Abstract
A photon spectrum of undulator radiation (UR) is calculated in the semi-classical approach. The UR intensity spectrum is determined by an electron trajectory in the undulator neglecting by energy losses for radiation. Using the Planck's law, the UR photon spectrum can be calculated from the classical intensity spectrum both for linear and nonlinear regimes. The radiation of an electron in a field of strong electromagnetic wave (radiation in the "light" undulator) is considered in the quantum electromagnetic frame. Comparison of results obtained by both approaches has been shown that UR spectra in the whole cone coincide with high accuracy for the case x<<1. Characteristics of the collimated UR beam were simulated with taking into account the discrete process of photon emission along an electron trajectory in both kinds of undulators.
Highlights
One of the options of the future International Linear Collider (ILC) includes the polarized positron source based on a helical undulator with length ~100 m placed downstream the main linear accelerator
The dependence of the emitted photons number on the harmonic number per an electron and per an undulator period for the case K = 1 is shown in figure 1
The spectral distribution for different harmonic numbers are presented in figure 2 and the resulting spectrum in figure 3
Summary
One of the options of the future International Linear Collider (ILC) includes the polarized positron source based on a helical undulator with length ~100 m placed downstream the main linear accelerator. Is outgoing photon angle, n is the number of the harmonic, Z The number of photons emitted at the n-th harmonic can be calculated after integration of the spectral distribution (5):
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