Electron trajectory simulations of time-of-flight spectrometers for core level high-energy photoelectron spectroscopy at pulsed X-ray sources

The advent of Free Electron Lasers (FELs), able to provide short (2-100 fs) and intense (1033 photons/s/mm2/mrad2/0.1%bandwidth) pulses of light also in the hard X-ray regime (ℏω> 2000 eV), opens new possibilities to study the ultrafast dynamics of processes, exploiting the capability of Hard X-ray Photoelectron Spectroscopy (HAXPES) to measure core-level spectra of elements with bulk sensitivity. In order to detect the intense bursts of high kinetic energy electrons generated by the X-ray pulses with an energy resolution comparable to the existing category of electron analyzers, a new class of spectrometers must be designed. We present a characterization of two different TOF spectrometers, namely one based on a retarding cylindrical lens and another one based on the spherical reflector geometry. SIMION® software has been used in order to evaluate electron trajectories of high kinetic energy electrons (5000-10,000 eV) and extract transmission properties, angular acceptance and energy resolution. It resulted that while the linear system is able to accept a larger solid angle (∼50 msr), the spherical mirror offers a better resolving power (around 71,000). Both analyzers are capable of a transmission above 90% within range of kinetic energies wide enough to measure the full line-shape of a core photoionization peak. Furthermore, we proved that both instruments are able to discriminate between two consecutive electron bunches having a temporal separation inferior than 220 ns, which is the distance between two consecutive photon pulses at the European X-ray Free Electron Laser (EXFEL), which is currently under construction in Hamburg.