Solid Density Plasma Research Articles

Spatiotemporal dynamics of fast electron heating in solid-density matter via XFEL

High-intensity, short-pulse lasers are crucial for generating energetic electrons that produce high-energy-density (HED) states in matter, offering potential applications in igniting dense fusion fuels for fast ignition laser fusion. High-density targets heated by these electrons exhibit spatially non-uniform and highly transient conditions, which have been challenging to characterize due to limitations in diagnostics that provide simultaneous high spatial and temporal resolution. Here, we employ an X-ray Free Electron Laser (XFEL) to achieve spatiotemporally resolved measurements at sub-micron and femtosecond scales on a solid-density copper foil heated by laser-driven fast electrons. Our X-ray transmission imaging reveals the formation of a solid-density hot plasma localized to the laser spot size, surrounded by Fermi degenerate, warm dense matter within a picosecond, and the energy relaxation occurring within the hot plasma over tens of picoseconds. These results validate 2D particle-in-cell simulations incorporating atomic processes and provide insights into the energy transfer mechanisms beyond current simulation capabilities. This work significantly advances our understanding of rapid fast electron heating and energy relaxation in solid-density matter, serving as a key stepping stone towards efficient high-density plasma heating and furthering the fields of HED science and inertial fusion energy research using intense, short-pulse lasers.

Enhanced energy deposition of laser-produced proton beams in high-density plasmas due to beam density self-steepening

The energy deposition of laser-accelerated proton beams in solid-density plasmas with different ion charge numbers is studied with detailed one-dimensional particle-in-cell simulations. In the plasma with a high ion charge number, in which the plasma collision frequency approaches electron oscillation frequency, the beam protons are strongly decelerated by the electric field induced by the plasma return current. The energy deposition is further enhanced as the beam travel distance increases due to beam density self-steeping, which is also confirmed by multi-dimensional particle-in-cell simulation. A simple analytical model is proposed to estimate the characteristic travel distance for significant density self-steeping, showing agreement with the simulation results. While in the plasma with a low ion charge number, in which the plasma collision frequency is much smaller than the electron oscillation frequency, the proton beam is modulated significantly by the excited two-stream instability.

Coherent radiation of an electron bunch colliding with an intense laser pulse

We study the conditions for coherent radiation of an electron bunch driven by a counterpropagating strong pulsed electromagnetic plane wave. We derive the spectrum of the coherent radiation and show that it is emitted backward with respect to the laser propagation direction and has a very narrow angular spread. We demonstrate that for a solid density plasma coherent radiation extends to frequencies up to hundreds of keV, thereby enhancing the low-frequency part of the spectrum by many orders of magnitude. Our analytical findings are tested with three-dimensional particle-in-cell simulations of an electron bunch passing through a laser pulse, clearly demonstrating how the coherence can essentially modify the observed radiation spectrum. Published by the American Physical Society 2024

Channeling acceleration in crystals and nanostructures and studies of solid plasmas: new opportunities

Plasma wakefield acceleration (PWFA) has shown illustrious progress and resulted in an impressive demonstration of tens of GeV particle acceleration in meter-long single structures. To reach even higher energies in the 1 TeV to 10 TeV range, a promising scheme is channeling acceleration in solid-density plasmas within crystals or nanostructures. The E336 experiment studies the beam-nanotarget interaction with the highly compressed electron bunches available at the FACET-II accelerator. These studies furthermore involve an in-depth research on dynamics of beam-plasma instabilities in ultra-dense plasma, its development and suppression in structured media like carbon nanotubes and crystals, and its potential use to transversely modulate the electron bunch.

Optimization of e+/e− pair yield during the interaction of a Doppler-boosted laser with a solid-density plasma

The interaction of a Doppler-boosted laser with a solid-density plasma is investigated with two-dimensional particle-in-cell simulations, with special attention paid to the influences of laser incident angle on the yield of e+/e− pairs. With normal laser incidence, it is found that parts of plasma electrons are accelerated by the reflected laser and radiate high-energy γ-photons, which further make nearly head-on collisions with the subsequent incoming laser pulses. The nonlinear quantum parameters of the produced photons can reach 4.6, and the yield of e+/e− pairs increases by a factor of 4 compared to an incident angle of 45°. The optimization is easy to implement and can improve the signal-to-noise ratio in the experiments.

