We describe the design and performance of a magnetic bottle electron spectrometer (MBES) for high-energy electron spectroscopy. Our design features a 2 m long electron drift tube and electrostatic retardation lens, achieving sub-electronvolt (eV) electron kinetic energy resolution for high energy (several hundred eV) electrons with a close to 4π collection solid angle. A segmented anode electron detector enables the simultaneous collection of photoelectron spectra in high resolution and high collection efficiency modes. This versatile instrument is installed at the time-resolved molecular and optical sciences instrument at the Linac Coherent Light Source x-ray free-electron laser (XFEL). In this paper, we demonstrate its high resolution, collection efficiency, and spatial selectivity in measurements where it is coupled to an XFEL source. These combined characteristics are designed to enable high-resolution time-resolved measurements using x-ray photoelectron, absorption, and Auger–Meitner spectroscopy. We also describe the pervasive artifact in MBES time-of-flight spectra that arises from a periodic modulation in electron collection efficiency and present a robust analysis procedure for its removal.
I. INTRODUCTION
Electron spectroscopy is a powerful tool for probing the electronic and molecular structure of gaseous and condensed phase systems. When used in combination with ultrashort light pulses, the technique offers a route to tracking ultrafast electronic and nuclear dynamics. Time-resolved photoelectron spectroscopy (TRPES) of valence electrons is an established technique for probing photo-initiated molecular dynamics on the femtosecond timescale.1–4 The binding energies of core orbitals can be particularly sensitive to the local chemical environment, so the ability to time-resolve small binding energy shifts in inner shells promises to be a useful tool for tracking dynamics in molecular systems.5–9 Resonant x-ray absorption measured using Auger–Meitner spectroscopy also offers a powerful probe of the transient localized valence electron density in molecules.10–12
A magnetic bottle electron spectrometer (MBES) combines a strong (∼1 T), inhomogeneous magnetic field at the interaction point with a weaker (∼1.5 mT) uniform magnetic field through a long drift region (or flight tube). This configuration achieves a high collection efficiency for electrons while maintaining good kinetic energy resolution. Electrons emitted in different directions from the interaction point are guided via the Lorentz force along the magnetic field lines and into the flight tube, where they undergo cyclotron oscillations about the flight tube axis as they travel toward the detector. The original MBES design afforded 2π solid angle collection volume by collecting all electrons emitted in the hemisphere directed toward the flight tube.13,14 Later developments increased the collection efficiency to 4π by exploiting the magnetic mirror effect.15 Some designs16–18 make use of an electrostatic retardation lens to reduce the electron velocity through the flight tube and so increase kinetic energy resolution. The high collection efficiency of the MBES is particularly advantageous for electron–electron coincidence or covariance measurements,19–24 for which the signal-to-noise is critically dependent on collection efficiency.25 The MBES has also proven particularly useful for electron spectroscopy at x-ray free-electron lasers (XFELs).11,20,22,26–28
In this work, we describe the design and performance of a MBES, which is installed at the time-resolved molecular and optical sciences (TMO) instrument at the Linac Coherent Light Source (LCLS).29 Our design features a ∼2 m long flight tube, an electrostatic retardation lens, and a segmented anode electron detector, which enables the simultaneous acquisition of electron spectra in two different collection modes: high resolution and high collection efficiency. We show that the high collection efficiency mode enables covariance mapping of photoelectron/Auger–Meitner electron emission in the core ionization of nitrous oxide (N2O). We employ spectral domain ghost imaging30–32 in combination with the single-shot spectral diagnostics available at the beamline to isolate the resolution of our spectrometer from the inherent spectral width associated with self-amplified spontaneous emission (SASE) XFEL. We achieve an electron energy resolution of .
II. INSTRUMENT DESIGN
A schematic of the MBES is shown in Fig. 1(a). The inhomogeneous magnetic field at the interaction point is generated by a nickel-coated neodymium permanent magnet. The magnet is grade N52 and has a thickness of 25.4 mm and a diameter of 25.4 mm, with a magnetic field of 0.66 T at its surface. There is a soft iron cone mounted to the surface of the magnet to act as a magnetic shunt. The soft iron cone has a diameter of 25.4 mm and a height of 12.7 mm. The permanent magnet is mounted to a remotely controlled three-axis manipulator to facilitate spectrometer alignment. The tip of the iron cone sits 6 mm opposite a copper nose cone with a 6 mm OD opening. The nose cone extends 48 mm from the end of the 1.95 m long drift tube, which has an outer diameter of 76 mm. The interaction point sits directly between the tip of the iron cone and the tip of the copper nose cone.
(a) Schematic of the MBES. Not to scale; the length of the flight tube has been truncated in this depiction. (b) Cross-section of MBES taken from the graphical representation in the SIMION software package. Red contour lines show regions of equivalent magnetic field strength of the permanent magnet and solenoid. (c) Blue contour lines show electric equipotential lines due to the electrostatic lens.
(a) Schematic of the MBES. Not to scale; the length of the flight tube has been truncated in this depiction. (b) Cross-section of MBES taken from the graphical representation in the SIMION software package. Red contour lines show regions of equivalent magnetic field strength of the permanent magnet and solenoid. (c) Blue contour lines show electric equipotential lines due to the electrostatic lens.
