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Multiple Coulomb scattering and range straggling effects in shielding against solar flare protons and trapped protons in Van Allen belt
The study of the inversion algorithm for the single scatter lidar equation, for quantitative determination of cloud (or aerosol) optical properties, has received much attention over the last thirty years. Some of the difficulties associated with the solution of this equation are not yet solved. One problem is that a single scatter lidar equation has two unknowns. Because of this, the determination of the far-end boundary value, in the case of Klett's algorithm, is a problem if the atmosphere is optically inhomogeneous. Another difficulty concerns multiple scattering. There is a large error in the extinction distribution solution, in many cases, if only the single scattering component is considered, while neglecting the multiple scattering component. However, the use of multiple scattering in the remote sensing of aerosol or cloud optical properties is promising. In our early study, an inversion method for simultaneous determination of the cloud (or aerosol) Extinction Coefficient Distribution (ECD) and its Forward Scattering Phase Function (FSPF) was proposed according to multiply scattered lidar returns with two fields of view for the receiver. The method is based on a parameterized multiple scatter lidar equation. This paper is devoted to further numerical tests and an experimental study of lidar measurements of cloud ECD and FSPF using this method.
Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.
Remote identification and measurement of subsurface water turbidity and oil on water was accomplished with analytical models which describe the backscatter from smooth surface turbid water, including single scatter and multiple scatter effects. Lidar measurements from natural waterways are also presented and compared with ground observations of several physical water quality parameters.
Recent theoretical advances now enable accurate characterization of both the single scattering and multiple scattering contributions to the lidar backscatter signals obtained from opaque water clouds (Hu et al., 2006). As a consequence, lidar measurements of opaque water clouds have increasingly broad applications, especially for space-based polarization-sensitive lidars such as CALIOP. Among the most prominent and useful of these are (1) calibration and assessments of calibration accuracy (e.g., O'Connor et al., 2004; Hu et al., 2006); (2) accurate estimates of extrinsic (e.g., optical depths) and intrinsic (e.g., extinction-to-backscatter ratios) optical properties of clouds and aerosol layers lying above opaque water clouds (Hu et al., 2007; Liu et al., 2015); and (3) retrievals of water cloud microphysical properties such as cloud droplet number concentrations (Hu et al., 2007; Li et al., 2011; Zeng et al., 2014). In the first part of this presentation we give an overview of the recent advances in this subject area. The second part introduces several new studies of water clouds using the multi-wavelength depolarization measurement capabilities of NASA's airborne high spectral resolution lidars (HSRL). We use these measurements to assess existing theory, validate the measurement concept and explore several new application concepts. The third part discusses changes in Arctic water clouds using CALIOP measurements. The HSRL water cloud study is supported by NASA's atmospheric composition program.
One of NASA’s Decadal Survey mission, Surface Biology and Geology (SBG), will include a hyperspectral remote sensing imager, which has a very high spatial resolution and a wide spectral coverage (from UV to Near IR). Unprecedented large data volumes will be generated by the SBG hyperspectral instrument. Before the launch of the new satellite, an Observing System Simulation Experiment (OSSE) can be used to study different designs of the new satellite system. One of the key components in an OSSE study is a radiative transfer model (RTM) or forward model. In this presentation, we will describe a Principal Component-based Radiative Transfer Model (PCRTM) which is capable of simulating atmospheric (TOA) radiance or reflectance spectra from far IR to visible and UV spectral regions (50 wavenumber to 30000 wavenumber) quickly and accurately. Multiple scattering from multiple layers of clouds/aerosols are included in the model. The PCRTM has a very good accuracy relative to reference line-by-line radiative transfer models (LBLRTM), and it saves 3-4 orders of magnitude computational time relative to LBLRTM or MODTRAN. The PCRTM model has been successfully used to analyze large volumes of data from hyperspectral sensors such as AIRS, CrIS, and IASI. It has also been used to perform OSSE studies for the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission. Another useful tool for the OSSE is surface Bidirectional Reflectance Distribution Function (BRDF) database. It is very crucial for the SBG OSSE to include realistic BRDF spectra. Currently, most of the surface reflectance spectra such as those in the ECOSIS and ECOSTRESS are measured at specific observation geometries. We have developed a hyperspectral bidirectional reflectance (HSBR) model which combines Ross-Li BRDF model with the existing reflectance spectral libraries using a principal component analysis. This HSBR model can provide realistic BRDF spectra under various observation conditions. It can also be used to generate realistic BRDF spectra using measurements from multi-band imagers or spectrometers such as MODIS or VIIRS.
