[en] The generation and capture of polarized positrons at a source with a superconducting helical undulator having 4.3 cm period and 500 GeV electron drive beam have been simulated. The positron polarization has been calculated for the different undulator K values (up to K=2.5). Without applying a photon collimator, the maximal polarization of positrons is about 25% for 231 meters active magnet length of undulator with K=0.7. Using an undulator with K=2.5 and a collimator with an aperture radius of 0.9 mm results in increase of positron polarization to 54%. The energy deposition, temperature rise and stress induced by high intense photon beam in the rotated titanium-alloy target have been estimated. The maximal thermal stress in the target is about 224 MPa for the source with photon collimation to achieve a positron polarization of 54%.