Part I Theory
6.4 Discussion
The detailed knowledge of the properties of transition radiation and the spec-trometer, which includes the radiation source, the transport to the spectrom-eter and the detector, is essential for the dspectrom-etermination of the spectral distri-bution and the absolute value of the longitudinal form factor by spectroscopy.
A campaign at the FELIX FEL facility was performed in order to measure the response function,R, of the double-prism spectrometer and the spectrom-eter CRISP4 [145]. The spectral response of the spectromspectrom-eter setup, i. e. the detector voltage reading for an incident FELO beam intensity, can be deter-mined only in regard to the specic properties of the FELO beam, such as bandwidth and transverse prole. The application of these results for another radiation source, to be specic, transition radiation, requires the consideration of several key dierences.
First, the spectrum of transition radiation is broad compared to the FELO beam, which yields spectral line widths smaller than the spectral resolution of the spectrometer. For transition radiation, a continuous spectral
distribu-6.4 Discussion tion is mapped to a specic detector element instead a single spectral line.
Second, the transverse beam prole of transition radiation yields a ring struc-ture, whereas the FELO delivers a Gaussian-like prole. The distortions in the detector voltage distributions add an additional uncertainty in the FELIX data. In addition, the band pass lter measurements and form factor compar-isons indicate deviations of the actual imaging properties to the spectrometer model in the upper half of the wavelength range that is covered by the prism spectrometer. These circumstances lead to the presented deviations in the comparisons of FELIX measurements to the calculated response function and the form factors with respect to CRISP4. Further studies and appropriate countermeasures on these issues are advisable, but the validity of the key con-clusions, that are depicted below, are not impaired:
• The dispersion of the spectrometer setup and the double-prism arrange-ment follows the expected distribution.
• The model of the partial response function was proven via measurements at FELIX to be appropriate for the given problem.
• The value of the scaling constant, CF, that was determined by com-parative measurements with the CRISP4 spectrometer, is on the same scale of the value estimated from the data taken during the calibration campaign.
• Albeit exhibiting dierences, the form factor comparisons for various charge and compression settings clearly show a coincidence in the slope of the spectral distribution and thus, in electron bunch length.
• The double-prism spectrometer shows high signal-to-noise ratios and low detection limits with respect to CRISP4. For specic beam conditions, the device is more sensitive than the bunch charge diagnostic devices at the FLASH facility (confer chapter 5). Its capability for single-shot mea-surements can mitigate uncertainties due to shot-to-shot uctuations.
In summary, the spectrometer setup and the model for the underlying par-tial response function,R∗, were conrmed to be suitable and valid for the given problem.
Summary and Outlook
The investigation of the longitudinal extension and the longitudinal current prole of electron bunches driving free-electron lasers or delivered from plasma wakeeld-based accelerators is of high importance for the investigation of the FEL process and the acceleration method respectively. These electron bunches are required to yield lengths on the micron scale and charges of well below 30 pC.
During this work, the diagnostic method of investigating the spectral com-position of the radial, but longitudinally compressed Coulomb eld of rela-tivistic electron bunches was studied. Transition radiation as a secondary radiation emitted by the electrons was investigated in the mid-infrared wave-length regime, that is of particular interest for electron bunches with wave-lengths below10µmor durations shorter approx.33 fs. A further constraint was given by the total charge per electron bunch. Established diagnostic devices at the FLASH FEL facility, e. g. the spectrometer CRISP4, approach their detection limit for mid-infrared wavelengths for charges less than ≈ 20 pC.
Subsequent to preparatory numerical studies of transition radiation and spectroscopic methods, a spectrometer with an arrangement of two consecu-tive zinc selenide prisms was developed, assembled and commissioned. The double-prism design allows for the imaging of the spectral band between2µm and 18µm onto a line array of MCT detector elements that is capable of single-shot operation. The commissioning show high signal-to-noise rations for bunch charges. At Q = 4.9 pC, a signal-to-noise ratio of ≈ 2000 was ob-served, whereas a detector signal was still present at 3.8 pC. The sensitivity of the spectrometer is higher than the bunch charge diagnostic devices at the FLASH facility.
A numerical model describing the spectrometer was developed in order to derive the longitudinal form factor of the electron bunches from measured
tran-sition radiation spectra. Furthermore, a calibration campaign at the FELIX FEL facility was conducted to investigate the spectral and intensity response characteristics of the double-prism spectrometer. Comparative measurements taken at the FLASH facility conrmed the validity of the results with respect to the well-understood grating spectrometer, whose accuracy was conrmed via a transverse deecting structure as a third longitudinal diagnostic. The intensity calibration of the double-prism spectrometer found with comparative measurements is on the same scale as the value estimated from results of the calibration campaign. However, the comparative assessment of the spectrom-eters revealed dierences in the derived form factors. Further studies on these dierences are advisable, but do not aect the validity of the developed setup, the obtained measurements and conclusions.
The double-prism concept in combination with sensitive MCT detectors was proved to be appropriate for the given problem. The spectrometer allows the determination of form factors which coincide with measurements taken with established diagnostic devices. In combination with high signal-to-noise ratios, the setup that was developed within this work is particularly suited for low-charge and short electron bunches. In a future step, the form factor measurements can be used with phase retrieval algorithms in order to estimate a likely time-domain current prole of the bunches in extension to further spectrometers as well as a stand-alone and single-shot diagnostic.