The interaction of intense laser pulses with nanometer scale atomic clusters has been an active area of study since the advent of amplified femtosecond lasers. In the case of infrared irradiation of noble gas clusters, direct field-driven ionization results in the ejection of energetic electrons, high ion charge states, and Coulomb explosion of the ion core of the clusters. These processes result from electron motion driven by the cluster potential and the large ponderomotive potential of the laser field. When extreme ultraviolet (XUV) pulses interact with clusters, the mechanisms responsible for the infrared response are 'turned off' because the ponderomotive potential is very small. We have conducted cluster experiments at 38nm using focused XUV pulses produced by high harmonic generation with a 15TW Ti:Sapphire laser. We measured the charge states and kinetic energy spectra of ions produced in the interaction, and observe substantial ion population up to Xe⁵⁺, with a small number of Xe⁶⁺-Xe⁸⁺ ions produced by collisional ionization by hot plasma electrons. The ion kinetic energy spectrum indicates a hydrodynamic expansion at an ion temperature of 8eV. This is in stark contrast to intense infrared/cluster interactions, where clusters are stripped of electrons to a large degree and expand by Coulomb forces, resulting in far higher ion kinetic energy for similar degrees of ionization. / text

The purpose of this thesis is to advance the understanding of strong-field QED processes in short laser pulses. The processes of non-linear one-photon and two-photon Compton scattering are studied, that is the scattering of photons in the interaction of relativistic electrons with ultra-short high-intensity laser pulses. These investigations are done in view of the present and next generation of ultra-high intensity optical lasers which are supposed to achieve unprecedented intensities of the order of 10^24 W/cm^2 and beyond, with pulse lengths in the order of some femtoseconds. The ultra-high laser intensity requires a non-perturbative description of the interaction of charged particles with the laser field to allow for multi-photon interactions, which is beyond the usual perturbative expansion of QED organized in powers of the fine structure constant. This is achieved in strong-field QED by employing the Furry picture and non-perturbative solutions of the Dirac equation in the presence of a background laser field as initial and final state wave functions, as well as the laser dressed Dirac-Volkov propagator. The primary objective is a realistic description of scattering processes with regard to the finite laser pulse duration beyond the common approximation of infinite plane waves, which is made necessary by the ultra-short pulse length of modern high-intensity lasers. Non-linear finite size effects are identified, which are a result of the interplay between the ultra-high intensity and the ultra-short pulse length. In particular, the frequency spectra and azimuthal photon emission spectra are studied emphasizing the differences between pulsed and infinite laser fields. The proper description of the finite temporal duration of the laser pulse leads to a regularization of unphysical infinities (due to the infinite plane-wave description) of the laser-dressed Dirac-Volkov propagator and in the second-order strong-field process of two-photon Compton scattering. An enhancement of the two-photon process is found in strong laser pulses as compared to the corresponding weak-field process in perturbative QED.

We have investigated processes of ionization, energy absorption and subsequent explosion of atomic and molecular clusters under intense laser illumination using numerical as well as analytical methods. In particular, we focused on the response of composite clusters, those consisting of different atomic elements, to intense light pulses. Another major theme is the effect of the molecular structure of clusters on their Coulomb explosion. The action of intense laser pulses on clusters leads to fundamental, irreversible changes: they turn almost instantaneously into nanoplasmas and subsequently disintegrate into separate ions and electrons. Due to this radical transformation, remarkable new features arise. Transient cluster nanoplasmas are capable of absorbing enormous amounts of laser energy. In some cases more than 90 % of incident laser energy is absorbed by a gas of clusters with a density much smaller than that of a solid. After the efficient absorption, the energy is transformed into production of energetic ions, electrons, photons, and even neutrons. Composite clusters show especially interesting behavior when they interact with intense laser pulses. Nanoplasmas formed in composite clusters may absorb even more laser energy, than those formed in homogeneous clusters, as we demonstrate in this work. One of the most important results of this thesis is the identification of a novel type of plasma resonance. This resonance is enabled by an unusual ellipsoidal shape of the nanoplasma created during the ionization process in a helium droplet doped with just a few xenon atoms. In contrast to the conventional plasma resonance, which requires significant ion motion, here, the resonant energy absorption occurs at a remarkably fast rate, within a few laser cycles. Therefore, this resonance is not only the most efficient (like the conventional resonance), but also, perhaps, the fastest way to transfer laser energy to clusters. Recently, dedicated experimental studies of this effect were performed at the Max Planck Institute in Heidelberg. Their preliminary results confirm our prediction of a strong, avalanche-like ionization of the helium droplet with a small xenon cluster inside. A conventional plasma resonance, which relies on the cluster explosion, also exhibits interesting new properties when it occurs in a composite xenon-helium cluster with a core-shell geometry. We have revealed an intriguing double plasma resonance in this system. This was the first theoretical study of the influence of the helium embedding on the laser- driven nanoplasma dynamics. Our results demonstrate the important role of the interaction between xenon and helium parts of the cluster. Understanding this interaction is necessary in order to correctly interpret the experimental results. We have elucidated several important properties of Coulomb explosion in atomic and molecular clusters. Specifically, it was found that the kinetic energy distribution of ions after the Coulomb explosion of an atomic cluster is quite similar to the initial potential energy distribution of ions and is only weakly influenced by ion overtake effects, as was believed before. For the case of molecular hydrogen clusters, we have shown that the alignment of molecules inside the cluster affects its Coulomb explosion. Investigation of the dynamical processes in composite and molecular clusters induced by intense laser pulses is a step towards understanding them in more complex nano-objects, such as biomolecules or viruses. This is of great interest in the context of x-ray diffractive imaging of biomolecules with atomic resolution, which is one of the main goals of new x-ray free electron laser facilities.