Diagnosis of fast electron transport by coherent transition radiation

Transport of fast electrons in overdense plasmas is of key importance in high energy density physics. However, it is challenging to diagnose the fast electron transport in experiments. In this article, we study coherent transition radiation (CTR) generated by fast electrons on the back surface of the target by using 2D and 3D first-principle particle-in-cell (PIC) simulations. In our simulations, aluminum targets of 2.7 g cc−1 are simulated in two different situations by using a newly developed high order implicit PIC code. Comparing realistic simulations containing collision and ionization effects, artificial simulations without taking collision and ionization effects into account significantly underestimate the energy loss of electron beams when transporting in the target, which fail to describe the complete characteristics of CTR produced by electron beams on the back surface of the target. Realistic simulations indicate the diameter of CTR increases when the thickness of the target is increased. This is attributed to synergetic energy losses of high flux fast electrons due to Ohm heating and colliding drags, which appear quite significant even when the thickness of the solid target only differs by micrometers. Especially, when the diagnosing position is fixed, we find that the intensity distribution of the CTR is also a function of time, with the diameter increased with time. As the diameter of CTR is related to the speed of electrons passing through the back surface of the target, our finding may be used as a new tool to diagnose the electron energy spectra near the surface of solid density plasmas.

On a modified Korteweg–de Vries equation for electrostatic structures in relativistic degenerate electron–positron plasma

In this paper, the propagation of acoustic solitons in an electron–positron (e–p) degenerate plasma with the relativistically degenerate electrons and positrons is studied. Moreover, we considered stationary positive ions for neutralizing the plasma background. Using the reductive perturbation method, we obtained a modified Korteweg–de Vries equation. By applying a Jacobi elliptic function expansion method, we have proposed the exact analytical solitary, kink, and periodic solutions for the nonlinear wave structures. Also, using the phase plane analysis three equilibrium points have been perceived two of them should be centers and the last is a saddle for quantum acoustic waves. The numerical and computational results show that firstly some of them should be discarded by physical values and then these solutions have been influenced by the plasma parameters such as the electron degenerate density parameter (ne0) and the ion-to-electron density ratio (δ) which peaked out in white dwarf stars. It is found that both the amplitude and the width of the nonlinear structures are affected by the mentioned parameters. This investigation is useful for the relativistically degenerate plasma media in ultra-dense astrophysical environments (such as neutron stars, white dwarfs, etc.), inertia fusion science, experiments involving the interaction of laser and solid density plasma, and inertial confinement fusion in which the relativistic effects play a major role.

Probing bulk electron temperature via x-ray emission in a solid density plasma

Bulk electron temperatures are calculated for thin Cu targets irradiated by the petawatt class Vulcan laser, from the Kα yield obtained using highly oriented pyrolytic graphite crystals. Cu-Kα emission studies have been used to probe the bulk electron temperature. A 30–80 eV core temperature extends homogeneously over distances up to ten times the laser focal spot size. Energy shifting has been observed due to different ionization states produced for different temperatures in the plasma. Polarization dependencies of plasma temperature are observed through the production of x-rays in different targets. 2D PIC simulations were performed to measure the polarization dependency of bulk electron temperature, which supports our experimental results. This paper could be of importance in understanding the different behavior of laser coupling at different polarizations and their role in x-ray production.

Isolated attosecond pulse generation from the interaction of intense laser pulse with solid density plasma