We revisit the calculation of the medium-induced gluon spectrum in a nite QCD medium and develop a new approach that goes beyond multiple soft scattering approximation. We show by expanding around the harmonic oscillator that the rst two orders encompass the two known analytic limits: single hard and multiple soft scattering regimes, valid at high and low frequencies, respectively. Finally, we investigate the sensitivity of our results to the infrared and observe that for large media the spectrum is weakly dependent on the infrared medium scale.
The study of single and multiple intrabeam scattering was carried out in the IOTA ring at Fermilab. The report discusses the results of the measurements and outlines still unresolved problems.
Many astronomical objects are surrounded by dusty environments. In such dusty objects, multiple scattering processes of photons by circumstellar (CS) dust grains can effectively alter extinction properties. In this paper, we systematically investigate the effects of multiple scattering on extinction laws for steady-emission sources surrounded by the dusty CS medium using a radiation transfer simulation based on the Monte Carlo technique. In particular, we focus on whether and how the extinction properties are affected by properties of CS dust grains by adopting various dust grain models. We confirm that behaviors of the (effective) extinction laws are highly dependent on the properties of CS grains, especially the total-to-selective extinction ratio R{sub V}, which characterizes the extinction law and can be either increased or decreased and compared with the case without multiple scattering. We find that the criterion for this behavior is given by a ratio of albedos in the B and V bands. We also find that either small silicate grains or polycyclic aromatic hydrocarbons are necessary for realizing a low value of R{sub V} as often measured toward SNe Ia if the multiple scattering by CS dust is responsible for their non-standard extinction laws. Using the derived relations between the properties of dust grains and the resulting effective extinction laws, we propose that the extinction laws toward dusty objects could be used to constrain the properties of dust grains in CS environments.
The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states. - Highlights: • A new description for electric polarization of hydrogen-like atoms. • Expression for multipole polarizabilities in terms of off-shell scattering functions. • Derivation of integral equation determining the off-shell scattering function. • Rigorous analytic solving the integral equations both for ground and excited states. • Study of contributions of virtual multiple scattering to electric polarizabilities.
Stimulated photon–photon scattering is a predicted consequence of quantum electrodynamics that has yet to be measured directly. Measuring the cross section for stimulated photon–photon scattering is the aim of a flagship experiment for NSF OPAL, a proposed laser user facility with two, 25-PW beamlines. We present optimized experimental designs for achieving this challenging and canonical measurement. A family of experimental geometries is identified that satisfies the momentum- and energy-matching conditions for two selected laser frequency options. Numerical models predict a maximum signal exceeding 1000 scattered photons per shot at the experimental conditions envisaged at NSF OPAL. Experimental requirements on collision geometry, polarization, cotiming and copointing, background suppression, and diagnostic technologies are investigated numerically. These results confirm that a beam cotiming shorter than the pulse duration and control of the copointing on a scale smaller than the shortest laser wavelength are needed to robustly scatter photons on a per-shot basis. Finally, we assess the bounds that a successful execution of this experiment may place on the mass scale of Born–Infeld nonlinear electrodynamics beyond the standard model of physics.