The drift tube has an outer diameter of 76 mm and is wrapped by Kapton-insulated, 22 AWG wire, which acts as an in-vacuum solenoid with ∼1.2 turns/mm. To achieve a uniform magnetic field of mT in the drift tube, a current of ∼1 A is applied to the coil. The drift tube is mounted inside a stainless-steel vacuum tube with DN160 CF flanges on each end, which is surrounded by a sleeve of high-magnetic-permeability metal to reduce the effects of external magnetic fields on electrons traveling through the tube by a factor of roughly 50.
There is an electrostatic lens in the drift tube to create a decelerating electric field to slow the electrons. This increases their overall time-of-flight, improving the energy resolution of the spectrometer. An illustration of the lens rendered in SIMION is shown in Fig. 1(c), with lines of electric equipotential shown in blue. Our design avoids metallic grids in the electrostatic lens stack to maximize the transmission efficiency through the flight tube. This is particularly important for coincidence and covariance mapping, such as the measurement described in Sec. III D.25 The lens consists of two sets of three electrostatic plates. Within each set of three plates, the plates are electrically connected and separated by 6.1 mm. The retarding potential is applied between the two sets of three plates. The two sets of plates are separated from each other by 30.5 mm. The lens begins 183 mm from the interaction point. The position of the lens was chosen such that the magnetic field lines created by the combined fields of the permanent magnet and solenoid are parallel to the electric field lines of the lens. The lens plates are mounted in a PEEK assembly, which is modeled as free space in the SIMION model. Some iterations of the SIMION model that we used featured two sets of two lens plates joined by a conducting outer tube. We verified that the electric field in the part of the lens that the electrons traverse is minimally affected by this change.
Electrons are detected at the end of the drift tube by a 40 mm diameter micro-channel plate (MCP) detector coupled to a conical anode (Surface Concept GmbH). The anode is segmented into two concentric sections of 3 and 40 mm diameter, with a 1 mm spacing ring between them. In operation, a ∼1.8 kV potential difference is applied across the chevron MCP stack with a further ∼300 V to the anode. The voltages on the two anodes are decoupled from the high voltage source and amplified (ORTEC 9306, 1 GHz preamplifier), digitized with 168 ps precision (Abaco Systems FMC134 analog-to-digital card), and read into our data recording system.
The performance of our spectrometer was modeled using the SIMION software (version 8.1) to simulate the trajectories of electrons through the MBES. The magnetic field in the MBES was modeled by defining two sets of magnetic dipoles, each represented by two infinite permeability magnetic poles at a set magnetic scalar potential. The first dipole defined the field of the permanent magnet, and the second dipole defined the weaker solenoid field. The dipole representing the permanent magnet was positioned so that it extended into the interaction point by the same amount as the soft iron cone, finishing 3 mm behind the interaction point. The two poles representing the solenoid field were positioned at the start and end of the flight tube. The values of the magnetic scalar potential were scaled to match experimental conditions and increased monotonically along the flight tube axis. As can be seen in Fig. 1(b), showing lines of constant magnetic equipotential in the region of the inhomogeneous magnetic field, this solution produces a magnetic field whose shape matches the 4π configuration of Cheshnovsky et al.,15 in which the interaction point is closer to the detector than the region of highest magnetic field.
The segmented anode detector was chosen to enable the simultaneous collection of spectra with high energy resolution (lower collection efficiency) and high collection efficiency (lower energy resolution). In a MBES, the time-of-flight distribution of monoenergetic electrons features a characteristic long tail, consisting of electrons emitted perpendicular to the time-of-flight axis but still directed down the flight tube by the inhomogeneous magnetic field.13 In simulation, we find that these electrons with longer time-of-flight impinge on the detector at larger radii (i.e., further from the center of the detector), as shown in Figs. 2(a)–2(c). The segmented anode enables the exclusion of this long time-of-flight tail (and improved kinetic energy resolution) by selectively detecting electrons that land close to the center of the detector. For measurements requiring higher collection efficiency, it is possible to also include electrons detected on the outer anode. Inclusion of these electrons causes a broadening of the peaks in time-of-flight, to the detriment of the kinetic energy resolution.
