Ionization Mechanisms

The ionization of clusters starts with the ionization of individual atoms. Especially at the beginning of the light pulse, the cluster environment does not influence the coupling of the light pulse to the atoms, therefore they can be regarded as if they were

FIG. 2.14: Photon energy dependent ionization processes. The predominant processes at the onset of ionization are shown. (a) In the infrared regime, the atomic potential is bent by the strong light field to such an extent that the electron can tunnel through the barrier. (b) At ultraviolet to extreme ultraviolet photon energies, the atom can be ionized at lower intensities via single- or multiphoton absorption. (c) In the x-ray regime, the photon energy is sufficient to directly address inner-shell electrons. Already low power densities lead to ionization. The schematic is based on a visualization by C. Bostedt. Adapted from Ref. [130].

isolated [114]. Hence, the following description of ionization mechanisms concentrates on theonset of ionization in atoms.

In general, for a photoionization event to take place at least one photon needs to be absorbed by the atom. This of course depends on the atom’s ionization potential𝐸_IP and the photon energy𝐸_ph of the incoming light field. Even if the photon energy is too small to overcome the ionization potential, the atom can get ionized by absorption of multiple photons [126] ortunneling of the electron through the potential barrier [127]

given a sufficiently high field intensity. Which process prevails is strongly wavelength-dependent. In Fig.2.14 the dominant processes at the onset of ionization for different photon energies are shown. In the infrared regime (𝐸_ph ∼ 1 eV), as illustrated in Fig.2.14 (a), the photon energy is far too small for single- or multiphoton ionization. At high intensities, however, the light field is strong enough to bend the atomic potential to such an extreme thattunnel ionization occurs where the electron can simply tunnel through the barrier. Therefore, the tunneling time has to match the period of the oscillating field, i.e., the frequency of the field has to be low enough to allow the electron to pass the barrier within a half-cycle of the light wave [115]. For even stronger fields, the barrier can be shifted below the ionization potential enablingbarrier suppression ionization [115]. In the case of higher photon energies, as shown in Fig. 2.14 (b) for the ultraviolet to extreme ultraviolet regime (𝐸_ph ∼10 eV), electrons from the valence shell can be promoted to the continuum by multiphoton ionization already at lower intensities, and a few photons are sufficient to further ionize the atom [128]. In the x-ray regime, as depicted in Fig. 2.14 (c), inner-shell electrons are addressed as the photon energy is sufficient fordirect ionization. In the course of the process, additional decay channels can lead to a further ionization of the atom [129]. For example, in an Auger decay the inner-shell vacancy is filled by an electron from a higher-lying shell which is accompanied by the emission of another electron carrying the excess energy.

The absorption of a single x-ray photon can therefore result in a multiply ionized atom.

Thus, already in low intensity x-ray beams highly charged ions can be produced.

In order to classify the interaction of the light field with matter, a field dominated and a photon dominated regime can be identified depending on the ability of the light field to couple to the atomic potential. Therefore, it is helpful to consider the quiver motion

2.4. Light-Cluster Interaction 27

FIG. 2.15: Photon energy and intensity dependent coupling regimes. The shaded areas depict the conditions attainable at different light sources. Free-electron lasers in the vacuum ultraviolet regime (VUV-FEL) and x-ray regime (XFEL) clearly induce photon dominated ionization processes. Reprinted from Ref. [115].

of a free electron induced by the light field. The cycle-averaged kinetic energy of the oscillating electron is called theponderomotive potential 𝑈_P, given by [115]

𝑈_P= 𝑒²ℰ₀²

4𝑚_e𝜔² (2.41)

with 𝑒and 𝑚e the electron charge and mass, respectively, 𝜔 the frequency of the light field and ℰ₀ its peak field strength. The ponderomotive potential can be calculated using the power density 𝐼 and the wavelength𝜆of the light field in convenient units by the relation𝑈P= 9.33×10⁻²⁰eV·𝐼[W cm⁻²]·(𝜆[nm])². The prevailing coupling mechanism is then given by a comparison of the electron’s ponderomotive potential to the atom’s ionization potential with a transition from field- to photon-dominated coupling at𝑈P=𝐸IP [115]. This is illustrated in Fig. 2.15as an intensity-frequency diagram for a typical ionization potential of a few electron volts. The shaded areas indicate the attainable intensities at photon energies from different light sources. It can be seen that ionization mechanisms in atoms exposed to infrared radiation are typically field dominated while in extreme ultraviolet or x-ray light fields, photon dominated ionization processes prevail. An estimate whether ionization proceeds predominantly via electron tunneling or (multi)photon absorption can be given using the Keldysh parameter 𝛾 [131],

𝛾 =𝜔·𝜏_t=

√︃𝐸_IP

2𝑈_P, (2.42)

that compares the tunneling time 𝜏_t=^√︀2𝑚_e𝐸_IP/(𝑒ℰ₀)² to the frequency of the light field. Tunnel ionization prevails if the tunneling time is shorter than or comparable to the period of the light field (i.e., 𝛾 ≲1), while for 𝛾 ≫ 1, single- or multiphoton ionization is the dominant process [115].

In the course of the ionization process the cluster environment is not negligible anymore.

For example, in studies at a short-wavelength FEL, irradiation with intense light pulses led to higher final charge states in clusters than in atoms [132,133]. This pronounced absorption of energy by clusters was investigated in further theoretical work [116,117, 134,135] showing it is caused by an efficient coupling of the light field to the nanoplasma.

A more detailed description of the dynamics following the initial ionization process is given in the next section.