We have investigated processes of ionization, energy absorption and subsequent explosion of atomic and molecular clusters under intense laser illumination using numerical as well as analytical methods. In particular, we focused on the response of composite clusters, those consisting of different atomic elements, to intense light pulses. Another major theme is the effect of the molecular structure of clusters on their Coulomb explosion. The action of intense laser pulses on clusters leads to fundamental, irreversible changes: they turn almost instantaneously into nanoplasmas and subsequently disintegrate into separate ions and electrons. Due to this radical transformation, remarkable new features arise. Transient cluster nanoplasmas are capable of absorbing enormous amounts of laser energy. In some cases more than 90 % of incident laser energy is absorbed by a gas of clusters with a density much smaller than that of a solid. After the efficient absorption, the energy is transformed into production of energetic ions, electrons, photons, and even neutrons. Composite clusters show especially interesting behavior when they interact with intense laser pulses. Nanoplasmas formed in composite clusters may absorb even more laser energy, than those formed in homogeneous clusters, as we demonstrate in this work. One of the most important results of this thesis is the identification of a novel type of plasma resonance. This resonance is enabled by an unusual ellipsoidal shape of the nanoplasma created during the ionization process in a helium droplet doped with just a few xenon atoms. In contrast to the conventional plasma resonance, which requires significant ion motion, here, the resonant energy absorption occurs at a remarkably fast rate, within a few laser cycles. Therefore, this resonance is not only the most efficient (like the conventional resonance), but also, perhaps, the fastest way to transfer laser energy to clusters. Recently, dedicated experimental studies of this effect were performed at the Max Planck Institute in Heidelberg. Their preliminary results confirm our prediction of a strong, avalanche-like ionization of the helium droplet with a small xenon cluster inside. A conventional plasma resonance, which relies on the cluster explosion, also exhibits interesting new properties when it occurs in a composite xenon-helium cluster with a core-shell geometry. We have revealed an intriguing double plasma resonance in this system. This was the first theoretical study of the influence of the helium embedding on the laser- driven nanoplasma dynamics. Our results demonstrate the important role of the interaction between xenon and helium parts of the cluster. Understanding this interaction is necessary in order to correctly interpret the experimental results. We have elucidated several important properties of Coulomb explosion in atomic and molecular clusters. Specifically, it was found that the kinetic energy distribution of ions after the Coulomb explosion of an atomic cluster is quite similar to the initial potential energy distribution of ions and is only weakly influenced by ion overtake effects, as was believed before. For the case of molecular hydrogen clusters, we have shown that the alignment of molecules inside the cluster affects its Coulomb explosion. Investigation of the dynamical processes in composite and molecular clusters induced by intense laser pulses is a step towards understanding them in more complex nano-objects, such as biomolecules or viruses. This is of great interest in the context of x-ray diffractive imaging of biomolecules with atomic resolution, which is one of the main goals of new x-ray free electron laser facilities.:1. Introduction 1 2. Interaction of clusters with intense laser pulses 5 2.1. Cluster formation and structure . . . . . . . . . . . . . . . . . . 5 2.1.1. Cluster formation . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2. Cluster structure . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3. Composite clusters . . . . . . . . . . . . . . . . . . . . . 7 2.2. Matter in intense light fields . . . . . . . . . . . . . . . . . . . . 9 2.2.1. Laser sources . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2. Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3. Clusters under intense laser pulses . . . . . . . . . . . . . . . . . 11 2.3.1. Three stages of intense laser-cluster interaction . . . . . 12 2.3.2. Pathways of cluster ionization and energy absorption . . 13 2.3.3. Composite clusters in intense laser fields . . . . . . . . . 14 2.4. Scenarios of cluster explosion . . . . . . . . . . . . . . . . . . . 15 2.4.1. Coulomb explosion vs. quasi-neutral expansion . . . . . 15 2.4.2. Anisotropic explosion . . . . . . . . . . . . . . . . . . . . 17 2.5. Comparison between experiment and theory . . . . . . . . . . . 18 3. Theoretical methods for intense laser-cluster interaction 21 3.1. The Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2. Survey of simulation methods . . . . . . . . . . . . . . . . . . . 22 3.2.1. Quantum methods . . . . . . . . . . . . . . . . . . . . . 22 3.2.2. Classical methods . . . . . . . . . . . . . . . . . . . . . . 23 3.3. Our method: classical microscopic molecular dynamics . . . . . 24 3.3.1. Initial configuration . . . . . . . . . . . . . . . . . . . . . 24 3.3.2. Integrating the equations of motion . . . . . . . . . . . . 