Motivation and performance of the segmented anode detector. (a) Simulated spatial distribution at the detector plane of 10 000 electrons. The electrons’ time-of-flight (ToF) is encoded in the color of the points. The initial kinetic energy of the electrons is ∼812 eV, and the retardation voltage is 400 V. (b) Time-of-flight spectrum for the electrons shown in panel a. The blue curve shows the ToF spectrum discriminating on electrons landing within 1.5 mm of the center of the detector. (c) Dependence of ToF on radius at which electrons impinge on the detector for multiple kinetic energies and a retardation of 100 V. (d) Experimental ToF spectrum for neon KLL Auger–Meitner electrons produced following ionization by ∼1.35 keV x rays, recorded with a retardation voltage of 400 V. The red curve shows electrons detected on the outer anode, and the blue curve shows electrons detected on the inner anode. The signal for the inner anode has been scaled by a factor of 30. (e) Kinetic energy representation of spectra in panel d, compared with the spectrum produced by ∼1.5 keV photons obtained using an electrostatic analyzer.36
Motivation and performance of the segmented anode detector. (a) Simulated spatial distribution at the detector plane of 10 000 electrons. The electrons’ time-of-flight (ToF) is encoded in the color of the points. The initial kinetic energy of the electrons is ∼812 eV, and the retardation voltage is 400 V. (b) Time-of-flight spectrum for the electrons shown in panel a. The blue curve shows the ToF spectrum discriminating on electrons landing within 1.5 mm of the center of the detector. (c) Dependence of ToF on radius at which electrons impinge on the detector for multiple kinetic energies and a retardation of 100 V. (d) Experimental ToF spectrum for neon KLL Auger–Meitner electrons produced following ionization by ∼1.35 keV x rays, recorded with a retardation voltage of 400 V. The red curve shows electrons detected on the outer anode, and the blue curve shows electrons detected on the inner anode. The signal for the inner anode has been scaled by a factor of 30. (e) Kinetic energy representation of spectra in panel d, compared with the spectrum produced by ∼1.5 keV photons obtained using an electrostatic analyzer.36
III. INSTRUMENT PERFORMANCE
Our MBES is available to users of the TMO instrument29 at the LCLS XFEL, where it has been installed in the LAMP33 chamber. In this work, we characterize the performance of the MBES for x-ray photoelectron spectroscopy with an XFEL source, making use of SASE pulses with a duration of fs and a median pulse energy of ∼50 μJ. X rays were focused to a ∼1 μm diameter at the interaction point of the MBES using a pair of Kirkpatrick–Baez mirrors.34 The base pressure of the chamber housing the MBES was below 2 × 10−9 Torr, and the sample gas was introduced to the interaction point using an effusive gas needle. The TMO instrument also features a transmissive Fresnel zone plate-based x-ray spectrometer, which enables a shot-to-shot characterization of the incoming x-ray spectrum.35 This measured x-ray spectrum is used for the spectral-domain ghost imaging analysis described in Sec. III F and for the multi-parameter partial covariance analysis described in Sec. III D.
A. Segmented anode
As described in Sec. II, the MBES features a segmented anode to discriminate the time-of-flight spectrum based on the position of electron impact on the MCP detector. The central part of the anode has a diameter of 3 mm and is separated from the outer anode (diameter 40 mm) by a ring of 1 mm thickness. Panels (a)–(c) in Fig. 2 illustrate the motivation for this design. Panels (a) and (b) show simulation results for 10 000 electrons sampled from an isotropic distribution of emission angles, with an initial kinetic energy of 812 eV and 400 V retardation applied to the electrostatic lens. The coupling between electron time-of-flight and arrival position at the detector plane is shown in Fig. 2(a). The simulations show that electrons contributing to the prompt peak in the time-of-flight distribution, which are initially emitted along the axis of the flight tube, impinge close to the center of the detector. The slower electrons, which produce the tail in the time-of-flight distribution and are emitted with a significant velocity component perpendicular to the time-of-flight axis, impinge on the detector at larger radii. This effect can be seen in Fig. 2(b), which shows the simulated time-of-flight spectrum for all electrons (black dotted line) and only those that arrive within 1.5 mm of the detector center (blue line). In panel (c), we explore the coupling between time-of-flight and detector position for different kinetic energies and find that it is a general effect: electrons that impinge at larger radii have a longer time-of-flight. The retardation voltage for the simulations in panel (c) was 100 V, but we have verified that this behavior persists for all retardation voltages.
We experimentally investigated the performance of the segmented anode detector in panels (d) and (e) of Fig. 2, which show the Auger–Meitner electron spectrum of neon ionized by 1060 eV x-rays. The plot shows the measured electron distributions for the same shots, measured by the inner and outer anodes. While the outer anode has a significantly higher electron count rate, which is a result of its much larger surface area, the energy resolution is degraded compared to the spectrum measured on the inner anode. In contrast, the resolution of the Auger–Meitner spectrum measured by the inner anode is improved but has a reduced overall count rate. The retardation voltage used for these measurements was 400 V. The overall spectrometer resolution can be much improved by using a higher retardation value (see Fig. 7). We note that the performance of the segmented anode strongly depends on the alignment of the spectrometer. We achieve good alignment by maximizing the electron yield on the inner anode by translating the permanent magnet using the motorized three-axis stage on which it is mounted.
B. Energy calibration
C. Collection efficiency
The collection efficiency of a MBES can be sensitive to the kinetic energy of the electrons, the strength of the magnetic fields, and the retardation voltage applied to the electrostatic lens. Figure 3 shows how the magnetic field strength of the solenoid influences the electron counts measured on the inner and outer anodes. This measurement was performed using nitrogen KLL Auger–Meitner and valence-shell photoemission from nitrous oxide (N2O) following x-ray ionization at a photon energy of 510 eV. A retardation potential of 300 V was applied to the electrostatic lens. The magnetic field strength was controlled by scanning the current applied to the solenoid coil. As the magnetic field strength of the solenoid is increased, we observe an approximately linear increase in the detected electron counts on the outer anode (red curve in Fig. 3), which reaches a maximum at ∼1 A. At this field strength, the cyclotron radius of the highest energy electrons emitted perpendicular to the spectrometer axis is small enough that almost all of the emitted electrons are directed onto the detector. As the current is further increased, the electron trajectories are squeezed closer to the center of the flight tube, and more electrons impinge on the inner anode, with a corresponding decrease in the electron count rate on the outer anode. We observe a small overall decrease in the total number of electrons detected across both anodes, with increasing solenoid current ( counts per mJ between a solenoid current of 1 and 1.75 A). We attribute this decrease to a larger fraction of the electrons impinging on the 1 mm spacing ring between the inner and outer anodes. Electrons impinging on this spacing ring will not be detected.
