In nonlinear Thomson scattering, a relativistic electron reflects and re-radiates the photons of a laser pulse, converting optical light to x rays or beyond. While this extreme frequency conversion offers a promising source for probing high-energy-density materials and driving uncharted regimes of nonlinear quantum electrodynamics, conventional nonlinear Thomson scattering has inherent tradeoffs in its scaling with laser intensity. Here we discover that the ponderomotive control afforded by spatiotemporal pulse shaping enables novel regimes of nonlinear Thomson scattering that substantially enhance the scaling of the radiated power, emission angle, and frequency with laser intensity. By appropriately setting the velocity of the intensity peak, a spatiotemporally shaped pulse can increase the power radiated by orders of magnitude. The enhanced scaling with laser intensity allows for operation at significantly lower electron energies and can eliminate the need for a high-energy electron accelerator.
The ponderomotive perturbation in the interaction region of laser radiation with a low density and low-temperature plasma is considered. Estimates of the perturbation magnitude are determined from the plasma parameters, geometry, intensity and wavelength of laser radiation. It is shown that ponderomotive perturbations can lead to large errors in the electron density when measured using Thomson scattering.
Incoherent Thomson scattering is a non-intrusive technique commonly used for measuring local plasma density. Within low-density, low-temperature plasma's and for sufficient laser intensity, the laser may perturb the local electron density via the ponderomotive force, causing the diagnostic to become intrusive and leading to erroneous results. A theoretical model for this effect is validated numerically via kinetic simulations of a quasi-neutral plasma using the Particle-in-Cell technique.
We study the laser-driven acceleration of electrons from overdense hydrogen clusters to energies of up to 13 MeV in laser forward direction and several hundreds of keV in an outer ring-like structure. The use of cryogenic hydrogen allows for high repetition-rate operation and examination of the influence of source parameters like temperature and gas flow. The outer ring-like structure of accelerated electrons, originating from the interaction, that is robust against the change of laser and target parameters can be observed for low electron densities of ca. 3$\times$10$^{16}$ cm$^{-3}$. For hig…
A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a non-uniform plasma is derived. We draw the readers' attention to the inconsistency in recent results on the Thomson scattering in inhomogeneous plasma, which leads to violation of the Fluctuation-Dissipation Theorem. We show that not only the imaginary part, but also the derivatives of the real part of the dielectric susceptibility determine the amplitude and the width of the Thomson scattering spectral lines. As a result of inhomogeneity, these properties become asymmetric with respect to inversion of the …
In this short communication, we draw the readers' attention to the inconsistency in the derivation of the Thomson scattering spectrum in inhomogeneous plasma, which leads to violation of the Fluctuation-Dissipation Theorem and a substantial deviation from the results of the rigorous kinetic theory. Moreover, the self-consistent kinetic theory predicts the asymmetry of the spectral lines in inhomogeneous plasma.
One factor determining the reliability of measurements of electron temperature using a Thomson scattering (TS) system is transmittance of the optical bandpass filters in polychromators. We investigate the system performance as a function of electron temperature to determine reliable range of measurements for a given set of the optical bandpass filters. We show that such a reliability, i.e., both bias and random errors, can be obtained by building a forward model of the KSTAR TS system to generate synthetic TS data with the prescribed electron temperature and density profiles. The prescribed pr…
The influence of the laser pulse temporal shape on the Nonlinear Thomson Scattering on-axis photon spectrum is analyzed in detail. Using the classical description, analytical expressions for the temporal and spectral structure of the scattered radiation are obtained for the case of symmetric laser pulse shapes. The possibility of reconstructing the incident laser pulse from the scattered spectrum averaged over interference fringes in the case of high peak intensity and symmetric laser pulse shape is discussed.
