In the baseline design of the International Linear Collider (ILC) an undulator-based source is foreseen for the positron source in order to match the physics requirements. The baseline parameters are optimized for the ILC at sqrt(s)=500 GeV, that means an electron drive beam of 250 GeV. Precision measurements in the Higgs sector, however, require measurements at sqrt(s)=250 GeV, i.e. running with the electron drive beam only at 125 GeV, which imposes a challenge for achieving a high yield. Therefore the baseline undulator parameters have to be optimized as much as possible within their technical performances. In this bachelor thesis we therefore present a theoretical study on the radiation spectra of a helical undulator, based on the equation for the radiated synchrotron energy spectral density per solid angle per electron in the relativistic, far-field and point-like charge approximation. From this starting point the following undulator properties are examined: the deposited power in the undulator vessel, which can disrupt the functionality of the undulator magnets, the protective property of a mask on this disturbances and the number of positrons produced by the synchrotron radiation in a Ti6Al4V target. Those quantities were evaluated for various values for parameters as undulator period, undulator length and magnetic flux in order to find optimal baseline parameter sets for sqrt(s)=250 GeV.
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