Yield of nitrogen KLL Auger–Meitner electrons from N2O measured on the inner and outer anodes as a function of applied solenoid current.
Yield of nitrogen KLL Auger–Meitner electrons from N2O measured on the inner and outer anodes as a function of applied solenoid current.
We also studied the effect of the voltage applied to the retardation lens on the MBES collection efficiency. SIMION simulations show that the collection efficiency is almost independent of electron kinetic energy when no retardation field is applied to the electrostatic lens. Once a retarding field is applied, the collection efficiency displays a dependence on the value of the electron kinetic energy (KE) over retardation, i.e., the final kinetic energy of the electron through the flight tube. The collection efficiency experiences a sharp decrease at a KE over retardation of between 50 and 100 eV. The exact position of this decrease shows a weak dependence on the value of the retardation voltage. This behavior is illustrated in Fig. 4(a).
(a) Simulated collection efficiency as a function of retardation voltage and electron kinetic energy over retardation. (b) Comparison of simulated detection efficiencies from panel (a) with experimentally measured yield of ∼100 eV photoelectrons measured at different retardation voltages (black points, retardation indicated by annotation). (c) Simulated electron transmission from panel (a) for lower retardation voltages and electron kinetic energies.
(a) Simulated collection efficiency as a function of retardation voltage and electron kinetic energy over retardation. (b) Comparison of simulated detection efficiencies from panel (a) with experimentally measured yield of ∼100 eV photoelectrons measured at different retardation voltages (black points, retardation indicated by annotation). (c) Simulated electron transmission from panel (a) for lower retardation voltages and electron kinetic energies.
We validate the performance of our SIMION model using the measured yield of ∼100 eV nitrogen K-shell photoelectrons ionized from N2O by 510 eV x rays. Since we do not have an independent measurement of the number of electrons generated at the interaction point, we compare the simulated collection efficiency to the measured electron yield. We validate our SIMION model and confirm the absolute collection efficiency of our spectrometer by comparing the kinetic energy dependence of the measured electron yield and the simulated collection efficiency. The black points in Fig. 4(b) show the yield of nitrogen K-shell photoelectrons (integrated over a kinetic energy range of 97–112 eV) as a function of kinetic energy over retardation. These data were collected by scanning the applied retardation voltage (annotation on black points) while keeping the x-ray photon energy fixed at 510 eV. The colored lines show the simulated collection efficiency for different retardation voltages from panel (a). We observe good agreement between experiment and simulation: at high KE over retardation, the collection efficiency is approximately constant, while there is a steep decrease in collection efficiency as the retardation voltage approaches the initial kinetic energy of the electron. Panel (c) shows the region of panel (a) corresponding to retardation voltages below 50 V. At lower retardation voltages and kinetic energies, the collection efficiency depends more strongly on the retardation voltage.
We note that our spectrometer is fundamentally different in design from the retarding-field type MBES.37–39 Our instrument is designed to collect all electrons generated at each shot, while the retarding-field type MBES is designed to only collect a subset of the electrons generated at each shot. In a retarding-field type MBES, the purpose of the retarding field is to stop electrons below a certain kinetic energy from reaching the detector. The energy of the electron is determined by the applied value of the retarding field. In our design, the purpose of the retarding field is to slow the electrons but still allow them to pass to the detector. The energy of the electrons is instead determined by their time-of-flight. This important distinction is what enables us to perform correlation-based measurements such as those shown in Figs. 5 and 8.
(a) Schematic of Auger–Meitner decay following nitrogen K-shell photoionization of N2O by ∼790 eV x rays. (b) Region of covariance map [Eq. (3)] of the electron kinetic spectrum following 790 eV ionization of N2O. (c) Partial covariance map [Eq. (4)] demonstrating suppression of spurious correlations in panel (b). This reveals correlation between photoelectrons from ionization of the nitrogen K-shell (∼380–400 eV) and Auger–Meitner emission (∼340–360 eV), highlighted with the blue rectangle. The inset shows the average spectral profile of the incoming x-ray pulse, which produces the bimodal structure of the nitrogen K-shell photoelectron spectrum.
(a) Schematic of Auger–Meitner decay following nitrogen K-shell photoionization of N2O by ∼790 eV x rays. (b) Region of covariance map [Eq. (3)] of the electron kinetic spectrum following 790 eV ionization of N2O. (c) Partial covariance map [Eq. (4)] demonstrating suppression of spurious correlations in panel (b). This reveals correlation between photoelectrons from ionization of the nitrogen K-shell (∼380–400 eV) and Auger–Meitner emission (∼340–360 eV), highlighted with the blue rectangle. The inset shows the average spectral profile of the incoming x-ray pulse, which produces the bimodal structure of the nitrogen K-shell photoelectron spectrum.
D. Electron–electron covariance
Coincidence and covariance mapping are powerful analysis tools for extracting information on correlated processes in experimental measurements.25 At the typical electron count rates encountered at a free-electron laser (tens to thousands of electrons produced per shot), coincidence measurements would be overwhelmed with false coincidences. Covariance mapping provides a solution to this problem through the mathematical removal of false coincidences.40 Even at the much reduced count rates required for coincidence, the statistical noise is typically lower in covariance mapping, considering the finite electron detection efficiency of micro-channel plates and other single-electron detectors.41
E. Collection volume of MBES
In contrast to open area spectrometers (such as traditional VMI42 or COLTRIMS43), time-of-flight spectrometers collect electrons from a localized region. In a magnetic bottle spectrometer, the volume of the collection region is small due to the strong spatial localization of the magnetic field. In other words, electrons that are not produced very close to the central axis of the magnetic field are not collected by the spectrometer. This small collection volume offers the opportunity to perform photoionization measurements that are highly selective to different positions along the focus of the ionizing radiation.
