Application of Boltzmann kinetic equations to model X-ray-created warm dense matter and plasma.

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'.

Kinetic Boltzmann approach adapted for modeling highly ionized matter created by x-ray irradiation of a solid.

We report on the kinetic Boltzmann approach adapted for simulations of highly ionized matter created from a solid by its x-ray irradiation. X rays can excite inner-shell electrons, which leads to the creation of deeply lying core holes. Their relaxation, especially in heavier elements, can take complicated paths, leading to a large number of active configurations. Their number can be so large that solving the set of respective evolution equations becomes computationally inefficient and another modeling approach should be used instead. To circumvent this complexity, the commonly used continuum models employ a superconfiguration scheme. Here, we propose an alternative approach which still uses "true" atomic configurations but limits their number by restricting the sample relaxation to the predominant relaxation paths. We test its reliability, performing respective calculations for a bulk material consisting of light atoms and comparing the results with a full calculation including all relaxation paths. Prospective application for heavy elements is discussed.

Linearly polarized superluminal electromagnetic solitons in cold relativistic plasmas.

We investigate a special class of coupled nonlinear superluminal solitons arising from the interaction of an intense linearly polarized electromagnetic pulse with a cold plasma. These modulated envelope structures are obtained as numerical solutions of the classic Akhiezer-Polovin model equations [Sov. Phys. JETP 3, 696 (1956)]. We also present a multiple time scale perturbation analysis in the small amplitude limit that provides a close analytic description of these nonlinear solutions.

Phase mixing of relativistically intense waves in a cold homogeneous plasma.

We report on spatiotemporal evolution of relativistically intense longitudinal electron plasma waves in a cold homogeneous plasma, using the physically appealing Dawson sheet model. Calculations presented here in the weakly relativistic limit clearly show that under very general initial conditions, a relativistic wave will always phase mix and eventually break at arbitrarily low amplitudes, in a time scale omegapetaumix approximately {3/64(omegape2delta3/c2k2)|Deltak/k|(|1+Deltak/k|)](1+1|1+Deltak/k|)}(-1). We have verified this scaling with respect to amplitude of perturbation delta and width of the spectrum (Deltakk) using numerical simulations. This result may be of relevance to ultrashort, ultraintense laser pulse-plasma interaction experiments where relativistically intense waves are excited.