The spectrum of neutrons emitted promptly after {sup 239}Pu(n,f)—a so-called prompt fission neutron spectrum (PFNS)—is a quantity of high interest, for instance, for reactor physics and global security. However, there are only few experimental data sets available that are suitable for evaluations. In addition, some of those data sets differ by more than their 1-σ uncertainty boundaries. We present the results of MCNP studies indicating that these differences are partly caused by underestimated multiple scattering contributions, over-corrected background, and inconsistent deconvolution methods. A detailed uncertainty quantification for suitable experimental data was undertaken including these effects, and test-evaluations were performed with the improved uncertainty information. The test-evaluations illustrate that the inadequately estimated effects and detailed uncertainty quantification have an impact on the evaluated PFNS and associated uncertainties as well as the neutron multiplicity of selected critical assemblies. A summary of data and documentation needs to improve the quality of the experimental database is provided based on the results of simulations and test-evaluations. Given the possibly substantial distortion of the PFNS by multiple scattering and background effects, special care should be taken to reduce these effects in future measurements, e.g., by measuring the {sup 239}Pu PFNS as a ratio to either the {sup 235}U or {sup 252}Cf PFNS.
Simulation of the transport of high-energy charged particles is difficult because of the large number of interactions experienced by these particles before being brought to rest. Possible strategies to deal with this difficulty were analyzed by Berger. Most modern Monte Carlo codes use a mixture of complete-grouping (class I) and mixed (class II) schemes. In class I simulations, the global effect of all the interactions that occur along a trajectory segment of a given length s is described by means of precalculated distributions derived from multiple-scattering theories. In class II simulations, hard (or catastrophic) interactions (with energy loss W or polar scattering angle {theta} larger than given cutoff values) are sampled individually, while the effect of soft interactions (with energy losses and scattering angles smaller than the respective cutoffs) is described using a multiple-scattering approach. Although Berger effectively employed class II simulation only for energy-loss events, he did recognize the advantages of class II over class I also for multiple elastic scattering. On the one hand, because hard interactions are described exactly according to the adopted differential cross sections (DCSs), class II schemes are more accurate. On the other hand, multiple-scattering approximations, which are still required to describe the cumulative effect of soft interactions, are simpler and more accurate when individual interactions are limited to small energy transfers and angular deflections. For instance, for path lengths that are not too small, but still much less than the CSDA range, the energy-loss distribution due to multiple soft events is approximately Gaussian, by virtue of the central limit theorem. Similarly, the angular distribution caused by multiple small-angle deflections is also approximately Gaussian. However, class II schemes are more difficult to implement because of their dependence on specificities of the DCSs. In this article we briefly present the essentials of the class II algorithm for charged particles implemented in the last version of the penelope code, and provide evidence of its accuracy and stability with the simulation parameters. (authors)
Here, we discuss a technique for measuring a charged particle's momentum by means of multiple Coulomb scattering (MCS) in the MicroBooNE liquid argon time projection chamber (LArTPC). This method does not require the full particle ionization track to be contained inside of the detector volume as other track momentum reconstruction methods do (range-based momentum reconstruction and calorimetric momentum reconstruction). We motivate use of this technique, describe a tuning of the underlying phenomenological formula, quantify its performance on fully contained beam-neutrino-induced muon tracks both in simulation and in data, and quantify its performance on exiting muon tracks in simulation. Using simulation, we have shown that the standard Highland formula should be re-tuned specifically for scattering in liquid argon, which significantly improves the bias and resolution of the momentum measurement. With the tuned formula, we find agreement between data and simulation for contained tracks, with a small bias in the momentum reconstruction and with resolutions that vary as a function of track length, improving from about 10% for the shortest (one meter long) tracks to 5% for longer (several meter) tracks. For simulated exiting muons with at least one meter of track contained, we find a similarly small bias, and a resolution which is less than 15% for muons with momentum below 2 GeV/c. Above 2 GeV/c, results are given as a first estimate of the MCS momentum measurement capabilities of MicroBooNE for high momentum exiting tracks.
