Ejecta Parameters Research Articles

The effect of projectile nose shape on the formation and expansion of impact-induced ejecta for sand target

Understanding the ejecting behavior of granular materials under impact conditions is of vital important for the asteroid sampling and defense. During the impact and penetration stages, the interaction between the projectile and the target controls the impact-induced ejecta behavior. However, the correlation between projectile nose shape and the formation and expansion characteristics of the ejecta remains unclear. In this study, a vertical launch system and high-speed camera were used to carry out the experiments of projectile impact on sand target at 100 m/s. The variations of ejecta parameters induced by different projectile shapes (cone and ogive) and sharpness (cone angles of 30°, 60°, 120°; Caliber-Radius-Head values of 0.5, 1.0, 3.0) were compared. The results showed that both the formation and expansion of the ejecta are influenced by the projectile shape, especially the sharpness of projectile nose. Ejecta parameters such as the emergence time, horizontal expansion velocity, and ejecta mass are positively correlated with the sharpness of projectile nose, while emergence diameter and ejecta angle exhibit a negative correlation. The above observed phenomena are attributed to the energy deposition rate of the projectile on the target during the impact stage and the flow direction of sand grains after the projectile-grain interaction during the penetration stage. These findings can gain an insight into the influence of projectile shape on the ejecting behavior of granular materials. In addition, these findings offer valuable references for the modification of ejecta models that incorporate projectile nose shapes and contribute to the design of impact sampling mechanisms in practical tasks.

An analytic description of electron thermalization in kilonovae ejecta

ABSTRACT A simple analytic description is provided of the rate of energy deposition by β-decay electrons in the homologously expanding radioactive plasma ejected in neutron star mergers, valid for a wide range of ejecta parameters – initial entropy, electron fraction {s0, Ye}, and scaled (time-independent) density ρt3. The formulae are derived using detailed numerical calculations following the time-dependent composition and β-decay emission spectra (including the effect of delayed deposition). The deposition efficiency depends mainly on ρt3 and only weakly on {s0, Ye}. The time te at which the ratio between the rates of electron energy deposition and energy production drops to 1 − e−1, is given by $t_e=t_{0e}\Big (\frac{\rho t^3}{0.5(\rho t^3)_0}\Big)^a$, where $(\rho t^3)_0=\frac{0.05\, {\rm M}_{\odot }}{4\pi (0.2c)^3}$, t0e(s0, Ye) ≈ 17 d, and 0.4 ≤ a(s0, Ye) ≤ 0.5. The fractional uncertainty in te due to nuclear physics uncertainties is $\approx 10~{{\ \rm per\ cent}}$. The result a ≤ 0.5 reflects the fact that the characteristic β-decay electron energies do not decrease with time (largely due to ‘inverted decay chains’ in which a slowly decaying isotope decays to a rapidly decaying isotope with higher end-point energy). We provide an analytic approximation for the time-dependent electron energy deposition rate, reproducing the numerical results to better than 50 per cent (typically $\lt 30~{{\ \rm per\ cent}}$, well within the energy production rate uncertainty due to nuclear physics uncertainties) over a 3–4 orders-of-magnitude deposition rate decrease with time. Our results may be easily incorporated in calculations of kilonovae light curves (with general density and composition structures), eliminating the need to numerically follow the time-dependent electron spectra. Identifying te, e.g. in the bolometric light curve, will constrain the ejecta density distribution.

Surrogate light curve models for kilonovae with comprehensive wind ejecta outflows and parameter estimation for AT2017gfo

The electromagnetic emission resulting from neutron star mergers have been shown to encode properties of the ejected material in their light curves. The ejecta properties inferred from the kilonova emission has been in tension with those calculated based on the gravitational wave signal and numerical relativity models. Motivated by this tension, we construct a broad set of surrogate light curve models derived for kilonova ejecta. The four-parameter family of two-dimensional anisotropic simulations and its associated surrogate explore different assumptions about the wind outflow morphology and outflow composition, keeping the dynamical ejecta component consistent. We present the capabilities of these surrogate models in interpolating kilonova light curves across various ejecta parameters and perform parameter estimation for AT2017gfo both without any assumptions on the outflow and under the assumption that the outflow must be representative of solar r-process abundance patterns. Our parameter estimation for AT2017gfo shows these surrogate models help alleviate the ejecta property discrepancy while also illustrating the impact of systematic modeling uncertainties on these properties, urging further investigation.