Effects of nonlinearity in Thomson scattering of a high intensity laser pulse from electrons are analyzed. Analytic expressions for laser pulse shaping in amplitude and frequency are obtained which control spectrum broadening for arbitrarily high laser pulse intensities. These analytic solutions allow prediction of the spectral form and required laser parameters to avoid broadening. The predictions are validated by numerical calculations. This control over the scattered radiation bandwidth allows of narrow bandwidth sources to be produced using high scattering intensities, which in turn greatl…
The average-atom model is applied to study Thomson scattering of x-rays from warm-dense matter with emphasis on scattering by bound electrons. Parameters needed to evaluate the dynamic structure function (chemical potential, average ionic charge, free electron density, bound and continuum wave-functions and occupation numbers) are obtained from the average-atom model. The resulting analysis provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum and titanium plasmas. In the case of titanium,…
Thomson scattering in non-ideal (collision-dominated) two-component plasmas is calculated accounting for electron-ion collisions as well as electron-electron correlations. This is achieved by using a novel interpolation scheme for the electron-electron response function generalizing the traditional Mermin approach. Also, ions are treated as randomly distributed inert scattering centers. The collision frequency is taken as a dynamic and complex quantity and is calculated from a microscopic quantum-statistical approach. Implications due to different approximations for the electron-electron corre…
Collective X-ray Thomson scattering has become a versatile tool for the diagnostics of dense plasmas. Assuming homogeneous density and temperature throughout the target sample, these parameters can be determined directly from the plasmon dispersion and the ratio of plasmon amplitudes via detailed balance. In inhomogeneous media, the scattering signal is an average of the density and temperature dependent scattering cross-section weighted with the density and temperature profiles. We analyse Thomson scattering spectra in the XUV range from near solid density hydrogen targets generated by free e…
This work proposes a novel method of Thomson microwave scattering for electron number density measurements of miniature plasmas at pressures < 10 Torr. This method is applied to determine electron number density in a positive column of glow discharge initiated at 5 Torr in air with a plasma column diameter of 3.4 mm. The Thomson Microwave Scattering(TMS) system measured the electron number density to be 3.36*10^10 cm^-3. The result obtained using the TMS system was validated against the measurements made using the well-known technique of microwave quarter-wave hairpin resonator. Measurements w…
We determine the spectral photon yield from a hot dense plasma irradiated by VUV-FEL light in a Thomson scattering experiment. The Thomson signal is compared to the emission background mainly caused by bremsstrahlung photons. We determine experimental conditions that allow for a signal-to-background ratio larger than unity. By derivation of the Thomson and the bremsstrahlung spectrum from linear response theory we present a consistent quantum statistical approach to both processes. This allows for a systematic treatment of medium and quantum effects such as dynamical screening and strong colli…
The theory of Thomson scattering from high-temperature high-density plasmas is revisited from the view point of plasma fluctuation theory. Three subtle effects are addressed with a unified theory. The first is the correction of the first order of $v/c$, where $v$ is the particle velocity and $c$ is the light speed, the second is the plasma dielectric effect, and the third is the finite scattering volume effect. When the plasma density is high, the first effect is very significant in inferring plasma parameters from the scattering spectra off electron plasma waves. The second is also be notable…
The traditional Thomson scattering diagnostic is based on measurement of the wavelength spectrum of scattered light, where electron temperature measurements are inferred from thermal broadening of the scattered laser light. At sufficiently high temperatures, especially those predicted for ITER and other burning plasmas, relativistic effects cause a change in the polarization state of the scattered photons. The resulting depolarization of the scattered light is temperature dependent and has been proposed elsewhere as a potential alternative to the traditional spectral decomposition technique. F…
In this paper, we propose a collective Thomson scattering diagnostic for fast ion measurements for the gas-dynamic trap (GDT) facility at the Budker Institute. The diagnostic utilizes 54.5 GHz gyrotron usually used for electron cyclotron resonance heating as a source of probe radiation and is aimed at reconstruction of distributions over transverse and longitudinal velocities of NBI-driven ions in the plasma core. Here we present a feasibility study of this concept.