Background: Proton elastic scattering at intermediate energy is widely employed as a tool for determining the matter radius of atomic nuclei. Here, the sensitivity of the approach relies on high-resolution measurements at small scattering angles and low-momentum transfer. Under these conditions, the Glauber multiple scattering theory accurately describes the proton-nucleus elastic cross section. Purpose: Investigate the sensitivity of the Glauber multiple scattering theory to uncertainties associated with input parameters such as the nuclear-matter density distribution and nucleon-nucleon data. Method: A joint Bayesian inference was performed using 12 angular distributions of elastic scattering at different energies on 58 Ni, 90 Zr, and 208 Pb targets. A Metropolis-Hastings algorithm was implemented to make an uncertainty quantification analysis for the input parameters used in the Glauber multiple scattering theory. Results: The experimental cross sections were fitted simultaneously using a joint Bayesian inference approach. Posterior probability density distributions of 42 input parameters were obtained from the analysis. A moderate correlation between the nuclear density parameters and the nucleon-nucleon cross sections was found. This correlation impacts the extraction of the nuclear-matter radius. Conclusions: The present analysis provided a consistent method for extracting the nuclear-matter density distribution of 58 Ni, 90 Zr, and 208 Pb from data across different incident energies. Due to the correlation of the nucleon-nucleon cross sections with the other input parameters, a constrained Bayesian inference using free nucleon-nucleon cross section data was performed. The nuclear-matter radii obtained from the analysis are in good agreement with multiple results reported in the literature.
Geophysical media are usually heterogeneous and contain multiple species of scatterers.
By measuring the depolarization of light Raman scattered from a gas of known number density (nitrogen), it is possible to determine the influence of multiple scattering on lidar signals. In order to realize such measurements, linearly polarized laser light is emitted and two components of the nitrogen Raman signals, with E vectors parallel (parallel P sub lambda R) and perpendicular (perpendicular P sub lambda R) to the plane of polarization of the laser light, are measured. The depolarization ratio, delta sub lambda R = perpendicular P sub lambda R/parallel P sub lambda R, is constant if only the Raman scattering process contributes to the signal. Any variation of the depolarization is caused by additional elastic, and, thus, multiple scattering. If the contribution of multiple scattered light to the lidar signals is known, other parameters determined with the systems such as extinction, backscattering, and the depolarization of elastically scattered light, can be corrected for this influence. The lidar system used for the polarization measurements, especially the receiver setup, is described. The calibration of the apparatus and a clear air measurement are discussed.
In recent years there has been increasing interest in scattering and depolarization characteristics of the vegetation canopies. Scattering models applied to the microwave remote sensing of vegetation canopies showed that multiple scattering effects can be important in simulating the backscattering coefficients correctly. In particular, in most applications, the cross-polarized backscattering coefficients are often underestimated by single scattering models. Recently, there have been concerted efforts to include the second order terms in the radiative transfer models of vegetation canopies in order to account for multiple scattering within the canopy. The coherent wave theory approach is extended to include multiple scattering effects to predict the coherent and incoherent backscattering contributions from a layer of vegetation canopy. The problem is initially formulated in terms of the exact equation for the correlation function of the field, i.e., the Bethe-Salpeter equation. Using fractional volume as a small parameter, a Foldy type approximation is made to obtain a more manageable correlation equation. This equation is iterated to obtain first and second order solutions. The iteration procedure assumes the variance of the field fluctuations are small compared to the coherent intensity. This assumption proved to be particularly successful in computing backscattering coefficients. First and second order backscattering coefficients are calculated from the iterants of the correlation equation. It is shown that the first order coefficients are the same as the distorted Born results used previously by the authors. These results contained enhancement terms in the direct-reflected contributions. The important contributions to second order backscattering are examined and interpreted in terms of scattering diagrams. Examples of situations in which second order backscattering coefficients are important are given.