(a) Schematic illustrating the coordinate definitions. x: flight tube axis of magnetic bottle and x-ray polarization direction, y: primary axis of gas jet propagation, and z: direction of x-ray propagation. (b) Electron yield from N2O ionized by 516 eV x rays as a function of magnet offset from interaction point (IP) according to coordinate definitions in panel (a). (c) Simulated collection efficiency of the MBES for a point source of electrons displaced from the magnet in the z direction [see panel (a)]. Simulation performed for magnet aligned to the flight tube axis (black solid line) and 1 mm offset in z from the flight tube axis (gray dashed curve).
(a) Schematic illustrating the coordinate definitions. x: flight tube axis of magnetic bottle and x-ray polarization direction, y: primary axis of gas jet propagation, and z: direction of x-ray propagation. (b) Electron yield from N2O ionized by 516 eV x rays as a function of magnet offset from interaction point (IP) according to coordinate definitions in panel (a). (c) Simulated collection efficiency of the MBES for a point source of electrons displaced from the magnet in the z direction [see panel (a)]. Simulation performed for magnet aligned to the flight tube axis (black solid line) and 1 mm offset in z from the flight tube axis (gray dashed curve).
The collection efficiency of the MBES is sensitive to the alignment between the permanent magnet, the flight tube, and the electron source. In our experiment, the electron source is defined by the interaction point (IP) of the spectrometer, where the x-rays intersect the gas jet. The most critical parameter is the alignment between the magnet and the electron source. We investigated the collection volume of the MBES using our SIMION model. Figure 6(c) shows the simulated collection efficiency as a function of the displacement of a point source of electrons from the magnet in the z-direction [see Fig. 6(a)]. We have performed this simulation for a spectrometer where the magnet and the flight tube are perfectly aligned (black solid line) and where the magnet is offset from the flight tube axis by 1 mm (gray dashed line) in z. Given the cylindrical symmetry of the spectrometer, displacement in z is representative of displacement in any direction in the yz plane. In this simulation, the electrons are emitted in an isotropic distribution with 103 eV of kinetic energy, and there is no retardation potential applied. These simulations demonstrate that the collection volume of the MBES is highly spatially localized. When the magnet is offset in z by 1 mm, the optimal position for the electron point source is also offset in z by 1 mm, but the spectrometer is not sufficiently misaligned to change its overall collection efficiency.
We experimentally investigated the collection volume of our MBES by scanning the position of the magnet relative to the IP and the flight tube using the three-axis manipulator on which the magnet is mounted. Given the results of the simulation, we expect this measurement to primarily probe the effect of displacing the magnet from the electron source. This measurement was performed using electrons with ∼100 eV kinetic energy produced by nitrogen K-shell ionization of N2O by ∼510 eV x rays. No retardation potential was applied to the lens. We plot the dependence of the electron yield on the magnet position in Fig. 6(b). The range of motion we are able to scan is limited by spatial constraints on the position of the magnet. The reduced sensitivity of the measured electron yield to motion along the axis of the spectrometer (x-axis) is expected. Moving the magnet in this direction can affect the collection efficiency of electrons, depending on their initial direction of emission.15 We find that the electron yield is slightly more sensitive to magnet displacement along the y-axis compared to motion along the z-axis. Both axes demonstrate a collection length of less than ∼1 mm. While this indicates a limited collection volume for the MBES, the dependence of the collection efficiency on the offset between the magnet and the interaction point is larger than indicated by simulation. This is likely to be a result of the extended electron source in the experiment. At the beam parameters available for the experiment, the electron signal was produced by linear x-ray interactions. As a result, our electron source was highly extended along the direction of beam propagation (z-direction), and due to the finite volume of the x-ray focus it was also extended in the y-direction. Electrons generated by the halo of the x-ray beam could also be collected by a significantly offset magnet.
F. Energy resolution
To investigate the energy resolution of the MBES and characterize the effect of the retardation lens, we performed a systematic scan of the retardation voltage. A higher retardation voltage is expected to produce higher energy resolution because the energy resolution of an MBES δE/E is approximately linearly proportional to ΔT/T.13
Figure 7 shows the measured photoemission kinetic energy spectrum of neon gas ionized by ∼1.35 keV x rays. We record this spectrum at six different retardation voltages, as indicated on the figure. The neon KLL Auger–Meitner emission has three dominant features separated by ∼30 eV, corresponding to different final states of the neon dication.36 The expected energetic position of these three features is indicated by the vertical dotted lines. We observe that increasing the retardation voltage improves the energy resolution of the spectrometer: at higher retardation voltages, the three primary KLL emission lines appear more clearly separated and align with the previously measured values.
