In this review, we describe the application of Boltzmann kinetic equations for modelling warm dense matter and plasma formed after irradiation of solid materials with intense femtosecond X-ray pulses. Classical Boltzmann kinetic equations are derived from the reduced N-particle Liouville equations. They include only single-particle densities of ions and free electrons present in the sample. The first version of the Boltzmann kinetic equation solver was completed in 2006. It could model non-equilibrium evolution of X-ray-irradiated finite-size atomic systems. In 2016, the code was adapted to study plasma created from X-ray-irradiated materials. Additional extension of the code was then also performed, enabling simulations in the hard X-ray irradiation regime. In order to avoid treatment of a very high number of active atomic configurations involved in the excitation and relaxation of X-ray-irradiated materials, an approach called 'predominant excitation and relaxation path' (PERP) was introduced. It limited the number of active atomic configurations by following the sample evolution only along most PERPs. The performance of the Boltzmann code is illustrated in the examples of X-ray-heated solid carbon and gold. Actual model limitations and further model developments are discussed. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Center for Free Electron Science CFEL Deutsches Elektronen Synchrotron DESY Notkestr 85 22607 Hamburg Germany

Department of Physics Indian Institute of Technology Delhi New Delhi 110016 India

European XFEL Holzkoppel 4 22869 Schenefeld Germany

Institute of Nuclear Physics Polish Academy of Sciences Radzikowskiego 152 31 342 Krakow Poland

Institute of Physics Czech Academy of Sciences Na Slovance 2 182 21 Prague 8 Czech Republic

Institute of Plasma Physics Czech Academy of Sciences Za Slovankou 3 182 00 Prague 8 Czech Republic

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