Plasma-based seeded soft-x-ray lasers have the potential to generate high energy and highly coherent short pulse beams. Due to their high density, plasmas created by the interaction of an intense laser with a solid target should store the highest amount of energy density among all plasma amplifiers. Our previous numerical work with a two-dimensional (2D) adaptive mesh refinement hydrodynamic code demonstrated that careful tailoring of plasma shapes leads to a dramatic enhancement of both soft-x-ray laser output energy and pumping efficiency. Benchmarking of our 2D hydrodynamic code in previous experiments demonstrated a high level of confidence, allowing us to perform a full study with the aim of the way for 10-100 μJ seeded soft-x-ray lasers. In this paper, we describe in detail the mechanisms that drive the hydrodynamics of plasma columns. We observed transitions between narrow plasmas, where very strong bidimensional flow prevents them from storing energy, to large plasmas that store a high amount of energy. Millimeter-sized plasmas are outstanding amplifiers, but they have the limitation of transverse lasing. In this paper, we provide a preliminary solution to this problem.

We present the theory of novel time-stepping algorithms for general nonlinear, non-smooth, coupled, and thermomechanical problems. The proposed methods are thermodynamically consistent in the sense that their solutions rigorously comply with the two laws of thermodynamics: for isolated systems, they preserve the total energy and the entropy never decreases. Extending previous works on the subject, the newly proposed integrators are applicable to coupled mechanical systems with non-smooth kinetics and can be formulated in arbitrary variables. The ideas are illustrated with a simple non-smooth problem: a rheological model for a thermo-elasto-plastic material with hardening. Numerical simulations verify the qualitative features of the proposed methods and illustrate their excellent numerical stability, which stems precisely from their ability to preserve the structure of the evolution equations they discretize. ENERGY-ENTROPY-MOMENTUM INTEGRATION SCHEMES 777As a result, symplectic, variational, and energy-momentum integrators, among others, have been developed and widely employed in the last decades. As these works show, preserving (part of) the Hamiltonian structure has proven very effective in the numerical solution of stiff models arising in nonlinear mechanics of solids [6,7], flexible and rigid multibody analysis [8,9], contact mechanics [10,11], elastic beams and shells [12][13][14], and so on. For practical applications in solid mechanics, however, all these models fall short because many (if not most) of the interesting problems are not elastic, but rather elastoplastic, or visco-elastic, or exhibit damage, or are coupled with temperature and so on.The class of solids that exhibit some kind of dissipative behavior is much larger than that of elastic solids, and a common mathematical structure for the former is not as apparent as in the Hamiltonian case. This lack of unifying formalism has hindered the formulation of structure preserving methods to nonlinear dissipative phenomena in solids. A few remarkable methods have been proposed in the past for single, specific problems (for example, [15][16][17][18]) but cannot be employed beyond the boundaries of the problem they were designed for.The only class of structure preserving methods for general (smooth) dissipative solids that have been proposed so far is, to the authors' knowledge, the energy-entropy-momentum (EEM) integrators initially proposed in [19] for finite dimensional thermomechanical problems and later extended to the infinite dimensional case [20,21]. In addition to thermoelastic problems, the EEM method has been applied to phase field modeling [22], discrete thermo-visco-plasticity [23], and thermo-visco-elasticity [24][25][26].Energy-entropy-momentum methods could be applied to a broad class of thermomechanical systems after realizing that many of the latter can be formulated as metriplectic models [27]. This mathematical and geometrical formalism generalizes the ideas of Hamiltonian problems and is able to encompass several dissipative phenomen...

The interaction of high intensity X-ray lasers with matter is modeled. A collisional-radiative timedependent module is implemented to study radiation transport in matter from ultrashort and ultraintense X-ray bursts. Inverse bremsstrahlung absorption by free electrons, electron conduction or hydrodynamic effects are not considered. The collisional-radiative system is coupled with the electron distribution evolution treated with a Fokker-Planck approach with additional inelastic terms. The model includes spontaneous emission, resonant photoabsorption, collisional excitation and de-excitation, radiative recombination, photoionization, collisional ionization, three-body recombination, autoionization and dielectronic capture. It is found that for high densities, but still below solid, collisions play an important role and thermalization times are not short enough to ensure a thermal electron distribution. At these densities Maxwellian and non-Maxwellian electron distribution models yield substantial differences in collisional rates, modifying the atomic population dynamics.

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