Photoelectron kinetic energy spectrum of neon recorded at a photon energy of 1.35 keV. The three primary peaks of the Ne KLL Auger–Meitner emission spectrum become increasingly better resolved as the voltage applied to the electrostatic retardation lens is increased. The three dashed lines correspond to previously measured values of these features.36
Photoelectron kinetic energy spectrum of neon recorded at a photon energy of 1.35 keV. The three primary peaks of the Ne KLL Auger–Meitner emission spectrum become increasingly better resolved as the voltage applied to the electrostatic retardation lens is increased. The three dashed lines correspond to previously measured values of these features.36
To quantify the resolving power of the MBES, we measured the widths of the photoionization features produced by K-shell ionization of N2O as a function of retardation voltage. This measurement was performed using x rays with a central photon energy of ∼516 eV. The target molecule was chosen because the nitrogen K-shell photoemission spectrum of N2O is well-studied and consists of two features corresponding to ionization of the central and terminal nitrogen sites, which have binding energies of 412.5 and 408.5 eV, respectively.44
The SASE XFEL has a broad (∼5 eV) spectral bandwidth and inherent shot-to-shot fluctuations in the spectral profile, which can significantly degrade spectroscopic resolution. To mitigate the effect of the SASE bandwidth and spectral jitter and isolate the resolution of the MBES, we employed spectral domain ghost imaging,31,45 as described in the Appendix.
An example of the two-dimensional map of photoelectron kinetic energy vs incoming photon energy is presented in Fig. 8(a). We extract the kinetic energy spectrum from the two-dimensional map by averaging across all photon energies after accounting for the energy dispersion of the photoelectron. The width of the measured photoelectron feature for different retardation values is shown in Fig. 8(b) and can be seen to decrease with increasing retardation. The MBES collection efficiency at very low values of kinetic energy over retardation is highly suppressed, as shown in Fig. 4. This effect results in a significant decrease in yield for the lower energy photoelectrons at a retardation of 90.5 V. We quantify the resolution by fitting a Gaussian curve to the photoline of the terminal nitrogen site at 107 eV. The dependence of this width on retardation is shown in Fig. 8(c). The results show that when there is no retardation voltage applied, it is still possible to discern the 4 eV separation between the central and terminal lines thanks to the long flight tube. Nonetheless, by increasing the retardation voltage, the kinetic energy resolution can be significantly improved.
(a) Dispersion of photoelectron kinetic energy vs photon energy for the N(1s) photoionization of N2O, obtained using spectral domain ghost imaging. (b) Binding energy spectrum for N(1s) photoionization of N2O obtained from dispersion plot in panel a. The measured peak width decreases with increasing retardation voltage. The black line shows previous high-resolution measurements made with a synchrotron source from Ref. 44. The change in relative intensities at larger retardation voltages is a result of the MBES transmission function [see Fig. 4(c)]. Widths correspond to Gaussian fits of the terminal photoline centered at 408.5 eV of binding energy. The dashed black line at 0.70 eV corresponds to the measured width from Ref. 44.
(a) Dispersion of photoelectron kinetic energy vs photon energy for the N(1s) photoionization of N2O, obtained using spectral domain ghost imaging. (b) Binding energy spectrum for N(1s) photoionization of N2O obtained from dispersion plot in panel a. The measured peak width decreases with increasing retardation voltage. The black line shows previous high-resolution measurements made with a synchrotron source from Ref. 44. The change in relative intensities at larger retardation voltages is a result of the MBES transmission function [see Fig. 4(c)]. Widths correspond to Gaussian fits of the terminal photoline centered at 408.5 eV of binding energy. The dashed black line at 0.70 eV corresponds to the measured width from Ref. 44.
IV. ENERGY-DEPENDENT MODULATION IN ELECTRON TRANSMISSION EFFICIENCY
Finally, we discuss an artifact that is common to magnetic bottle electron spectrometers: a strongly energy-dependent modulation of the electron transmission function, which is often amplified when a retarding field is applied to the electrostatic lens. This artifact is a result of the cyclotron oscillations of the electrons as they travel through the magnetic-field of the flight tube and propagate toward the detector.46
This oscillatory behavior of the electron trajectories is illustrated in the simulations shown in Fig. 9. We plot ten trajectories of electrons emitted in arbitrary directions uniformly sampled on a sphere with ∼300 eV of initial kinetic energy. The dependence of the cyclotron radius on the direction of the electron velocity described in Eq. (5) manifests as the dependence of the trajectory on the initial emission angle from the flight tube axis, as shown in panel (c). This effect is often colloquially referred to as “sausaging,” because the three-dimensional shape of the electron trajectories through the flight tube is reminiscent of the shape of a link of sausages.
(a) SIMION simulation of trajectories of ∼300 eV electrons with different initial emission angles relative to the flight tube axis. The retardation voltage is 0 V, and the solenoid current has been reduced from the standard operation parameters to amplify the radius of the cyclotron oscillation. (b) Zoom-in of the trajectories at the end of the flight tube, close to the electron detector. (c) Dependence of electron trajectories through the flight tube on the angle of direction of initial emission relative to the flight tube axis. The dotted black line shows the central axis of the flight tube.
(a) SIMION simulation of trajectories of ∼300 eV electrons with different initial emission angles relative to the flight tube axis. The retardation voltage is 0 V, and the solenoid current has been reduced from the standard operation parameters to amplify the radius of the cyclotron oscillation. (b) Zoom-in of the trajectories at the end of the flight tube, close to the electron detector. (c) Dependence of electron trajectories through the flight tube on the angle of direction of initial emission relative to the flight tube axis. The dotted black line shows the central axis of the flight tube.