A Population Study of the Radio Emission of Fast Blue Optical Transients

Despite the fact that the progenitor of fast blue optical transients (FBOTs) is still a subject of debate, FBOTs are sometimes suggested to originate from the core collapse of ultra-stripped stars and be powered by a spinning-down neutron star. Following this consideration, it is expected that the late-time evolution of the progenitor stars can leave important imprints in the circumstellar material (CSM) of FBOTs, due to the strong mass loss of the stars. The interaction of the FBOT ejecta with the CSM can drive a long-lasting shock to generate radio emission, which thus enables us to probe the CSM properties through radio observation although such observations are still rare. Within the framework of the magnetar-powered model, Liu et al. fitted the multi-band optical light curves of 40 FBOTs, and hence, the statistical distributions of the FBOT magnetar and ejecta parameters were obtained. Based on these FBOT population results, we investigate the dependence of the radio emission on the mass-loss rate of the progenitors and evaluate the detectability of radio emission from FBOTs with current and future telescopes. It is found that the distribution of the peak time and peak luminosity of the emission at 8.4 GHz are primarily in the regions of t peak,ν = 102.12±0.63 days and L peak,ν = 1028.73±0.83 erg s−1 Hz−1, respectively. A joint detection of the Zwicky Transient Facility and Very Large Array could achieve success in about 8.7% FBOTs of z ≤ 1. Furthermore, if considering a joint detection of the Chinese Space Station Telescope and the Square Kilometer Array, this rate of success could be increased to about 23.9%.

Spectroscopic r-Process Abundance Retrieval for Kilonovae. I. The Inferred Abundance Pattern of Early Emission from GW170817

Freshly synthesized r-process elements in kilonovae ejecta imprint absorption features on optical spectra, as observed in the GW170817 binary neutron star merger. These spectral features encode insights into the physical conditions of the r-process and the origins of the ejected material, but associating features with particular elements and inferring the resultant abundance pattern is computationally challenging. We introduce Spectroscopic r-Process Abundance Retrieval for Kilonovae (SPARK), a modular framework to perform Bayesian inference on kilonova spectra with the goals of inferring elemental abundance patterns and identifying absorption features at early times. SPARK inputs an atomic line list and abundance patterns from reaction network calculations into the TARDIS radiative transfer code. It then performs fast Bayesian inference on observed kilonova spectra by training a Gaussian process surrogate for the approximate posteriors of kilonova ejecta parameters, via active learning. We use the spectrum of GW170817 at 1.4 days to perform the first inference on a kilonova spectrum, and recover a complete abundance pattern. Our inference shows that this ejecta was generated by an r-process with either (1) high electron fraction Y e ∼ 0.35 and high entropy s/k B ∼ 25, or, (2) a more moderate Y e ∼ 0.30 and s/k B ∼ 14. These parameters are consistent with a shocked, polar dynamical component, and a viscously driven outflow from a remnant accretion disk, respectively. We also recover previous identifications of strontium absorption at ∼8000 Å, and tentatively identify yttrium and/or zirconium at ≲4500 Å. Our approach will enable computationally tractable inference on the spectra of future kilonovae discovered through multimessenger observations.

Modelling populations of kilonovae

AbstractThe 2017 detection of a kilonova coincident with gravitational-wave emission has identified neutron star mergers as the major source of the heaviest elements and dramatically constrained alternative theories of gravity. Observing a population of such sources has the potential to transform cosmology, nuclear physics, and astrophysics. However, with only one confident multi-messenger detection currently available, modelling the diversity of signals expected from such a population requires improved theoretical understanding. In particular, models that are quick to evaluate and are calibrated with more detailed multi-physics simulations are needed to design observational strategies for kilonovae detection and to obtain rapid-response interpretations of new observations. We use grey-opacity models to construct populations of kilonovae, spanning ejecta parameters predicted by numerical simulations. Our modelling focuses on wavelengths relevant for upcoming optical surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST). In these simulations, we implement heating rates that are based on nuclear reaction network calculations. We create a Gaussian-process emulator for kilonova grey opacities, calibrated with detailed radiative transfer simulations. Using recent fits to numerical relativity simulations, we predict how the ejecta parameters from binary neutron star (BNS) mergers shape the population of kilonovae, accounting for the viewing-angle dependence. Our simulated population of BNS mergers produce peak i-band absolute magnitudes of −20 ≤ Mi ≤ −11. A comparison with detailed radiative transfer calculations indicates that further improvements are needed to accurately reproduce spectral shapes over the full light curve evolution.

