Equation 1.
In September 2023 a so-called APPLE-III type afterburner undulator has been installed behind the main undulator line of FLASH2. This new afterburner undulator allows for generation of FEL radiation with variable polarization at the third harmonic of the FLASH2 SASE radiation, i.e., down to 1.33 nm, corresponding to 930 eV photon energy and can be tuned to produce differently polarized X-ray pulses (including circular left and right).
During the commissioning of the afterburner we characterized the emitted radiation by sophisticated photon-diagnostics measurements. For this study we used an instrument comprising a set of circularly arranged photoelectron time-of-flight (TOF) spectrometers to determine the angular distribution of photoelectron emitted from atomic gas targets in the plane perpendicular to the FEL beam propagation. In the dipole approximation for a one-photon ionization process, the angular distribution intensity I depending on the polar angle θ in the detection plane can be described by eqn.1.
Here, σ and β are the cross section and the anisotropy parameter, respectively, for the ionization of the particular electronic subshell of the target gas, Plin is the degree of linear polarization and Ψ the angle of the linear polarization direction with respect to the horizontal axis, i.e. Ψ = 0 represents horizontal linear polarization. While the linear polarization is usually characterized by the Stokes parameters S1 and S2 , Plin and Ψ constitute an alternative representation as depicted in eqn.2.
From eqn. 1 it is obvious that with this kind of experimental setup only the linear polarization component of the FEL radiation can be measured directly. In fact, the circular polarization component Pcirc = S3 corresponds to an isotropic angular distribution pattern which in principle cannot be distinguished from unpolarized radiation. However, for FELs one can assume almost perfect polarization with a negligible unpolarized component fraction in the order of the Pierce parameter ρ =~10-3. Hence, the degree of circular polarization can be determined by eqn.3 – without being able to differentiate between right and left helicity.
The capability of this method has been successfully demonstrated previously for different undulator types and polarization setup schemes at FERMI and LCLS.
For the afterburner undulator characterization at FLASH we used rare gases as ionization targets. Values of ionization cross section σ and anisotropy parameters β for these gases, which are needed for reference, can be found in literature over a wide range of photon energies. Angular distribution measurements have been performed for different linear and circular polarization settings of the afterburner undulator at various photon energies of the third harmonic in the range from 74 to 414 eV. Details about the commissioning campaign will be published elsewhere.
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References:
S. Marotzke et al., First experiments with ultrashort, circularly polarized soft X-ray pulses at FLASH2 , http://arxiv.org/abs/2502.03301 (2025). Article