This article gives an overview on recent progress in the generation of isolated attosecond pulse and isolated half-cycle attosecond pulse. As an isolated attosecond pulse is preferred in the pump-probe experiments for the dynamics of electrons in atom, molecule, or solid, we focus on the isolated attosecond pulses generation from the intense laser pulses interaction with solid density plasma, which have higher intensity and narrower pulse width than that generated in the interaction of laser pulse with gas target. We have firstly discussed the physical mechanism of isolated attosecond pulse generation, such as polarization gating, two-color laser pulses, attosecond light houses, and capacitor target mechanism. In the polarization gating mechanism, we have discussed the physical mechanism that the higher-order harmonic efficiency decreases with the increase of ellipticity. Both the coherent synchrotron radiation mechanism and the relativistic oscillation mechanism can control the intensity of high-order harmonic generation by controlling ellipticity of the incident laser pulse. We also discussed other mechanism to enhance the isolated attosecond pulse bursts in detail. Secondly, we focus on the isolated half-cycle attosecond pulses, which can also be generated from the intense laser pulses interaction with solid density plasma by double foil target mechanism, gas-foil target mechanism, cascaded generation mechanism, microstructured target mechanism, and three-color laser pulse mechanism. The half-cycle attosecond pulses can be useful for probing ultrafast electron dynamics in matter via asymmetric manipulation. Accordingly we discussed the physcial mechanism, experimental feasibility, calibration measurement, and application prospect of half-cycle attosecond pulse in this article. The above mechanism can directly generate ultra-intense isolated attosecond pulses in the transmission direction without requiring extra filters and gating techniques. The dense electron sheet is crucial for the generation of intense attosecond pulses in different mechanisms, such as coherent wake emission (CWE), relativistic oscillating mirror (ROM) and coherent synchrotron emission (CSE). In this article, all the mechanism for half-cycle attosecond pulses generation can ensure only one electron sheet contributing to the transmitted radiation. We discuss the theoretical model of nanobunching of the electron sheet, which shows that the relativistic oscillation is crucial for the formation of electron sheet.

Effects of laser waveform on the generation of fast electrons in laser–solid interactions

In the scheme of fast ignition of inertial confinement fusion, the fuel temperature mainly relies on fast electrons, which act as an energy carrier, transferring the laser energy to the fuel. Both conversion efficiency from the laser to the fast electron and the energy spectrum of the fast electron are essentially important to achieve highly effective heating. In this study, a two-dimensional particle in cell simulation is applied to study the generation of fast electrons from solid-density plasmas with different laser waveforms. The results have shown that the slope of the rising edge has a significant effect on fast electron generation and energy absorption. For the negative skew pulse with a relatively slow rising edge, the J×B mechanism can most effectively accelerate the electrons. The overall absorption efficiency of the laser energy is optimized, and the fast electron yield in the middle- and low-energy range is also improved.

Theoretical studies of the spectral characteristics and electron impact dynamics of Ti XXI placed in the hot dense regimes

We describe a theoretical approach to calculate the electron impact dynamics of atoms/ions placed in a dense plasma. The model takes into consideration that the continuous electron and the guest atom/ion are affected by a recently proposed (dense) plasma shielding parameter potential. As a test case, the present numerical method is employed to study the electron-impact excitation of He-like Ti XXI by using the distorted-wave wavefunction in the framework of the fully relativistic theory. The finite temperature and density effects as well as solid density plasma effects on the excitation energies, transition properties, and integrated cross sections are discussed in detail, which shed light on the shielding parameter potential in resolving practical problems. Results are compared with the available measurements and previous computations. The present work is not only providing a new implementation of the finite-temperature method by a self-consistent methodology, but also of great interest for the high energy density physics community, i.e., our results are of interest to the fusion researches.

Achieving relativistically intense X-rays from structured plasma lens

Focusing of high-power X-rays is still a great challenge and the intensity of X-ray attained in existing focusing schemes is still far below the relativistic threshold. Here, we propose that solid density plasma lens can potentially focus X-ray lasers at very high power levels. The interaction of high-power X-ray laser with solid-density plasmas is systematically studied. It is theoretically shown that there exists a certain range of wavelengths for X-ray lasers that can be focused in solid-density plasmas when the input power and plasma density are determined. To avoid the essential laser-plasma instabilities and obtain high-gain intensity amplification for X-ray, we design concave structured plasma lens. Particle-in-cell simulation results show that such regime can effectively avoid the instabilities and focus X-ray of micrometer-sized spot and multi-TW power, and thus lead to the generation of relativistic intensity X-ray. The parameters of the concave structures and the effects of quantum electrodynamics are also discussed and it indicates that our scheme is quite robust. We further demonstrate that the relativistic X-ray laser interacting with thin-foil leads to high-quality attosecond electron bunches.

