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An insertion device (ID) with medium strength parameter was hard to be defined as a wiggler or an undulator. Usually, this kind of ID was classified according to the user’s definition and to select the spectrum calculation formula of wiggler or undulator. The spectrum calculation formula for wiggler or undulator is quite difference and consequently obtain a big different flux density by using the same strength parameter. So, it is no way that the spectrum calculation of them is consistent. Therefore, a universal formula will be developed for the spectrum analysis for the different kinds of insertion devices that is with large different strength parameter (deflection parameter). Consequently, a modified spectrum calculation formula of ID with medium strength parameter was studied by reviewing the difference of existing spectrum formulas. The familiar formula of calculating undulator spectrum was modified and can be used on ID with arbitrary strength parameter. The algorithm of formula modification was described. Some relative issue, like the effect of phase error and energy spread, and taper undulator were also discussed herein.
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