The critical role of nuclear heating rates, thermalization efficiencies, and opacities for kilonova modelling and parameter inference

ABSTRACT We present an improved version of the 3D Monte Carlo radiative transfer code possis to model kilonovae from neutron star mergers, wherein nuclear heating rates, thermalization efficiencies, and wavelength-dependent opacities depend on local properties of the ejecta and time. Using an axially symmetric two-component ejecta model, we explore how simplistic assumptions on heating rates, thermalization efficiencies, and opacities often found in the literature affect kilonova spectra and light curves. Specifically, we compute five models: one (FIDUCIAL) with an appropriate treatment of these three quantities, one (SIMPLE-HEAT) with uniform heating rates throughout the ejecta, one (SIMPLE-THERM) with a constant and uniform thermalization efficiency, one (SIMPLE-OPAC) with grey opacities, and one (SIMPLE-ALL) with all these three simplistic assumptions combined. We find that deviations from the FIDUCIAL model are of several (∼1–10) magnitudes and are generally larger for the SIMPLE-OPAC and SIMPLE-ALL compared to the SIMPLE-THERM and SIMPLE-HEAT models. The discrepancies generally increase from a face-on to an edge-on view of the system, from early to late epochs and from infrared to ultraviolet/optical wavelengths. This work indicates that kilonova studies using either of these simplistic assumptions ought to be treated with caution and that appropriate systematic uncertainties ought to be added to kilonova light curves when performing inference on ejecta parameters.

Non-thermal emission from mildly relativistic dynamical ejecta of neutron star mergers

ABSTRACT Binary neutron star mergers are expected to produce fast dynamical ejecta, with mildly relativistic velocities extending to β = v/c > 0.6. We consider the radio to X-ray synchrotron emission produced by collisionless shocks driven by such fast ejecta into the interstellar medium. Analytical expressions are given for spherical ejecta with broken power-law mass (or energy) distributions, M(> γβ) ∝ (γβ)−s with s = sKN at γβ < γ0β0 and s = sft at γβ > γ0β0 (where γ is the Lorentz factor). For parameter values characteristic of merger calculation results – a ‘shallow’ mass distribution, 1 < sKN < 3, for the bulk of the ejecta (at γβ ≈ 0.2), and a steep, sft > 5, ‘fast tail’ mass distribution – our model provides an accurate (to tens of per cent) description of the evolution of the flux, including at the phase of deceleration to subrelativistic expansion. This is a significant improvement over earlier results, based on extrapolations of results valid for γβ ≫ 1 or ≪1 to γβ ≈ 1, which overestimate the flux by an order of magnitude for typical parameter values. It will enable a more reliable inference of ejecta parameters from future measurements of the non-thermal emission. For the merger event GW170817, the existence of a ‘fast tail’ is expected to produce detectable radio and X-ray fluxes over a time-scale of ∼104 d.

On the X-Ray, Optical, and Radio Afterglows of the BdHN I GRB 180720B Generated by Synchrotron Emission

Gamma-ray bursts (GRBs) are systems of unprecedented complexity across all the electromagnetic spectrum, including the radio, optical, X-rays, gamma rays in the MeV and GeV regimes, as well as ultrahigh-energy cosmic rays, each manifested in seven specific physical processes with widely different characteristic evolution timescales ranging from 10−14 s to 107 s or longer. We here study the long GRB 180720B originating from a binary system composed of a massive carbon-oxygen (CO) star of about 10M ⊙ and a companion neutron star (NS). The gravitational collapse of the CO star gives rise to a spinning newborn NS (νNS), with an initial period of P 0 = 1 ms that powers the synchrotron radiation in the radio, optical, and X-ray wavelengths. We here investigate solely the GRB 180720B afterglows and present a detailed treatment of its origin based on the synchrotron radiation released by the interaction of the νNS and the SN ejecta. We show that in parallel to the X-ray afterglow, the spinning νNS also powers the optical and radio afterglows and allows to infer the νNS and ejecta parameters that fit the observational data.

