Ion Guide

As charged clusters tend to repel each other, they have to be focused in order to travel through the experimental setup. Furthermore the mechanical alignment of the different parts of the experimental setup can not be achieved perfectly. Thus the clusters have to be deflected towards the correct direction in order to travel through the apparatus, fit through the interaction zone (about 2 mm in diameter), and hit the detector. This guidance is achieved by applying electrostatic lenses and

3.3 Time-Of-Flight Mass Spectrometer steerers. A typical realization is displayed in figure 3.6. Using electrostatic fields to manipulate the paths of the clusters has the advantage that the effect of the field only depends on the cluster’s kinetic energy and is therefore independent of its mass.

Figure 3.6: Schematic drawing of an electrostatic lens and an X-Y steerer, which is employed in the experimental setup. The applied voltages are: ground potential (V₀), lens voltage (V_lens) and the steerer plus and minus volt-ages for x and y (V_sx/sy^+/−).

Electrostatic Steerer

The steerer is built like a simple capacitor with two plates. At the two plates the same voltage with opposite sign is applied (V_sx/sy^+/−). Before and after the plates a cylindrical electrode is situated. These electrodes are kept at ground potential (V₀) to ensure that the clusters have the same kinetic energy before and after traversing the steerer. The field between the plates is quasi linear. When a cluster travels through the field it is deflected into another direction. As the field is linear, clusters that do not travel through the center of the steerer get deflected into the same direction as the cluster that is traveling through the center.

Electrostatic Lens

The electrostatic lens consists of three cylindrical electrodes. The outer electrodes are kept at ground potential (V₀), which ensures that the clusters have the same kinetic energy before and after passing the lens. The electrode in the middle is set to a certain voltage (V_lens). The potential lines of the resulting electric field look similar to an optical lens and have similar effects on a cluster beam. Clusters which travel through the center of the lens are not deflected. However, the ones farther

details on how to interpret a spectrum of kinetic energy are presented in section 2.2.

The standard method to measure the kinetic energy of electrons is to use electric or magnetic fields, where the hemispherical analyzer is the most commonly used spectrometer, employing electric fields. This type of spectrometer has the main disadvantage that only a few percent of the omnidirectional emitted electrons are collected.

The goal of this thesis is to measure two-photon electron signals from clusters using two femtosecond laser pulses. In this technique the intensity of the laser pulse has to be kept at moderate levels to minimize two-photon signals from one pulse only, thus the signals are often very faint. A magnetic-bottle-type time-of-flight spectrometer is employed, which permits to collect practically all emitted electrons.

This is achieved by applying a strong divergent magnetic field. As the Lorentz force for charged particles is perpendicular to the direction of motion, the kinetic energy is maintained throughout the magnetic field. This spectrometer was first employed by Kruit and Read [75] to analyze electrons and shortly thereafter by Chesnovsky et al. ([67]), and Ganteför et al. [76] to analyze photoelectrons generated from clusters in the gas phase.

The working principle of this electron spectrometer is basically the same as for the mass spectrometer. The electrons require a certain amount of time to travel through the electric field free area depending on the kinetic energy according to the relation tα^√_E¹

kin (see equation 3.1). The time axis of the spectrometer can be calibrated to kinetic energy by measuring electronic states with known binding energy. Charged particles are traveling in spirals around magnetic field lines due to the Lorentz force. When a particle enters a region where the magnetic field strength becomes stronger, the field lines are not parallel anymore. This results in a net force against the direction of motion. Depending on the velocity of the particle and the magnetic field strength this force can turn around the travel direction. Such a strong divergent field is called a magnetic mirror as charged particles which travel towards the strong field region are reflected. A combination of two magnetic mirrors is called

3.4 PES Spectrometer - Magnetic Bottle a magnetic bottle as charged particles can be stored in such a configuration.

In figure 3.7 the working principle of the spectrometer is illustrated. The charged clusters travel through the region where the magnetic field lines diverge.