We have developed a non-collective Thomson scattering diagnostic for measurements of electron density and temperature on the Large Plasma Device. A triple grating spectrometer with a tunable notch filter is used to discriminate the faint scattering signal from the stray light. In this paper we describe the diagnostic and its calibration via Raman scattering, and present the first measurements performed with the fully commissioned system. Depending on the discharge conditions, the measured densities and temperatures range from 4.0$\times$10$^{12}$ cm$^{-3}$ to 2.8$\times$10$^{13}$ cm$^{-3}$, an…
For the last decade numerous researchers have been trying to develop experimental techniques to use X-ray Thomson scattering as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. With the advent of the X-ray free electron laser (X-FEL) at the SLAC Linac Coherent Light Source (LCLS) we now have such a source available in the keV regime. One challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas. Most Thomson scattering…
X-ray Thomson scattering is being developed as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. Most experiments are currently done at large laser facilities that can create bright X-ray sources, however the advent of the X-ray free electron laser (X-FEL) provides a new bright source to use in these experiments. One challenge with X-ray Thomson scattering experiments is understanding how to model the scattering for partially ionized plasmas in order to include the contributions of the b…
We propose a collective Thomson scattering experiment at the VUV free electron laser facility at DESY (FLASH) which aims to diagnose warm dense matter at near-solid density. The plasma region of interest marks the transition from an ideal plasma to a correlated and degenerate many-particle system and is of current interest, e.g. in ICF experiments or laboratory astrophysics. Plasma diagnostic of such plasmas is a longstanding issue. The collective electron plasma mode (plasmon) is revealed in a pump-probe scattering experiment using the high-brilliant radiation to probe the plasma. The distinc…
A recent and unexpected discrepancy between \textit{ab initio} simulations and the interpretation of a laser shock experiment on aluminum, probed by X-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable,…
The total number of electrons in a classical microplasma can be non-intrusively measured through elastic in-phase coherent microwave scattering (CMS). Here, we establish a theoretical basis for the CMS diagnostic technique with an emphasis on Thomson and collisional scattering in short, thin unmagnetized plasma media. Experimental validation of the diagnostic is subsequently performed via linearly polarized, variable frequency microwave scattering off laser induced air-based microplasmas with diverse ionization and collisional features. Namely, conducted studies include a verification of short…
The influence of finite relaxation times on Thomson scattering from warm-dense plasmas is examined within the framework of the average-atom approximation. Presently most calculations use the collision-free Lindhard dielectric function to evaluate the free-electron contribution to the Thomson cross section. In this work, we use the Mermin dielectric function, which includes relaxation time explicitly. The relaxation time is evaluated by treating the average atom as an impurity in a uniform electron gas and depends critically on the transport cross section. The calculated relaxation rates agree …
We calculate the Thomson scattering cross section in a non-relativistic, magnetized, high density plasma -- in a regime where collective excitations can be described by magnetohydrodynamics. We show that, in addition to cyclotron resonances and an elastic peak, the cross section exhibits two pairs of peaks associated with slow and fast magnetosonic waves; by contrast, the cross section arising in pure hydrodynamics possesses just a single pair of Brillouin peaks. Both the position and the width of these magnetosonic-wave peaks depend on the ambient magnetic field and temperature, as well as tr…
Angular distributions of Thomson scattering are researched in the combined fields with a circularly polarization of laser field and a strong uniform magnetic field. The trajectories of the electron and the dependence of it on the initial phase are also given. It is found that the angular distributions with respect to the azimuthal angle show twofold symmetry whatever the laser intensity, the order of harmonics, the resonance parameter, and the initial axial momentum are. On the other hand, the radiation with respect to the polar angle is mainly distributed in two regions which are roughly symm…
We present experimental measurements of a pulsed plasma gun, using two-colour imaging laser interferometry and spatially resolved Thomson scattering. Interferometry measurements give an electron density $n_e\approx2.7\times10^{17}$ cm$^{-3}$ at the centre of the plasma plume, at 5 mm from the plasma gun nozzle. The Thomson scattered light is collected from two probing angles allowed us to simultaneously measure the collective and non-collective spectrum of the electron feature from the same spatial locations. The inferred electron densities from the location of the electron plasma waves is in …
The design of inertial confinement fusion (ICF) ignition targets requires radiation-hydrodynamics simulations with accurate models of the fundamental material properties (i.e., equation of state, opacity, and conductivity). Validation of these models are required via experimentation. A feasibility study of using spatially-integrated, spectrally-resolved, X-ray Thomson scattering (XRTS) measurements to diagnose the temperature, density, and ionization of the compressed DT shell and hot spot of a laser direct-drive implosion at two-thirds convergence was conducted. Synthetic scattering spectra w…
