## 2 Materials and Methods
### Magnetic Bottle Electron Spectrometer  
The magnetic bottle time-of-flight electron spectrometer (MBES) has a high collection efficiency, covering up to the full 4\(\pi\) solid angle [26]. Thus, a large number of electrons can be efficiently detected, which is especially important in experiments with dilute samples. The magnetic bottle spectrometer is characterized by a strong and inhomogeneous magnetic field of about 1 Tesla at the interaction region, which joins onto a much weaker (\(\sim\)1 mT), homogeneous magnetic field created by a solenoid around the flight tube. Electrons ejected in the interaction region into any direction are thus confined into the flight tube. The time-of-flight (TOF) of the electrons from the interaction region to detection is determined and subsequently transformed into kinetic energy. Our specific design is illustrated in Figure 3. A vacuum tube with DN160 flanges houses the flight tube, which is protected from external magnetic fields by a \(\upmu\)-metal shield. Wound onto the flight tube, a solenoid is generating the weak homogeneous field along the electron flight path. The coil has 1450 windings and is fed by a current of 400 mA producing a magnetic field of around 0.4 mT. Winding the coil directly on the flight tube has the advantage that the solenoid can be brought close to the interaction region. In addition, the design allows that the whole instrument can be taken out of the main chamber by unbolting a single DN 250 flange at the central cross. Close to the interaction region, right at the entrance of the flight tube, a stack of electrostatic lenses can be used to retard/repel the electrons. A permanent magnet with a soft iron pole tip generates the strong, inhomogeneous field in the interaction region. The space available at the beamline is used efficiently to maximize the instruments resolution, resulting in an optimal flight tube length of 1.7 m.  
The transition from the inhomogeneous to homogeneous field occurs over a short distance of about 10 cm. The lens stack is placed inside the front of the flight tube, at the beginning of the homogeneous part of the magnetic field. At this point, the momentum in direction of the center axis of the flight tube is approximately equal for electrons of equal kinetic energy. The permanent magnet of the instrument is mounted in a temperature-controlled holder on a manipulator. By this construction, the magnet can be brought close to the interaction region as well as retracted if other equipment is brought into the interaction region, such as a diode or a Ce-YAG screen. Elevated temperatures of 60 \({}^{\circ}\)C generally prevent sample building up on the magnet tip and introducing electrostatic inconsistencies. The detector assembly (purchased from Roentdek Handels GmbH) consists of a grid, followed by a chevron MCP stack with an 80 mm diameter and an anode. The grid is held at the potential of the flight tube (i.e., the retardation potential). The electrons are then accelerated towards the front MCP by a +300 V potential change over 3 mm. Subsequently, the electrons are multiplied by the MCP arrangement using a potential on the MCP backside of 1950 V. The anode, used for picking up the signal is held at 2300 V. The signal is picked up by a high-pass filter and sent to a 12 bit analog-digital converter, which we use at a sample rate of 2 Gs. A single electron pulse has a width of 10 ns. The data we present in this paper has been accumulated in the integration mode, i.e., all individual TOF traces have been added. Alternatively, for lower electron yield, individual electron hits can be identified by using a (software) constant fraction discriminator and then added individually to a TOF array. We transform spectra taken in the TOF domain to the kinetic energy domain by the following procedure. The distance from the interaction region to the detector is divided into three parts.