Simultaneous application of photon Doppler velocimetry and coherent backscattering for probing ejecta from shock-loaded samples

We present the results of experiments on simultaneous probing of a shock-loaded layer of aluminum oxide particles by the methods of photon Doppler velocimetry (PDV) and coherent backscattering (CBS). The measurements of the angular profiles of CBS from a dynamically expanding medium are reported for the first time. The powder of particles was applied to the surface of an explosively driven steel plate. The particle velocities ranged from 0.9 to 1.3 km/s. The main characteristics of the cloud of ejected particles (the areal density, mass–velocity distribution, etc.) are recovered from the PDV and CBS probing data using an approach based on theoretical modeling of the measurement results with the transport equation. By varying the parameters of the particle cloud (the transport optical thickness and the parameters of the initial velocity distribution), it is managed to fit the dynamics of the calculated Doppler spectra and CBS angular profiles to the data of measurements in given time intervals and, thereby, recover the values of these parameters. As applied to the diagnostics of ejecta from shock-loaded samples, the CBS method is shown to provide independent data on the spatial distribution of particles over the cloud thickness. The presented results demonstrate that the joint application of PDV- and CBS-based channels of measurements to ejecta diagnostics makes it possible to halve the error in recovering the ejecta parameters compared to using PDV alone.

Radioactively Powered Gamma-Ray Transient Associated with a Kilonova from Neutron Star Merger

The association of GW170817/GRB 170817A/AT2017gfo provides the first direct evidence for neutron star mergers as significant sources of r-process nucleosynthesis. A gamma-ray transient (GRT) would be powered by the radioactive decay of the freshly synthesized r-process elements. By analyzing the composition and gamma-ray opacity of the kilonova ejecta in detail, we calculate the lightcurve and spectrum of the GRT for a range of spherically symmetric merger ejecta models with mass M ej = 0.001 to ∼0.05M ⊙ and expansion velocity v ej = 0.1c to ∼0.4c. It is found that the peak of the GRT lightcurve depends on M ej and v ej as and . Most radiating photons are in the 100–3000 keV band and the spectrum peaks at about 800 keV for different nuclear physics inputs. The line features are blurred out by the Doppler broadening effect. Adopting the ejecta parameters reported in the literature, we examine the detection probability of the possible GRT associated with AT2017gfo. We show that the GRT cannot be convincingly detected with either current or proposed missions in the MeV band, such as ETCC and AMEGO. The low gamma-ray flux, together with the extremely low event rate at local universe, makes a discovery of GRTs a great challenge.

Kilonova Detectability with Wide-field Instruments

Abstract Kilonovae are ultraviolet, optical, and infrared transients powered by the radioactive decay of heavy elements following a neutron star merger. Joint observations of kilonovae and gravitational waves can offer key constraints on the source of Galactic r-process enrichment, among other astrophysical topics. However, robust constraints on heavy element production require rapid kilonova detection (within ∼1 day of merger) as well as multiwavelength observations across multiple epochs. In this study, we quantify the ability of 13 wide-field-of-view instruments to detect kilonovae, leveraging a large grid of over 900 radiative transfer simulations with 54 viewing angles per simulation. We consider both current and upcoming instruments, collectively spanning the full kilonova spectrum. The Roman Space Telescope has the highest redshift reach of any instrument in the study, observing kilonovae out to z ∼ 1 within the first day post-merger. We demonstrate that BlackGEM, DECam, GOTO, the Vera C. Rubin Observatory’s LSST, ULTRASAT, VISTA, and WINTER can observe some kilonovae out to z ∼ 0.1 (∼475 Mpc), while DDOTI, MeerLICHT, PRIME, Swift/UVOT, and ZTF are confined to more nearby observations. Furthermore, we provide a framework to infer kilonova ejecta properties following nondetections and explore variation in detectability with these ejecta parameters.

Post maximum light and late time optical imaging polarimetry of type I superluminous supernova 2020znr

ABSTRACTOptical imaging polarimetry was conducted on the hydrogen poor superluminous supernova 2020znr during three phases after maximum light (≈ +34 d, +288 d, and +289 d). After instrumental and interstellar polarization correction, all measurements are consistent with null-polarization detection. Modelling the light curve with a magnetar spin-down model shows that SN2020znr has similar magnetar and ejecta parameters to other SLSNe. A comparison of the best-fitting values discussed in the literature on SN 2017egm and SN 2015bn, two hydrogen poor SLSNe showing an increase of polarization after maximum light, suggests that SN 2020znr has higher mass ejecta that may prevent access to the geometry of the inner ejecta with optical polarimetry. The combined information provided by spectroscopy and light-curve analysis of type I SLSNe may be an interesting avenue to categorize the polarization properties of this class of transients. This approach would require to expand the sample of SLSNe polarimetry data currently available with early and late time epochs new measurements.

