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We analyse the oblique impact of linear-viscoelastic spheres by numerical models based on the Method of Dimensionality Reduction and the Boundary Element Method. Thereby we assume quasi-stationarity, the validity of the half-space hypothesis, short impact times and Amontons-Coulomb friction with a constant coefficient for both static and kinetic friction. As under these assumptions both methods are equivalent, their results differ only within the margin of a numerical error. The solution of the impact problem written in proper dimensionless variables will only depend on the two parameters necessary to describe the elastic problem and a sufficient set of variables to describe the influence of viscoelastic material behaviour; in the case of a standard solid this corresponds to two additional variables. The full solution of the impact problem is finally determined by comprehensive parameter studies and partly approximated by simple analytic expressions.

The Boundary Element Method (BEM) for elastic materials is extended to deal with viscoelastic media. This is obtained by making use of a similar form of the fundamental solution for both the materials. Some considerations are attributed to the difference of the normal and the tangential contact problem. Both normal and tangential problems are furthermore assumed to be decoupled. Then the oblique impact of hard spheres with an incompressible viscoelastic half-space (linear standard-model) is studied. By assuming stick conditions during impact, one obtains the dependence of the two coefficients of restitution as functions of two input parameters. This result is expressed in an elegant and compact form of the fitting function.

Abstract The structures, strain fields, and defect distributions in solid materials underlie the mechanical and physical properties across numerous applications. Many modern microstructural microscopy tools characterize crystal grains, domains and defects required to map lattice distortions or deformation, but are limited to studies of the (near) surface. Generally speaking, such tools cannot probe the structural dynamics in a way that is representative of bulk behavior. Synchrotron X-ray diffraction based imaging has long mapped the deeply embedded structural elements, and with enhanced resolution, dark field X-ray microscopy (DFXM) can now map those features with the requisite nm-resolution. However, these techniques still suffer from the required integration times due to limitations from the source and optics. This work extends DFXM to X-ray free electron lasers, showing how the $$10^{12}$$ 10 12 photons per pulse available at these sources offer structural characterization down to 100 fs resolution (orders of magnitude faster than current synchrotron images). We introduce the XFEL DFXM setup with simultaneous bright field microscopy to probe density changes within the same volume. This work presents a comprehensive guide to the multi-modal ultrafast high-resolution X-ray microscope that we constructed and tested at two XFELs, and shows initial data demonstrating two timing strategies to study associated reversible or irreversible lattice dynamics.

Plasma wakefield accelerators can be driven either by intense laser pulses (LWFA) or by intense particle beams (PWFA). A third approach that combines the complementary advantages of both types of plasma wakefield accelerator has been established with increasing success over the last decade and is called hybrid LWFA→PWFA. Essentially, a compact LWFA is exploited to produce an energetic, high-current electron beam as a driver for a subsequent PWFA stage, which, in turn, is exploited for phase-constant, inherently laser-synchronized, quasi-static acceleration over extended acceleration lengths. The sum is greater than its parts: the approach not only provides a compact, cost-effective alternative to linac-driven PWFA for exploitation of PWFA and its advantages for acceleration and high-brightness beam generation, but extends the parameter range accessible for PWFA and, through the added benefit of co-location of inherently synchronized laser pulses, enables high-precision pump/probing, injection, seeding and unique experimental constellations, e.g., for beam coordination and collision experiments. We report on the accelerating progress of the approach achieved in a series of collaborative experiments and discuss future prospects and potential impact.