There they are illuminated by a laser pulse and electrons are photo detached in all directions. This region, where the laser interacts with the clusters is called interaction zone. The path of one electron moving away from the detector is drawn in blue and illustrates that the electron’s direction of motion is turned around, guiding the electron towards the detector.

Figure 3.7: A Schematic drawing is illustrating the magnetic-bottle-type time-of-flight spectrometer. A cluster Xn- enters the divergent magnetic field from the left. An electron is photo detached from the cluster and the neutral cluster exits the magnetic field. The electron traveling away from the detector turns around and travels up to the detector, as indicated by the electron path in blue. (Adapted from [37].)

The major limitation of the energy resolution of the detector is Doppler broad-ening resulting from the motion of the cluster. The electron velocities measured at the detector are a combination from the cluster velocity (|~v_cluster |) and from the photoelectron velocity (| ~v_photon |) due to the detachment process. The resulting velocity can be calculated by vector addition of the two velocities, with maximum and minimum values ranging from |~v_photon | + |~v_cluster | to |~v_photon | − | ~v_cluster |, respectively. The resulting kinetic energy of the electron can in turn be calculated as follows

single peak of Ag , which appears at a kinetic energy of 1.77 eV, splits up into two peaks separated by about 380 meV. This splitting occurs since the laser is polarized along the direction of motion of the clusters and the probed state emits most of the electrons in the direction of the polarization of the laser. The center of the peaks in (b) nicely fit values calculated using equation 3.2 and 1kV for the applied acceleration field. The splitting of Ag^- agrees with measurements and simulations for photoelectron spectra of Cu^- presented in [67].

Figure 3.8: PES spectrum of Ag^-. (a) shows the resulting spectrum with proper de-celeration. Here a single peak at a kinetic energy of 1.77 eV is measured.

In (b) there is no deceleration and the peak splits up into two peaks separated by about 380 meV.

3.4 PES Spectrometer - Magnetic Bottle

Interaction Zone

The setup of the interaction zone is shown in figure 3.9. When investigating the mass spectrum of the clusters (deceleration is turned off), the clusters cross the interaction zone through the copper tubes from right to left. The laser crosses the chamber through the aluminum tube from bottom right to top left. The paths of clusters and laser meet at the center of the interaction zone, above a permanent magnet, which provides the strong inhomogeneous field for the electron spectrometer. The magnetic field lines from the permanent magnet are paralleled with a weak magnetic field which is provided by an electromagnetic solenoid around the housing of the drift area. The field lines hit the detector at the end of the drift area. Additionally, two Helmholtz coil pairs are mounted around the housing of the drift area to correct for influences of earth’s magnetic field.

Figure 3.9: Drawing of the interaction zone. The clusters transverse the interaction zone through the copper tubes coming from the upper right side. The laser enters from the bottom right side through the aluminum tube. In the center, the permanent magnet is visible.

To slow down a specific cluster size, an electric field is applied to the first copper tube while the bunch is inside. The other copper tube is kept at ground potential.

The electric field between the two copper tubes slows down and additionally focuses the clusters into the interaction zone. As the deceleration field is a little stronger

in figure 3.10. An electronic state of Ag3- is measured and the time when the laser hits the clusters is varied. In the case that the laser interacts with the cluster bunch when all cluster, including the ones with fast velocities, are within the interaction zone (figure 3.10 (a)), the measured PES peak is broad. This happens because the electrons gain extra velocity from the residual motion of the fast clusters. In the case that the laser interacts with the cluster bunch when the clusters with high residual motion have already left the interaction zone (figure 3.10 (b)), the peak is narrower, indicating better resolution.

Figure 3.10: PES measurements of Ag3- are presented. In (a) the laser irradiates the cluster bunch while the clusters with a high residual motion are still present in the interaction zone. In (b), the time when the laser irradiates the cluster bunch is delayed until the clusters with a high residual motion have left the interaction zone.