Félicie Albert (16-ERD-041)
Characterizing material properties under extreme conditions of temperature and pressure is critical for different fields of physics, such as astrophysics, high-energy-density science, and Inertial Confinement Fusion. For example, knowing the structure of planets from the surface to the core is fundamental to understanding their evolution and origins. However, the behavior of solid-density plasmas in stars and toward the center of the giant planets is still poorly understood under extreme conditions of temperatures and pressure. Novel x-ray measurement techniques are needed for the study of these extreme states of matter, to penetrate plasmas and directly access the evolution of relevant quantities such as density, ionization state, temperature, and structure. Our objective was to perform the first x-ray pump, x-ray probe experiment to study the ultrafast electronic transitions of a solid-density aluminum plasma by means of x-ray absorption spectroscopy. The goal of the experiment was to heat metallic samples with the bright x-rays from the SLAC Linac Coherent Light Source free-electron laser in Menlo Park, California, and then study how the samples relaxed back to equilibrium by probing them with ultrafast x-ray absorption spectroscopy using laser-based betatron radiation. Our work enabled collaborations between Livermore, the SLAC National Accelerator Laboratory, Lawrence Berkeley National Laboratory, and institutions in France and in the United Kingdom, while providing training to undergraduate and graduate students during the experiment. Following this project, we were awarded a five-year DOE Early Career research grant to further develop applications of laser-driven x-ray sources for high-energy-density science experiments and warm dense matter states.
Background and Research Objectives
The field of high-energy-density science aims to resolve grand challenges to understand how the Sun works, how the planets were formed, how to harness fusion energy, or how to explain the mechanisms of stellar explosions. It is now possible to recreate astrophysical conditions of extreme temperatures and pressures at large-scale laser and x-ray free-electron laser facilities such as the Linac Coherent Light Source. However, such conditions are transient in nature and can be extremely difficult to probe. Phenomena such as shock physics, opacity, ultra-relativistic laser and matter interactions, and x-ray and matter interactions are central to this field of physics, but their investigation often requires diagnostics that are massive, costly, and limited in temporal or spatial resolution. Laser-wakefield accelerators, relying on intense laser fields to drive plasma waves and subsequently accelerate particles, can produce bright x-ray sources at a fraction of the cost but with a thousandfold increase in time resolution. However, they have not yet been fully exploited for applications in high-energy-density science, especially at large-scale facilities. Betatron x-ray radiation, a broadband, femtosecond, collimated x-ray source produced when relativistic electrons oscillate in a laser-wakefield accelerator, has been successfully developed at Livermore.1
We planned to use betatron x-ray radiation from the Matter under Extreme Conditions end station at the Linac Coherent Light Source to probe an aluminum plasma heated by the x-ray free electron laser and to study the ultrafast electronic transitions of a solid-density aluminum plasma by means of x-ray absorption spectroscopy. The plasma can be produced with the Linac Coherent Light Source x-ray beam via K-shell photo-absorption, and probed with laser-based betatron x-ray radiation. Because of its unique colocation with a multi-terawatt, femtosecond laser system, the Matter under Extreme Condition end station at the Linac Coherent Light Source is currently the only facility capable of hosting this experiment.
We demonstrated a new diagnostic capability to measure the transient charge state of materials with high temporal accuracy. We obtained femtosecond time-resolved x-ray absorption spectra of heated matter at well-defined density and temperature conditions, giving access to its electron temperature, ion temperature, and charge state as the sample relaxes back to equilibrium. Our plan was to use ultrafast single-shot x-ray-absorption near-edge spectroscopy around the aluminum K-edge (1.56 keV) to probe the electronic structure modifications of aluminum at conditions of density (∼1-times solid density) and temperature (1–5 eV) uniquely accessible at the Linac Coherent Light Source.
Because of lower-than-expected performance of the short-pulse optical laser at the Matter under Extreme Conditions end station, the betatron x-ray source did not produce sufficient x-ray photons near the aluminum K-edge (1.56 keV) for us to perform the desired experiment. Instead, we performed our measurements using the same technique at the iron L-edge (0.707 eV) on iron heated by Linac Coherent Light Source to a few electronvolt temperatures. With proper data accumulation and acquisition, we were able to demonstrate the possibility of using betatron x-ray radiation for ultrafast absorption spectroscopy of plasmas created by the Linac Coherent Light Source.
Scientific Approach and Accomplishments
The experiment we conducted at the Linac Coherent Light Source is presented in Figure 1. The x rays (7.5 keV, 3 mJ, and 70 fs) are focused onto a solid iron foil (100–300 nm) to bring it to temperatures of a few electronvolts. Simultaneously, the Matter under Extreme Conditions short laser pulse (1 J and 40 fs) is focused onto a gas cell to accelerate electrons and produce betatron x rays. The radiation is collected by a 3.4° grazing-incidence ellipsoidal mirror (multilayer coating) and focused onto the iron samples. The spectrum of the betatron x-ray beam transmitted through the iron foils is analyzed with an imaging grating spectrometer and compared with a reference spectrum.
