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A relativistic electron passing through an undulator generates electromagnetic radiation at the expenses of its own kinetic energy. This effect is usually not taken into account if the number of periods of the undulator is relatively small (100 - 200). However, at FEL facilities, long installations have been built, planned or are under construction, where many undulators are installed one after another for a total of several thousand undulator periods. For instance, the SASE1 and SASE2 lines at the European XFEL will consist of 35 undulators with 124 periods each. In this case, because of the electron energy decrease along its trajectory, the radiation from different undulators will drop out of synchronism. As a result, the radiation spectral line will be much wider. In the presented report, this effect was analyzed analytically and numerically. An expression for the critical number of undulator periods, when the effect of electron energy loss should be properly taken into account, is derived. It is found that, for the case of the European XFEL, this number is about 1200 periods.
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