X-ray Thomson scattering is being developed as a method to measure the temperature, electron density, and ionization state of high energy density plasmas such as those used in inertial confinement fusion. X-ray laser sources have always been of interest because of the need to have a bright monochromatic x-ray source to overcome plasma emission and eliminate other lines in the background that complicate the analysis. With the advent of the xray free electron laser (X-FEL) at the SLAC Linac Coherent Light Source (LCLS) and other facilities coming online worldwide, we now have such a source avail…
The Wendelstein 7-X (W7-X) Thomson scattering (TS) diagnostic was upgraded to transiently achieve kilohertz sampling rates combined with adjustable measuring times. The existing Nd:YAG lasers are employed to repetitively emit "bursts", i.e. multiple laser pulses in a short time interval. Appropriately timing burst in the three available lasers, up to twelve evenly spaced consecutive measurements per burst are possible. The pulse-to-pulse increment within a burst can be tuned from 2 ms to 33.3 ms (500 kHz - 30 Hz). Additionally, an event trigger system was developed to synchronize the burst Tho…
A scalable system for real-time analysis of electron temperature and density based on signals from the Thomson scattering diagnostic, initially developed for and installed on the NSTX-U experiment, was recently adapted for the Large Helical Device (LHD) and operated for the first time during plasma discharges. During its initial operation run, it routinely recorded and processed signals for four spatial points at the laser repetition rate of 30 Hz, well within the system's rated capability for 60 Hz. We present examples of data collected from this initial run and describe subsequent adaptation…
With the Thomson scattering (TS) system in KSTAR, temporal evolution of electron temperature ($T_e$) is estimated using a weighted look-up table method with fast sampling ($1.25$ or $2.5$ GS/s) digitizers during the 2014 KSTAR campaign. Background noise level is used as a weighting parameter without considering the photon noise due to the absence of information on absolute photon counts detected by the TS system. Estimated electron temperature during a relatively quiescent discharge are scattered, i.e., $15$\% variation on $T_e$ with respect to its mean value. We find that this $15$\% variatio…
The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and …
For the purpose of laser wakefield acceleration, it turned out that also the injection of electron bunches longer than a plasma wavelength can generate accelerated femtosecond bunches with relatively low energy spread. This is of high interest because such injecting bunches can be provided, e.g., by state-of-the-art photo cathode RF guns. Here we point out that when an e-bunch is injected in the wakefield it is important to take into account the ponderomotive scattering of the injecting bunch by the laser pulse in the vacuum region located in front of the plasma. At low energies of the injecte…
The primary purpose of the collective Thomson scattering (CTS) diagnostic at ITER is to measure the properties of fast-ion populations, in particular those of fusion-born $α$-particles. Based on the present design of the diagnostic, we compute and fit synthetic CTS spectra for the ITER baseline plasma scenario, including the effects of noise, refraction, multiple fast-ion populations, and uncertainties on nuisance parameters. As part of this, we developed a model for CTS that incorporates spatial effects of frequency-dependent refraction. While such effects will distort the measured ITER CTS s…
Recent calculations [Nilsen et al. arXiv:1212.5972] predict that contributions to the scattered photon spectrum from 3s and 3p bound states in chromium (Z=24) at metallic density and T=12 eV resonate below the respective bound-state thresholds. These resonances are shown to be closely related to continuum lowering, where 3d bound states in the free atom dissolve into a resonant l=2 partial wave in the continuum. The resulting d-state resonance dominates contributions to the bound-free dynamic structure function, leading to the predicted resonances in the scattered X-ray spectrum. Similar reson…
We present a new analytical solution for the equation of motion of relativistic electrons in the focus of a high-intensity laser pulse. We approximate the electron's transverse dynamics in the averaged field of a long laser pulse focused to a Gaussian transverse profile. The resultant ponderomotive scattering is found to feature an upper boundary of the electrons' scattering angles, depending on the laser parameters and the electrons' initial state of motion. In particular, we demonstrate the angles into which the electrons are scattered by the laser scale as a simple relation of their initial…
Conceptual design of Thomson scattering system with high wavelength resolution in magnetically confined plasmas for electron phase-space measurements
National Institute for Fusion Science（国立研究开发法人核融合科学研究所）；Division of Quantum Science and Engineering, Graduate School of Engineering, Hokkaido University（北海道大学工学研究科量子科学与工程专攻）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）；Graduate School of Science, Nagoya University（名古屋大学理学研究科）
Many astrophysical environments such as X-ray binaries, active galactic nuclei, and accretion disks of compact objects have photoionized plasmas. The strong photoionizing environment found near these bright X-ray sources can be produced in a scaled laboratory experiment, and direct measurements can form a testbed for spectroscopic models and photoionization codes used in analysis of these astrophysical objects. Such scaled experiments are currently being conducted using Ne filled gas cells on the Z-facility as part of the Z Astrophysical Plasma Properties (ZAPP) collaboration. The plasma is di…
We consider the Thomson scattering of an electron in an ultra-intense chirped laser pulse. It is found that the introduction of a negative chirp means the electron enters a high frequency region of the field while it still has a large proportion of its original energy. This results in a significant enhancement of the energy and intensity of the emitted radiation as compared to the case without chirping.
