map of a magnetic quadrupole.
Keywords :
Runge-Kutta methods; algebra; integration; mathematics computing; particle optics; symbol manipulation; Mathematica code; Mathematica language; Runge-Kutta differential algebra module; arbitrary motion equations; charged particle optical system; fringe-fields; magnetic quadrupole; nonautonomous motion equations; nonsymplectic integrator; numerical solver; soft-fringe map; symbolic system; transfer map; truncated power series algebra; Algebra; Differential algebraic equations; Differential equations; Integrated optics; Magnetic analysis; Optical computing; Packaging; Polynomials; Taylor series; Trajectory;
Conference_Titel :
Particle Accelerator Conference, 2007. PAC. IEEE
Conference_Location :
Albuquerque, NM
Print_ISBN :
978-1-4244-0916-7
DOI :
10.1109/PAC.2007.4440380
