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SubjectF SAD Update V1.0.10.3.8a TouschekLifetime
Article NoF 741
DateF 2009/10/03(Sat) 06:46:51
ContributorF K. Oide
Dear Users,

The new version modifies calculation of Touschek lifetime:

1. The table of lifetime vs. Nx/Nz in EMIT with INTRA is extended to cover below Nx <10. Thus TouschekLifetime returns more accurate number for such a case.

2. The loss rate integral C[x]/x:

C[x_] = (-3/2 + Integrate[(1 + 3/2 x + x/2 Log[t/x + 1]) Exp[-t]/(t + x), {t,
0, Infinity}]) * Exp[-x]]

has been approximated by an expression

fib[x_] := (Log[1/x/e + 1]*(b + e x)/(b + x*(a + 2 x)))] * Exp[-x]

where e = Exp[EulerGamma+3/2]. The numerical parameters a and b have been updated to

a = 5.62966, b = 0.75159

from

a = 5.5077, b = 1.1274 ,

which have been used for more than 15 years. The new values give the relative error of C[x] less than 1% for entire x, while the old ones 2%.