The effect of the oscillatory behavior of the electron trajectories on the time-of-flight spectrum can be seen in the experimental measurement in Fig. 10(a). This figure shows the measured electron time-of-flight spectrum following the ionization of N2O molecules by a 520 eV x-ray pulse. The strong periodic modulation of electron collection efficiency with the electron time-of-flight is apparent in the spectrum recorded on the inner anode of the detector. According to Eq. (6), the modulation frequency should increase with increasing magnetic field and, therefore, increasing solenoid current. This effect can be seen in Figs. 10(b) and 10(c), where the Fourier transform of the electron time-of-flight spectra recorded on the outer [(b)] and inner [(c)] sections of the detector is shown as a function of the current applied to the solenoid coil. There is a dominant Fourier component, indicated by the white dashed-line, whose frequency increases linearly with solenoid current in accordance with the well-known dependence of cyclotron frequency on magnetic field strength. Below ∼1.1 A, the modulation is particularly pronounced on the outer section of the detector (outer anode), while above this value the effect dominates the inner anode. This is a result of the geometry of the two detectors: as we increase the solenoid current, the electron trajectories flatten to the central axis of the flight tube, and the modulation amplitude grows stronger on the inner anode and less prominent on the outer.
(a) Time-of-flight (ToF) spectrum for photoelectrons produced by ionization of N2O by 520 eV x rays, measured on the inner anode at a solenoid current of 2 A, showing a strong periodic modulation in the electron transmission. (b) Fourier transform of the ToF spectra as a function of applied solenoid current for the outer anode. (c) Fourier transform of the ToF spectra as a function of applied solenoid current for the inner anode. For frequency values greater than 0.01 GHz, the color scales in panels (b) and (c) have been multiplied by 50 and 25, respectively.
(a) Time-of-flight (ToF) spectrum for photoelectrons produced by ionization of N2O by 520 eV x rays, measured on the inner anode at a solenoid current of 2 A, showing a strong periodic modulation in the electron transmission. (b) Fourier transform of the ToF spectra as a function of applied solenoid current for the outer anode. (c) Fourier transform of the ToF spectra as a function of applied solenoid current for the inner anode. For frequency values greater than 0.01 GHz, the color scales in panels (b) and (c) have been multiplied by 50 and 25, respectively.
One solution to the periodic modulation in electron collection efficiency is to increase the solenoid current to reduce the cyclotron radius such that all electrons fall on the detector. However, increasing the solenoid current to the required value may be technically challenging and also result in a decrease in electron energy resolution.13 Careful alignment of the spectrometer can suppress the amplitude of the modulation. We have achieved good spectrometer alignment in our design by maximizing the number of counts detected on the inner anode vs the number of counts detected on the outer anode. However, some periodic modulation in electron collection efficiency remains a general feature for measurements performed with a MBES. Here we develop an analytical method to remove this artifact in data post-processing.47 We demonstrate this routine using the electron spectrum recorded by our MBES following the ionization of gas-phase para-aminophenol at ∼252 eV. The time-of-flight spectrum was recorded with a retardation of 190 V and is shown in Fig. 11(a) before (dashed red) and after (solid blue) removal of this artifact.
Demonstration of the filtering algorithm to remove structure caused by cyclotron motion of electrons in the magnetic bottle for the x-ray valence ionization spectrum of para-aminophenol. (a) Time-of-flight representation with the raw spectrum showing the artifact before (dashed red) and after (blue) applying the filtering algorithm. (b) FFT power spectrum at different points in the filtering algorithm. Red lines show the spectrum of the raw data before (tick dotted red line) and after (thin dotted red line) taking the logarithm, i.e., D(ω) and . Blue lines show the spectrum of the log-filtered data before (thick blue line) and after (thin blue line) exponentiating, i.e., F[ln Df(ω)] and . (c) Data in the electron kinetic energy representation before (blue dashed line) and after (black line) the filtering algorithm.
Demonstration of the filtering algorithm to remove structure caused by cyclotron motion of electrons in the magnetic bottle for the x-ray valence ionization spectrum of para-aminophenol. (a) Time-of-flight representation with the raw spectrum showing the artifact before (dashed red) and after (blue) applying the filtering algorithm. (b) FFT power spectrum at different points in the filtering algorithm. Red lines show the spectrum of the raw data before (tick dotted red line) and after (thin dotted red line) taking the logarithm, i.e., D(ω) and . Blue lines show the spectrum of the log-filtered data before (thick blue line) and after (thin blue line) exponentiating, i.e., F[ln Df(ω)] and . (c) Data in the electron kinetic energy representation before (blue dashed line) and after (black line) the filtering algorithm.