Reconstruction of ejecta field based on photon Doppler velocimetry from shock-loaded samples in vacuum

Photon Doppler velocimetry (PDV) has been extensively used to measure the velocity of single objection or fragments under the impact; however, with the PDV measurement, how to recover the ejecta field, which is a high-velocity multiple-particles system, remains a challenge. Mie theory is applied to describe the light-particle scattering process, and Monte Carlo algorithm is introduced to simulate PDV spectrums. By the simulations, how the PDV spectrum is qualitatively influenced by the velocity profile, particle size, and total area mass of ejecta is revealed. Then a novel optical model is proposed to derive the quantitative relationships between these ejecta parameters and PDV spectrum characteristics. With this model, the ejecta parameters can be extracted from PDV spectrum directly. Estimated values of the ejecta parameters from experimental spectrum are in good agreement with those measured by piezoelectric probe.

Effect of lunar landing on its surface, surrounding environment and hardware: A numerical perspective

With renewed interest in lunar exploration, soft landing on the Moon has gained prominence in the recent past. Most of the modern-day landers use throttleable thrusters to make a safe and soft landing. However, the jet plume produced by the exhaust of these thrusters creates disturbance on the lunar surface which first leads to surface disturbance and subsequently create damage by the ejected particles to the surroundings and hardware present in the vicinity of the landing site. Understanding this disturbance and assessing the damage is significant both for science as well as mission safety, particularly, keeping in view the plans for ISRU (In-situ Resource Utilisation)/Lunar outpost activities in future. In the present study, an attempt is made to assess the extent of damage caused to the surrounding hardware left by an earlier landing in the vicinity of the landing site. A damage model in conjunction with plume dynamics and its interaction with the lunar surface is used to arrive at the estimates. A Direct Simulation Monte Carlo (DSMC) solver is used for the analysis of plume dynamics and gaseous interactions of the plume with the in-situ lunar soil. The output of the DSMC solver is employed to quantify the ejecta parameters such as eject velocity, mass flux rate, ejecta kinematics, which are used to estimate the expected damage to a lunar outpost or hardware present in its vicinity. Estimates are made on the total amount of damage (defined as the amount of lunar regolith ejected from the surface in to the surrounding environment) at different stages of landing, ejecta kinematics and overall volume of pit/dent formed on the surface of surrounding hardware due to the high velocity ejecta particles. The study considers a typical test case using a landing trajectory of a small class lander mission for these calculations and presents a picture of surface disturbance, ejecta profile and damage that could happen to the surroundings up to few 100s of meters. An ejecta amount of 7.5 ​kg beneath the lander and a damage of 1500 ​mm3 to the surrounding hardware (situated at 100m from landing site) is estimated from the configuration considered in the present study. Although the disturbance and damage caused due to small class landers seems to be minimal, large class landers and landing in a close vicinity of an earlier landing would cause significant threat to the existing hardware which needs to be mitigated for all future lunar ISRU/outpost activities.

AT2017gfo: Bayesian inference and model selection of multicomponent kilonovae and constraints on the neutron star equation of state

ABSTRACTThe joint detection of the gravitational wave GW170817, of the short γ-ray burst GRB170817A and of the kilonova AT2017gfo, generated by the the binary neutron star (NS) merger observed on 2017 August 17, is a milestone in multimessenger astronomy and provides new constraints on the NS equation of state. We perform Bayesian inference and model selection on AT2017gfo using semi-analytical, multicomponents models that also account for non-spherical ejecta. Observational data favour anisotropic geometries to spherically symmetric profiles, with a log-Bayes’ factor of ∼104, and favour multicomponent models against single-component ones. The best-fitting model is an anisotropic three-component composed of dynamical ejecta plus neutrino and viscous winds. Using the dynamical ejecta parameters inferred from the best-fitting model and numerical–relativity relations connecting the ejecta properties to the binary properties, we constrain the binary mass ratio to q < 1.54 and the reduced tidal parameter to $120\lt \tilde{\Lambda }\lt 1110$. Finally, we combine the predictions from AT2017gfo with those from GW170817, constraining the radius of a NS of 1.4 M⊙ to 12.2 ± 0.5 km (1σ level). This prediction could be further strengthened by improving kilonova models with numerical-relativity information.

Reconstruction and interpretation of photon Doppler velocimetry spectrum for ejecta particles from shock-loaded sample in vacuum* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11902043 and 11772065) and the Science Challenge Project (Grant No. TZ2016001).