26 3.3.3. Observables . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4. The role of quantum effects . . . . . . . . . . . . . . . . . . . . 31 4. Cluster nanoplasma: a statistical approach 33 4.1. Vlasov-Poisson formalism . . . . . . . . . . . . . . . . . . . . . . 33 4.2. Nanoplasma electrons at quasi-equilibrium . . . . . . . . . . . . 34 4.2.1. Self-consistent potential and electron density . . . . . . . 34 4.2.2. Energy distribution of nanoplasma electrons . . . . . . . 36 4.3. Harmonic oscillator model . . . . . . . . . . . . . . . . . . . . . 41 4.3.1. Derivation from kinetic equations . . . . . . . . . . . . . 42 4.3.2. Comparison with the molecular dynamics results . . . . 44 4.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5. Ionization and energy absorption in helium droplets doped with xenon clusters 47 5.1. Local ignition and anisotropic nanoplasma growth . . . . . . . . 48 5.1.1. Cluster size dependence . . . . . . . . . . . . . . . . . . 50 5.1.2. Nanoplasma resonance during its anisotropic growth . . 51 5.1.3. Range of laser frequencies and intensities . . . . . . . . . 55 5.1.4. Plasma resonance for circular polarization . . . . . . . . 56 5.1.5. Summary and future work . . . . . . . . . . . . . . . . . 57 5.2. Electron migration and its influence on the cluster expansion . . 59 5.2.1. Charging dynamics . . . . . . . . . . . . . . . . . . . . . 59 5.2.2. Explosion dynamics . . . . . . . . . . . . . . . . . . . . . 61 5.3. Interplay between nanoplasma expansion and its electronic response 63 5.3.1. Single pulse: time-dependence . . . . . . . . . . . . . . . 64 5.3.2. Two pulses: a pump-probe study . . . . . . . . . . . . . 67 5.4. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 71 6. Coulomb explosions of atomic and molecular clusters 75 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.2. Analytical treatment of the Coulomb explosion . . . . . . . . . . 76 6.2.1. Steplike density profile . . . . . . . . . . . . . . . . . . . 76 6.2.2. Kinetic approach . . . . . . . . . . . . . . . . . . . . . . 79 6.2.3. Gradually decreasing initial density . . . . . . . . . . . . 83 6.3. Coulomb explosions of atomic and molecular hydrogen clusters: a molecular dynamics study . . . . . . . . . . . . . . . . . . . . 84 6.3.1. Kinetic energy distributions of ions (KEDI) . . . . . . . 85 6.3.2. Information loss during the explosion . . . . . . . . . . . 87 6.3.3. Ion overtake processes . . . . . . . . . . . . . . . . . . . 90 6.3.4. Non-radial motion of ions . . . . . . . . . . . . . . . . . 91 6.3.5. Three-body effects in Coulomb explosion . . . . . . . . . 93 6.4. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . 96 7. Conclusions and outlook 97 7.1. Physical conclusions . . . . . . . . . . . . . . . . . . . . . . . . 97 7.2. Methodological conclusions . . . . . . . . . . . . . . . . . . . . . 99 7.3. Research perspectives . . . . . . . . . . . . . . . . . . . . . . . . 100 A. Suppression of the cluster barrier 101 B. Structure determination for Xen@Hem clusters 103 C. Calculation of the time-dependent phase shift 107 D. Potential of a uniformly charged spheroid 109 E. On the possibility of molecular alignment inside hydrogen clusters 111 Bibliography

The purpose of this thesis is to advance the understanding of strong-field QED processes in short laser pulses. The processes of non-linear one-photon and two-photon Compton scattering are studied, that is the scattering of photons in the interaction of relativistic electrons with ultra-short high-intensity laser pulses. These investigations are done in view of the present and next generation of ultra-high intensity optical lasers which are supposed to achieve unprecedented intensities of the order of 10^24 W/cm^2 and beyond, with pulse lengths in the order of some femtoseconds. The ultra-high laser intensity requires a non-perturbative description of the interaction of charged particles with the laser field to allow for multi-photon interactions, which is beyond the usual perturbative expansion of QED organized in powers of the fine structure constant. This is achieved in strong-field QED by employing the Furry picture and non-perturbative solutions of the Dirac equation in the presence of a background laser field as initial and final state wave functions, as well as the laser dressed Dirac-Volkov propagator. The primary objective is a realistic description of scattering processes with regard to the finite laser pulse duration beyond the common approximation of infinite plane waves, which is made necessary by the ultra-short pulse length of modern high-intensity lasers. Non-linear finite size effects are identified, which are a result of the interplay between the ultra-high intensity and the ultra-short pulse length. In particular, the frequency spectra and azimuthal photon emission spectra are studied emphasizing the differences between pulsed and infinite laser fields. The proper description of the finite temporal duration of the laser pulse leads to a regularization of unphysical infinities (due to the infinite plane-wave description) of the laser-dressed Dirac-Volkov propagator and in the second-order strong-field process of two-photon Compton scattering. An enhancement of the two-photon process is found in strong laser pulses as compared to the corresponding weak-field process in perturbative QED.