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L R Moore, K T Taylor, J S Parker, K J Meharg and G S J Armstrong DAMTP, David Bates Building, Queen's University Belfast, Belfast, BT7 1NN, UK Revolutionary x-ray free electron lasers (FEL) are presently under construction in the USA, in Europe and in Japan. They promise to generate x-ray pulses with much higher intensities and with much shorter durations than the currently available third generation synchrotron sources, moving laser physics into a new uncharted territory. In this new intensity wavelength regime, theoretical models of the laser-atom interactions will be of crucial importance in the quest to understanding potential new physical phenomena. An initial key task is to explore fundamental laser-atom interactions occurring in the ultra-fast ultra-intense regime accessed by x-ray FELs. We report on the development of a theoretical approach designed to calculate double ionization rates of two-electron positive ions exposed to an intense x-ray FEL pulse. The foundation of this work is the direct numerical integration of the full six-dimensional time-dependent Schroedinger equation [1]. A finite-difference grid is used to model the two radial co-ordinates and a basis set of coupled spherical harmonics replaces the four angular variables of the system. The numerical method is an extension of the existing computer code (HELIUM) that has been developed over the last decade to model interactions between the two-electron helium atom and high intensity laser light in the optical and XUV wavelength ranges [2,3,4]. At these longer wavelengths, HELIUM operates within the electric dipole approximation and is capable of solving the time-dependent Schroedinger equation in its full generality with quantitative accuracy. The electric dipole approximation may break down as the laser wavelength approaches atomic dimensions. Therefore to enable HELIUM to model the two-electron K shell response to an intense x-ray FEL pulse we are incorporating the magnetic dipole and electric quadrupole interactions in the Hamiltonian. These non-dipole terms account for retardation effects across the atom and thus remove the symmetry along the axis of laser polarization that was present in the dipole approximation. This loss of symmetry means that the total magnetic quantum number M is no longer conserved and all six degrees of freedom in the system come into play. The jump from 5- to 6-dimensions requires a substantial increase in computing resource due predominantly to two factors. Firstly, the basis set in HELIUM needs to be extended to include all coupled spherical harmonics Y{l1 l2 L M} where M is now able to assume non-zero values. Secondly, through inclusion of the non-dipole interaction terms, each of these basis states can also couple to an increased number of other states. It should be possible to meet the increased computational demand required to handle these extensions to HELIUM by using the highest performance computers available at present in the UK. We report on the implementation of these modifications to HELIUM and discuss our planned calculations. [1] Meharg KJ, Parker JS and Taylor KT 2005 J Phys B:At Mol Opt Phys 38 237 [2] Parker JS, Doherty BJS, Taylor KT, Schultz KD, Blaga CI and DiMauro LF 2006 Phys Rev Lett. 96 133001 [3] Parker JS, Meharg KJ, McKenna GA and Taylor KT 2007 J Phys B:At Mol Opt Phys 40 1729 [4] Parker JS, Moore LR, Meharg KJ, Dundas D and Taylor KT 2001 J Phys B:At Mol Opt Phys 34 L69 |
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