Measurements of ionization states in warm dense aluminum with betatron radiation

Plasma ionization balance in chemical-picture and average-atom models

We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.

Nonideal effect of free electrons on ionization equilibrium and radiative property in dense plasmas

The thermodynamic as well as optical properties of strongly coupled plasmas depend crucially on the average degree of ionization and the ionic state composition, which, however, cannot be determined by using the normal Saha equation usually used for the ideal plasmas. Hence, an adequate treatment of the ionization balance and the charge state distribution of strongly coupled plasmas is still a challenge for theory due to the interactions between the electrons and ions and among the electrons themselves. Based on a local density temperature-dependent ion-sphere model, the Saha equation approach is extended to the regime of strongly coupled plasmas by taking into account the free-electron-ion interaction, the free-free-electron interaction, the nonuniform free-electron space distribution, and the free-electron quantum partial degeneracy. All the quantities, including the bound orbitals with ionization potential depression, free-electron distribution, and bound and free-electron partition function contributions, are calculated self-consistently in the theoretical formalism. This study shows that the ionization equilibrium is evidently modified by considering the above nonideal characteristics of the free electrons. Our theoretical formalism is validated by the explanation of a recent experimental measurement of the opacity of dense hydrocarbon.

Laser wakefield acceleration based x ray source using 225-TW and 13-fs laser pulses produced by thin film compression

We show that 13-fs laser pulses associated with 225 TW of peak power can be used to produce laser wakefield acceleration (LWFA) and generate synchrotron radiation. To achieve this, 130-TW high-power laser pulses (3.2 J, 24 fs) are efficiently compressed down to 13 fs with the thin film compression (TFC) technique using large chirped mirrors after propagation and spectral broadening through a 1-mm-thick fused silica plate. We show that the compressed 13-fs laser pulse can be properly focused even if it induces a 10% degradation of the Strehl ratio. We demonstrate the usability of such a laser beam. We observe both an increase of the electron energy and of the betatron radiation critical energy when the pulse duration is reduced to 13 fs compared with the 24-fs case.

Plasma-Generated X-ray Pulses: Betatron Radiation Opportunities at EuPRAXIA@SPARC_LAB

EuPRAXIA is a leading European project aimed at the development of a dedicated, ground-breaking, ultra-compact accelerator research infrastructure based on novel plasma acceleration concepts and laser technology and on the development of their users’ communities. Within this framework, the Laboratori Nazionali di Frascati (LNF, INFN) will be equipped with a unique combination of an X-band RF LINAC generating high-brightness GeV-range electron beams, a 0.5 PW class laser system and the first fifth-generation free electron laser (FEL) source driven by a plasma-based accelerator, the EuPRAXIA@SPARC_LAB facility. Wiggler-like radiation emitted by electrons accelerated in plasma wakefields gives rise to brilliant, ultra-short X-ray pulses, called betatron radiation. Extensive studies have been performed at the FLAME laser facility at LNF, INFN, where betatron radiation was measured and characterized. The purpose of this paper is to describe the betatron spectrum emitted by particle wakefield acceleration at EuPRAXIA@SPARC_LAB and provide an overview of the foreseen applications of this specific source, thus helping to establish a future user community interested in (possibly coupled) FEL and betatron radiation experiments. In order to provide a quantitative estimate of the expected betatron spectrum and therefore to present suitable applications, we performed simple simulations to determine the spectrum of the betatron radiation emitted at EuPRAXIA@SPARC_LAB. With reference to experiments performed exploiting similar betatron sources, we highlight the opportunities offered by its brilliant femtosecond pulses for ultra-fast X-ray spectroscopy and imaging measurements, but also as an ancillary tool for designing and testing FEL instrumentation and experiments.

The need for speed

This paper reviews the challenges posed by the physics of the interaction of high-peak power femtosecond lasers with ultrathin foil targets. Initially designed to produce warm solid-density plasmas through the isochoric heating of solid matter, the interaction of an ultrashort pulse with ultrathin foils is becoming more and more complex as the laser intensity is increased. The dream of achieving very hot solid density matter with extreme specific energy density faces several bottlenecks discussed here as related to the laser technology, to the complexity of the physical processes, and to the limits of our current time-resolved instrumentations.

Single-Shot Multi-keV X-Ray Absorption Spectroscopy Using an Ultrashort Laser-Wakefield Accelerator Source

Single-shot absorption measurements have been performed using the multi-keV x rays generated by a laser-wakefield accelerator. A 200 TW laser was used to drive a laser-wakefield accelerator in a mode which produced broadband electron beams with a maximum energy above 1 GeV and a broad divergence of ≈15  mrad FWHM. Betatron oscillations of these electrons generated 1.2±0.2×10^{6}  photons/eV in the 5 keV region, with a signal-to-noise ratio of approximately 300∶1. This was sufficient to allow high-resolution x-ray absorption near-edge structure measurements at the K edge of a titanium sample in a single shot. We demonstrate that this source is capable of single-shot, simultaneous measurements of both the electron and ion distributions in matter heated to eV temperatures by comparison with density functional theory simulations. The unique combination of a high-flux, large bandwidth, few femtosecond duration x-ray pulse synchronized to a high-power laser will enable key advances in the study of ultrafast energetic processes such as electron-ion equilibration.

Probing warm dense matter using femtosecond X-ray absorption spectroscopy with a laser-produced betatron source

Exploring and understanding ultrafast processes at the atomic level is a scientific challenge. Femtosecond X-ray absorption spectroscopy (XAS) arises as an essential experimental probing method, as it can simultaneously reveal both electronic and atomic structures, and thus potentially unravel their nonequilibrium dynamic interplay which is at the origin of most of the ultrafast mechanisms. However, despite considerable efforts, there is still no femtosecond X-ray source suitable for routine experiments. Here we show that betatron radiation from relativistic laser−plasma interaction combines ideal features for femtosecond XAS. It has been used to investigate the nonequilibrium dynamics of a copper sample brought at extreme conditions of temperature and pressure by a femtosecond laser pulse. We measured a rise-time of the electron temperature below 100 fs. This experiment demonstrates the great potential of the table-top betatron source which makes possible the investigation of unexplored ultrafast processes in manifold fields of research.

Understanding the ultrafast dynamics of materials under extreme conditions is challenging. Here the authors use a femtosecond betatron X-ray source to investigate the solid to dense plasma phase transition in copper using XAS with unprecedented time resolution.

Ionization-potential depression and dynamical structure factor in dense plasmas

The properties of a bound electron system immersed in a plasma environment are strongly modified by the surrounding plasma. The modification of an essential quantity, the ionization energy, is described by the electronic and ionic self-energies, including dynamical screening within the framework of the quantum statistical theory. Introducing the ionic dynamical structure factor as the indicator for the ionic microfield, we demonstrate that ionic correlations and fluctuations play a critical role in determining the ionization potential depression. This is, in particular, true for mixtures of different ions with large mass and charge asymmetry. The ionization potential depression is calculated for dense aluminum plasmas as well as for a CH plasma and compared to the experimental data and more phenomenological approaches used so far.