Investigation of resistive magnetic field generation by intense proton beams in dense plasmas

Current and future applications of intense proton sources abound, including radiography, cancer therapy, warm dense matter generation, and inertial confinement fusion. With increasingly efficient acceleration and focusing mechanisms, proton current densities may soon approach and exceed 1010 A/cm2, e.g., via intense laser drivers. Simulations have previously shown that in this current density regime, beam-induced field generation plays a significant role in beam transport through dense plasmas. Here, we present a theoretical model for the generation of resistive magnetic fields by intense proton beam transport through solid density plasmas. The theoretical evolution of the magnetic field profile is calculated using an analytic model for aluminum resistivity, heat capacity, and stopping power, applicable from cold matter to hot plasma. The effects of various beam and material parameters on the field are investigated and explained for both monoenergetic and Maxwellian proton beams. For a proton beam with Maxwellian temperature 5 MeV and total energy 10 J, the model calculates resistive magnetic fields up to 150 T in aluminum. The calculated field profiles from several beam cases are compared with 2D hybrid particle-in-cell simulations, with good agreement found in magnitude and time scale.

Stimulated-Raman-scattering amplification of attosecond XUV pulses with pulse-train pumps and application to local in-depth plasma-density measurement.

We present a scheme for amplifying an extreme-ultraviolet (XUV) seed isolated attosecond pulse via stimulated Raman scattering of a pulse-train pump. At sufficient seed and pump intensity, the amplification is nonlinear, and the amplitude of the seed pulse can reach that of the pump, one order of magnitude higher than the initial seed amplitude. In the linear amplification regime, we find that the spectral signature of the pump pulse train is imprinted on the spectrum of the amplified seed pulse. Since the spectral signature is imprinted with its frequency downshifted by the plasma frequency, it is possible to deduce the electron density in the region of interaction. This region can be of micrometer length scale longitudinally. By varying the delay between the seed and the pump, this scheme provides a local electron-density measurement inside solid-density plasmas that cannot be probed with optical frequencies, with micrometer resolution.

Streaked sub-ps-resolution x-ray line shapes and implications for solid-density plasma dynamics (invited).

A high-resolution x-ray spectrometer was coupled with an ultrafast x-ray streak camera to produce time-resolved line shape spectra measured from hot, solid-density plasmas. A Bragg crystal was placed near laser-produced plasma to maximize throughput; alignment tolerances were established by ray tracing. The streak camera produced single-shot, time-resolved spectra, heavily sloped due to photon time-of-flight differences, with sufficient reproducibility to accumulate photon statistics. The images are time-calibrated by the slope of streaked spectra and dewarped to generate spectra emitted at different times defined at the source. The streaked spectra demonstrate the evolution of spectral shoulders and other features on ps timescales, showing the feasibility of plasma parameter measurements on the rapid timescales necessary to study high-energy-density plasmas.

Powerful laser-produced quasi-half-cycle THz pulses.

The Maxwell equations-based 3D-analytical solution for the terahertz (THz) half-cycle electromagnetic wave transition radiation pulse has been found. This solution describes generation and propagation of transition radiation into free space from laser-produced relativistic electron bunch which crosses a target-vacuum interface as a result of ultrashort laser pulse interaction with a thin high-conductivity target. The analytical solution found complements the theory of laser initiated transition radiation. It describes the THz wave half-cycle pulse at the arbitrary distance from a target surface including near-field zone rather than its standard far-field characterization. The analytical research has also been supplemented with the 3D simulations using the finite-difference time-domain method, which makes it possible for description of much wider spatial domain as compared to that from the particle-in-cell approach. The presented result sheds light fundamentally on the interference of the electron bunch field and the generated THz field of broadband transition radiation from laser-plasma interaction. The latter is studied for a long time in the experiments with solid density plasma and the theory developed may inspire to targeted measurements and investigations of unique super intense half-cycle THz radiation waves near the laser target.

