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(a) The order of accuracy ζ for each element M i;j of the quadrupole transfer matrix is plotted for various integrators where the numbers in the labels inside the parentheses (n k ,n tot ) refer to the amount of kicks n k and the total maps needed to construct the integrator n tot . The order of accuracy of μ, in a FODO cell that include dipoles, for different K Q and L Q with the use of (b) the CSABA 2 and (c) the TEAPOT 5 symplectic integrators. The area below the white dashed curve guarantees stable motion through the FODO cell.
Source publication
The Hamiltonian describing particle motion in an accelerator belongs to a large class of systems, the members of which can be integrated with a new set of high order symplectic integrators. One benefit of these integrators is their strong numerical stability, which results from the inclusion of only forward integration steps, independent of the ord...
Context in source publication
Context 1
... by Eqs. (3b) and (4) through the term Oðλ ζ Þ. Performing this expansion to the exact transfer matrix of a quadrupole and comparing the elements that describe the horizontal motion (M 1;1 , M 1;2 , M 2;1 , and M 2;2 ), the order of accuracy ζ for different symplectic integrators like the LEAPFROG [33], the CSABA m and the TEAPOT m is plotted in Fig. 1(a). The numbers in the labels inside the parentheses (n k ,n tot ) refer to the amount of kicks n k and the total maps needed to construct the integrator n tot , e.g., (4, 7) the integrator consists of seven maps from which the n k ¼ 4 are kicks and the others are drifts. The CSABA 1 and all the studied TEAPOT integrators can describe the ...
