Manual for COMSYN: A orbit integration code for the study of beam dynamics in compact synchrotrons Page: 2 of 11
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orbit for the real lattice structure. Then, four particles are selected, which
have initial small departures in horizontal and vertical coordinates, x, x', y,
y/ with respect to the reference particle, respectively. Based on their tracking
simulation over one superperiod, one four-dimensional transport matrix for the
transverse oscillation can be determined numerically. By comparing its elements
with that of the parameterized matrix described by Courant and Snyder[91, both
3 and a functions can be obtained. The values of # , a and y at any position
can be evaluated in terms of transformations of twiss parameters. The linear
horizontal and vertical tunes are given in terms of the matrix trace. For those
particles with big amplitude, the fast Fourier translation(FFT) method is used
to analyse their tune spectrum. The dispersion function, q, is calculated through
the definition 77 = xp(bp/p) z , where xp is the distance betwc, n the reference
orbit with momentum p and the off-momentum(Sp) particle equilibrium orbit.
The natural chromaticity, , is computed by formulae ( = S/(hp/p) , ., where
S is the difference of tune between the oscillation around the reference orbit
and the off-momentum orbit. The synchrotron radiation integrals I1 through Is
are evaluated by the procedure as described by Hehn.
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Huang, Y. Manual for COMSYN: A orbit integration code for the study of beam dynamics in compact synchrotrons, report, October 1, 1991; United States. (https://digital.library.unt.edu/ark:/67531/metadc1058671/m1/2/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.