Ultrafast time-resolved two-dimensional velocity mapping of the hot-dense plasmas generated by intense-laser pulses

Experimental measurements of spatially resolved ultrafast dynamics of the critical surface in ultra-intense laser–solid interactions are essential for a proper understanding of the physical mechanism of the interaction. Resolving ultrafast motion at both the relevant length scales (micrometers) and timescales (femtoseconds) simultaneously has been a challenging task. Here, we demonstrate a novel technique for mapping the spatiotemporal dynamics of hot and solid dense plasma created by high contrast (picosecond contrast ∼10−9) femtosecond relativistic intensity laser pulses. This pump–probe Doppler spectrometry technique offers hundreds of femtosecond temporal resolution, together with a few micrometer spatial resolution across the transverse profile of the plasma. We present the evolution of the plasma surface critical for the probe pulse at the target front as well as the rear. Early time measurements (< 5 ps) using this technique provide very important information about shock wave generation and propagation and the state of the target rear.

Ionization potential depression in dense iron plasmas near solid density

In a dense hot plasma, the energy levels of an embedded ion are lowered by the induced screening potential, which is termed as the ionization potential depressions (IPDs) for the continuum levels. Recent experiments on the precision measurements of the IPDs in solid-density plasmas made it feasible to validate the widely used models. Yet, to date, most of the renewed experimental and theoretical verifications were focused on the low Z dense plasmas. In this work, the IPDs of heavier Fe plasmas were studied near solid density using a recently developed self-consistent temperature dependent ion-sphere model. The present results show reasonable agreement with the b4-potential method at some densities and temperatures, yet there exist large discrepancies between our predicted IPDs and those by the widely used simple closed analytical models. Namely, for Fe plasmas in a density range of 1–16 g cm−3 and a temperature range of 100–1000 eV, a simplified modification of Ecker–Kröll model predicts a much higher IPD than our model, whereas the Stewart–Pyatt, the ion-sphere, and the Debye–Hückel models predict much lower IPDs, which indicates the need of further study on the plasma screening potential. The results obtained in this work should be helpful for the astrophysical and inertial-fusion applications where the IPDs are vital parameters in determining the ionization balance.

The Strong Enhancement of Electron-Impact Ionization Processes in Dense Plasma by Transient Spatial Localization.

Recent experiments have observed much higher electron–ion collisional ionization cross sections and rates in dense plasmas than predicted by the current standard atomic collision theory, including the plasma screening effect. We suggest that the use of (distorted) plane waves for incident and scattered electrons is not adequate to describe the dissipation that occurs during the ionization event. Random collisions with free electrons and ions in plasma cause electron matter waves to lose their phase, which results in the partial decoherence of incident and scattered electrons. Such a plasma-induced transient spatial localization of the continuum electron states significantly modifies the wave functions of continuum electrons, resulting in a strong enhancement of the electron–ion collisional ionization of ions in plasma compared to isolated ions. Here, we develop a theoretical formulation to calculate the differential and integral cross sections by incorporating the effects of plasma screening and transient spatial localization. The approach is then used to investigate the electron-impact ionization of ions in solid-density magnesium plasma, yielding results that are consistent with experiments. In dense plasma, the correlation of continuum electron energies is modified, and the integral cross sections and rates increase considerably. For the ionization of Mg, the ionization cross sections increase several-fold, and the rates increase by one order of magnitude. Our findings provide new insight into collisional ionization and three-body recombination and may aid investigations of the transport properties and nonequilibrium evolution of dense plasma.

Isochoric heating of solid-density plasmas beyond keV temperature by fast thermal diffusion with relativistic picosecond laser light.

The interaction of relativistic short-pulse lasers with matter produces fast electrons with over megaampere currents, which supposedly heats a solid target isochorically and forms a hot dense plasma. In a picosecond timescale, however, thermal diffusion from hot preformed plasma turns out to be the dominant process of isochoric heating. We describe a heating process, fast thermal diffusion, launched from the preformed plasma heated resistively by the fast electron current. We demonstrate the fast thermal diffusion in the keV range in a solid density plasma by a series of one-dimensional particle-in-cell simulations. A theoretical model of the fast thermal diffusion is developed and we derive the diffusion speed as a function of the laser amplitude and target density. Under continuous laser irradiation, the diffusion front propagates at a constant speed in uniform plasma. Our model can provide a guideline for fast isochoric heating using future kilojoule petawatt lasers.