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In this chapter we have reviewed the modelization of seeded soft X-ray lasers using plasma amplifiers from solid. Since these sources present different temporal and spatial scales from nanoseconds (plasma characteristic time), picoseconds (atomic system) and femtoseconds (HOH electric field envelope), specific multiscale tools are needed. The creation and evolution of the plasma amplifier is studied with a 2D hydrodynamic code, optimized for this kind of problem. Atomic parameters, as gain and saturation fluence, are obtained postprocessing hydrodynamic data. Then, amplification is studied in different ways: a 3D ray-tracing code is used to study the role of refraction and focusing in the amplification process, whereas a Maxwell-Bloch code is used to model the temporal evolution of the seeded radiation and its coupling with the atomic system. Powerful visualization tools are also used to properly display the 3D properties of the system. The results obtained with these computational tools provide an invaluable aid to comprehend experimental results and design and optimize new schemes, by identifying the key parameters of the experiments.

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