Many interesting effects result from the ionization of atoms by very intense, ultrashort, laser pulses. For an ensemble of a large number of atoms in a strong laser field, macroscopic dynamical effects emerge in the resulting ionized plasma that are a direct result of microscopic interactions, yet cannot be foreseen by understanding the atomic system alone. The standard computational method of addressing many-particle dynamics in a strong laser field involves explicitly calculating the interactions between each particle in the system with every other particle, leading to a computational load that scales as the square of the total number of particles. The largest systems that can be reasonably addressed with this method can include no more than 1000 atoms. In this thesis two computational approaches are used to increase the computable system size. First, a 3d microscopic particle in cell (MPIC) code is introduced which takes into account all important microscopic effects in the evolution of laser driven large clusters.

Second, a treecode has been implemented which overcomes the unfavorable N^2 scaling of conventional molecular dynamics (MD) simulations by approximating the force of a group of distant particles by multipole expansion. Both approaches have their advantages and disadvantages and differ in their range of application. The MPIC code is an enhancement of regular particle in cell (PIC) codes. Regular PIC codes solve the Maxwell equations and the relativistic classical equations of motion on a stationary grid using the mean field approximation. The charged particles are represented by boxes with macroscopic dimensions that represent the average over many particles. As a result, microscopic effects such as inverse bremsstrahlung heating, impact ionization, electron-electron scattering, electron-ion scattering, and charge enhanced ionization (CEI) cannot be taken into account. In the MPIC code the box size is shrunk to the order of 1 a.u. containing only one charged particle. In this limit, the microscopic interac-tion of all charged particles are taken care of by the PIC formalism. The MPIC code is inherently relativistic and opens the possibility to look microscopically at relativistic plasma dynamics. It contains no free parameters and presents a virtual experiment. To test its reliability recent experiments reporting an asym-metric explosion of Ar and Xe clusters with N = 10.000 have been calculated. The calculated spectra and angular distributions of electrons and ions are found to be in good agreement with the experiments. The MPIC simulations reveal the first complete picture of the explosion of large clusters with several 10.000 atoms. Treecodes use the fact the the force of a group of distant particles can be well approximated by a low-order multipole expansion.

Computing time of a treecode scales with N log(N) compared to the N^2 scaling of conventional MD codes. In this work a treecode has been used to simulate a recent experiment performed with the first free electron laser at DESY in Hamburg. The calculated charge state distribution and energy absorption rates show a good agreement with the experiment and reveals that the electron heating is a consequence of the strongly coupled plasma dynamics in which collisonal processes are strongly modified. Understanding the dynamics of cluster explosions can be seen as a stepping stone to understanding intense laser-induced phase transitions in solids. By further extending these novel numerical tools, it will be possible to address the dynamics of macroscopic systems that is, with a size of the order of the laser wavelength in the near future.