A Particle-in-Cell Simulation Framework for Thomson Scattering Analysis in Inertial Confinement Fusion
University of Science and Technology of China（中国科学技术大学）；Shanghai Jiao Tong University（上海交通大学）；Hunan University（湖南大学）；China Academy of Engineering Physics（中国工程物理研究院）
Overview of X-ray Thomson scattering measurements of extreme states of matter
Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿罗森多夫亥姆霍兹中心）；Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（先进系统理解中心，德累斯顿罗森多夫亥姆霍兹中心）；Institut für Physik, Universität Rostock（罗斯托克大学物理研究所）；University of Warwick（华威大学）
Spectral Deconvolution without the Deconvolution: Extracting Temperature from X-ray Thomson Scattering Spectra without the Source-and-Instrument Function
Center for Advanced Systems Understanding (CASUS)（先进系统理解中心）；Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心）；Center for Computing Research, Sandia National Laboratories（桑迪亚国家实验室计算研究中心）；Institut für Physik, Universität Rostock（罗斯托克大学物理研究所）；Quantum Simulations Group, Physics and Life Science Directorate, Lawrence Livermore National Laboratory (LLNL)（劳伦斯利弗莫尔国家实验室物理与生命科学部量子模拟组）；Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心辐射物理研究所）；European XFEL（欧洲X射线自由电子激光装置）
The spectrum of relativistic electron bunches with large energy dispersion is hardly obtainable with conventional magnetic spectrometers. We present a novel spectroscopic concept, based on the analysis of the photons generated by Thomson Scattering of a probe laser pulse inpinging with arbitrary incidence angle onto the electron bunch. The feasibility of a single-pulse spectrometer, using an energy-calibrated CCD device as detector, is investigated. Numerical simulations performed in conditions typical of a real experiment show the effectiveness and accuracy of the new method.
Understanding the behaviour of the confined fast ions is important in both current and future fusion experiments. These ions play a key role in heating the plasma and will be crucial for achieving conditions for burning plasma in next-step fusion devices. Microwave-based Collective Thomson Scattering (CTS) is well suited for reactor conditions and offers such an opportunity by providing measurements of the confined fast-ion distribution function resolved in space, time and 1D velocity space. We currently operate a CTS system at ASDEX Upgrade using a gyrotron which generates probing radiation a…
We present optical Thomson scattering measurements of electron density and temperature in a large-scale (~2 cm) exploding laser plasma produced by irradiating a solid target with a high energy (5-10 J) laser pulse at high repetition rate (1 Hz). The Thomson scattering diagnostic matches this high repetition rate. Unlike previous work performed in single shots at much higher energies, the instrument allows point measurements anywhere inside the plasma by automatically translating the scattering volume using motorized stages as the experiment is repeated at 1 Hz. Measured densities around 4$\tim…
If an electric charge is accelerated by a sufficiently intense electromagnetic field, the effects of the radiation emitted by the charge on the charge dynamics (radiation reaction) cannot be ignored. Here we show that classical radiation-reaction effects alter qualitatively and quantitatively the infrared behavior of the spectrum of the radiation emitted by an electron in the presence of an intense electromagnetic plane wave (nonlinear Thomson scattering). An analytical expression of the infrared limit of nonlinear Thomson scattering is provided, which includes radiation-reaction effects and i…