The technique used to analyze evolution of the iron sample temperature is x-ray absorption near-edge structure. At room temperature, a metal such as iron exhibits sharp absorption edges. For example, the iron K-edge (7.1 keV), corresponds to a 1s to 4p transition, while the iron L-edge corresponds to a 2p to 3d transition. Iron is a transition metal, with a partially filled 3d band. When it is heated to warm dense matter states (a few electronvolts), electrons in the 3d band are excited above the Fermi level, which changes the occupation states and therefore the slope of the L-edge absorption spectrum. By measuring the slope of the iron L-edge with x-ray-absorption near-edge spectroscopy, it is possible to access the sample temperature.
Simulations, performed at LLNL (Figure 2), show the sensitivity of the x-ray-absorption near-edge spectroscopy spectrum to electron temperature at the iron L-edge. These calculations use a theoretical model derived from first-principles density functional theory and local-density approximation. This code can calculate the fine structure near the edge with high accuracy in the x-ray-absorption near-edge spectroscopy region. It first calculates the absorption spectrum at room temperature—the Fermi distribution for 300 K is applied to the solid x-ray absorption cross section. For the initial state (before Linac Coherent Light Source heating), a face-centered cubic solid at 300 K is assumed. Following the laser pulse, liquid-atomic configurations are used, with electron temperatures up to a few electronvolts and solid densities. Data that have been obtained at the Advanced Light Source synchrotron (Lawrence Berkeley National Laboratory) at the L-edge of warm dense copper2 and warm dense iron3 (temperature of ∼1 eV, optical laser heating, and 2-ps temporal resolution) are showing good agreement with these calculations.
Impact on Mission
Our project leverages Livermore's expertise in accelerator, laser, and x-ray sciences and will strengthen leadership in developing novel, ultrafast x-ray light sources. It will help to better understand material properties under extreme conditions, which is important for stockpile stewardship and in situ material characterization during manufacturing, and supports the Laboratory's core competency in high-energy-density science. The research is also closely aligned with the Laboratory's goal to create an integrated center for the application of advanced lasers to address 21st-century national security challenges, and in support of the strategic focus area in inertial fusion science and technology. Our novel combination of an x-ray and matter interaction experiment with a femtosecond x-ray probe from laser-produced plasmas will elucidate the mechanisms of ion–electron equilibration and energy transport in high-energy-density plasmas, which is relevant to the Laboratory's inertial fusion science and technology strategic focus area.
In conclusion, we demonstrated a new diagnostic capability of warm dense matter states at the Linac Coherent Light Source. The warm dense iron was produced with the x-ray beam at the Matter under Extreme Conditions end station via K-shell photo-absorption and probed with laser-based betatron x-ray radiation. We used x-ray-absorption near-edge spectroscopy around the iron L-edge (0.707 keV) to probe the electronic structure modifications of iron at conditions of density (∼1-times solid density) and temperature (1–5 eV) uniquely accessible at the Linac Coherent Light Source. This novel combination of an x-ray and matter interaction experiment with a femtosecond x-ray probe from laser-produced plasmas will open up new possibilities to inform and design future high-x-ray-intensity experiments and to improve current opacity and radiation transport models that are essential for high-energy-density science. The high visibility and success of this work resulted in a DOE Early Career award ($2.5 million over 5 years) to develop more applications of laser-driven betatron x-rays for high-energy-density science experiments and warm dense matter states4,5 in support of Laboratory missions. Our work enabled large collaborations between Livermore, the SLAC National Accelerator Laboratory, Lawrence Berkeley National Laboratory, and institutions in France and the United Kingdom, while providing training to undergraduate and graduate students during the experiment. Several of the graduate students and postdoctoral researchers who participated in this project have been recruited for LLNL high-energy-density science programs.
- Albert, F., et al., "Angular dependence of betatron x-ray spectra from a laser-wakefield accelerator." Phys. Rev. Lett. 111, 235004 (2013). LLNL-JRNL-642092. https://doi.org/10.1103/PhysRevLett.111.235004
- Cho, B. I., et al., "Electronic structure of warm dense copper studied by ultrafast x-ray absorption spectroscopy." Phys. Rev. Lett. 106, 167601 (2011). https://doi.org/10.1103/PhysRevLett.106.167601
- Fernandez-Pañella, A., et al., "Suppression of electron–phonon coupling factor of iron in warm dense matter regime." Submitted to Phys. Rev. Lett. (2016).
- Albert, F., and A. G. R. Thomas, “Applications of laser-wakefield accelerator-based light sources.” Plasma Phys. Control. Fusion 58, 103001 (2016). LLNL-JRNL-682217. https://doi.org/10.1088/0741-3335/58/10/103001
- Albert, F., et al., "Laser wakefield accelerator based light sources: Potential applications and requirements." Plasma Phys. Control. Fusion 56, 084015 (2014). LLNL-PROC-666251. https://doi.org/10.1088/0741-3335/56/8/084015
Publications and Presentations
- Albert, F., Betatron x-rays from laser-wakefield accelerators: A novel probe for time-resolved high-energy-density science experiments. BELLA-I Workshop, Berkeley, CA, Jan. 20–22, 2016. LLNL-ABS-680211.
- Albert, F., and A. G. R. Thomas, 2016. "Applications of laser-wakefield accelerator-based light sources." Plasma Phys. Control. Fusion 58, 103001 (2016). LLNL-JRNL-682217. https://doi.org/10.1088/0741-3335/58/10/103001