After applying the logarithm, the broadening at the harmonic 0.045 rad/ns due to the convolution in Eq. (8) is suppressed, and we instead observed a narrow peak in the Fourier amplitude, as shown in Fig. 11(b). To recover the signal S(t), we filter out the harmonics of ωs from the log-scaled spectra using Butterworth filters to generate the frequency-domain filtered data . To recover the filtered data in real space Df(t), we apply an inverse Fourier transform and then exponentiate. This method of examining the Fourier transform of the logarithm has been used to study situations where the Fourier transform contains periodic peaks because it maps the convolution of two functions onto their sums.48
We also implemented the log-space Fourier filter algorithm on a two-dimensional measurement of the electron emission from para-aminophenol following excitation close to the oxygen K-edge. The x-ray photon energy was scanned over the oxygen K-edge region from ∼505 to ∼550 eV, and the high-energy electron emission spectrum was recorded with 400 V applied to the electrostatic lens. The resonant Auger–Meitner map (incoming x-ray photon energy vs outgoing photoelectron energy) is shown in Fig. 12. The photoelectrons produced by x-ray ionization of the valence shell show a clear linear dispersion, and the resonant Auger–Meitner emission after promotion of an electron from the oxygen 1s to the 2pπ* orbital is clear at ∼532 eV. Above the oxygen 1s ionization potential, the electron emission converges to the normal KLL Auger–Meitner emission.
Two-dimensional map of electron emission from para-aminophenol following excitation at the oxygen K-edge before (a) and after (b) the filtering algorithm to remove the periodic modulation in collection efficiency. The x-axes show the electron kinetic energy spectrum measured with a retardation of ∼400 eV, and the y-axes show the x-ray central photon energy. Between x-ray photon energies of 530–535 eV, we observe resonant Auger–Meitner emission following resonant oxygen 1s → valence excitation. At photon energies above 535 eV, the spectrum converges to normal oxygen KLL Auger–Meitner emission. We also observe dispersive lines due to x-ray valence ionization.
Two-dimensional map of electron emission from para-aminophenol following excitation at the oxygen K-edge before (a) and after (b) the filtering algorithm to remove the periodic modulation in collection efficiency. The x-axes show the electron kinetic energy spectrum measured with a retardation of ∼400 eV, and the y-axes show the x-ray central photon energy. Between x-ray photon energies of 530–535 eV, we observe resonant Auger–Meitner emission following resonant oxygen 1s → valence excitation. At photon energies above 535 eV, the spectrum converges to normal oxygen KLL Auger–Meitner emission. We also observe dispersive lines due to x-ray valence ionization.
V. CONCLUSION
In this paper, we have presented the design and performance of a MBES for x-ray photoelectron, absorption, and Auger–Meitner spectroscopy. Our spectrometer is installed at the TMO instrument of the Linac Coherent Light Source and is available to users of the facility. It is equipped with electrostatic retardation lenses and a segmented anode, which enables high kinetic energy resolution (δE/E ∼ 1%) measurements of high energy (several hundred eV) photoelectrons. The segmented anode also enables the simultaneous collection of data in two different modes: high collection efficiency, using electrons detected on both anodes, and high resolution, using only electrons detected on the inner anode. The small collection volume due to the strongly inhomogeneous magnetic field at the interaction point affords a small collection volume, enabling measurements that are selective to different positions along the focus of the ionizing radiation. We achieve high resolution x-ray photoelectron spectroscopy measurements when coupled to a noisy x-ray free-electron laser by employing spectral domain ghost imaging, and we achieve covariance measurements of correlated photoelectron/Auger–Meitner electron emission from N2O. We present a robust analysis procedure to correct for the well-known periodic modulation in collection efficiency due to cyclotron motion of the electron in the MBES flight tube. Upgrades to the instrument will include the integration of an ion time-of-flight spectrometer for concurrent ion/electron spectroscopy. Our spectrometer can currently be used for a variety of user experiments and will be capable of operating in the MHz regime with the upgraded high-repetition-rate LCLS-II source.
ACKNOWLEDGMENTS
We are grateful to Jan Metje, Markus Gühr, and Richard Squibb for useful discussions on the design of the MBES and to John Pennachio and Denise Welch for excellent technical support. K.B. and D.R. acknowledge the support of the Department of Energy, Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, Grant No. DE-FG02-86ER13491. K.B. acknowledges the support of the US Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education (ORISE) for the DOE. ORISE is managed by ORAU under Contract No. DE-SC0014664. D.R. acknowledges the hospitality and support of SLAC during his sabbatical. N.B. acknowledges the support of the Department of Energy, Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, Grant No. DE-SC0012376.
Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515.
The work by J.P.C., T.J.A.W., J.W., E.I., J.T.O., E.T., and T.D. is supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Kurtis Borne: Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jordan T. O’Neal: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jun Wang: Formal analysis (equal); Investigation (equal); Software (equal); Validation (equal); Writing – review & editing (equal). Erik Isele: Formal analysis (equal); Investigation (equal); Writing – review & editing (supporting). Razib Obaid: Conceptualization (supporting); Investigation (supporting); Writing – review & editing (supporting). Nora Berrah: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Resources (equal); Writing – review & editing (equal). Xinxin Cheng: Investigation (equal); Writing – review & editing (equal). Philip H. Bucksbaum: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Justin James: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Andrei Kamalov: Investigation (equal); Writing – review & editing (equal). Kirk A. Larsen: Investigation (equal); Writing – review & editing (equal). Xiang Li: Investigation (equal); Writing – review & editing (equal). Ming-Fu Lin: Investigation (equal); Writing – review & editing (equal). Yusong Liu: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Agostino Marinelli: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Adam M. Summers: Investigation (equal); Writing – review & editing (equal). Emily Thierstein: Investigation (equal); Writing – review & editing (equal). Thomas J. A. Wolf: Investigation (equal); Writing – review & editing (equal). Daniel Rolles: Investigation (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Peter Walter: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). James P. Cryan: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Taran Driver: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon request.