The photon Doppler velocimetry (PDV) spectrum is investigated in an attempt to reveal the particle parameters of ejecta from shock-loaded samples in a vacuum. A GPU-accelerated Monte–Carlo algorithm, which considers the multiple-scattering effects of light, is applied to reconstruct the light field of the ejecta and simulate the corresponding PDV spectrum. The influence of the velocity profile, total area mass, and particle size of the ejecta on the simulated spectra is discussed qualitatively. To facilitate a quantitative discussion, a novel theoretical optical model is proposed in which the single-scattering assumption is applied. With this model, the relationships between the particle parameters of ejecta and the peak information of the PDV spectrum are derived, enabling direct extraction of the particle parameters from the PDV spectrum. The values of the ejecta parameters estimated from the experimental spectrum are in good agreement with those measured by a piezoelectric probe.

Standardizing kilonovae and their use as standard candles to measure the Hubble constant

The detection of GW170817 is revolutionizing many areas of astrophysics with the joint observation of gravitational waves and electromagnetic emissions. These multi-messenger events provide a new approach to determine the Hubble constant, thus, they are a promising candidate for mitigating the tension between measurements of Type Ia supernovae via the local distance ladder and the Cosmic Microwave Background. In addition to the "standard siren" provided by the gravitational-wave measurement, the kilonova itself has characteristics that allow to improve existing measurements or to perform yet another, independent measurement of the Hubble constant without gravitational-wave information. Here, we employ standardization techniques borrowed from the type-Ia community and apply them to kilonovae, not using any information from the gravitational-wave signal. We use two versions of this technique, one derived from direct observables measured from the lightcurve, and the other based on inferred ejecta parameters, e.g., mass, velocity, and composition, for two different models. These lead to Hubble Constant measurements of $H_0 = 109^{+49}_{-35}$\,km $\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$ for the measured analysis, and $H_0 = 85^{+22}_{-17}$\,km $\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$ and $H_0 = 79^{+23}_{-15}$\,km $\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$ for the inferred analyses. This measurement has error bars within ~$\sim$\,2 to the gravitational-wave measurements ($H_0=74^{+16}_{-8}$\,km $\mathrm{s}^{-1}$ $\mathrm{Mpc}^{-1}$), showing its promise as an independent constraint on $H_0$.

Constraints on the Physical Properties of SNe Ia from Photometry

Abstract We present a photometric study of 17 SNe Ia based on multi-color (Johnson–Cousins–Bessell BVRI) data taken at Piszkéstető mountain station of Konkoly Observatory, Hungary between 2016 and 2018. We analyze the light curves (LCs) using the publicly available LC-fitter SNooPy2 to derive distance and reddening information. The bolometric LCs are fit with a radiation-diffusion Arnett model to get constraints on the physical parameters of the ejecta: the optical opacity, the ejected mass and the initial nickel mass in particular. We also study the pre-maximum, dereddened color evolution by comparing our data with standard delayed detonation and pulsational delayed detonation models, and show that the 56Ni masses of the models that fit the colors are consistent with those derived from the bolometric LC fitting. We find similar correlations between the ejecta parameters (e.g., ejecta mass, or 56Ni mass versus decline rate) as published recently by Scalzo et al. (2019).

Application of multiple scattering theory to Doppler velocimetry of ejecta from shock-loaded samples

We address the actual problem of retrieving the physical parameters of ejecta from data of heterodyne Doppler velocimetry. Under the assumption that ejected particles are randomly spaced and their number within the probed volume is great, the noise-free component of the power spectrum of heterodyne beats is shown to be expressed in terms of a solution to the transport equation for the field correlation function which accounts for multiple scattering and absorption of the probing beam in the ejecta cloud. This provides a means for theoretical modeling of experimental Doppler data. The ejecta cloud is considered as a plane layer of particles moving in the air away from the free-surface of the shock-loaded sample. The spatial profile of the scattering coefficient and the cloud thickness are related directly to the distribution of ejected particles over velocities and coordinates. The slowing-down of ejected particles in the air leads to an ambiguous relation between the velocity of particles and their position, resulting in essential complication of the particle distribution. Using a multi-group description of the ejecta cloud, we reduce the transport equation to a system of linked Milne-like equations. The system is solved numerically with the discrete ordinate code. Varying the values of the cloud optical thickness and the parameters of the particle distribution over sizes and initial velocities, we fit the calculated spectrum to the time-resolved data of heterodyne Doppler measurements. Such an approach enables retrieving the primary ejecta characteristics (the total ejected mass, the density-velocity profile and the size distribution of ejected particles) directly from heterodyne experiments. Application of the proposed method to the velocimetry data on ejecta is presented.