Photon Transport Equation Research Articles

Axion-photon mixing in 3D: classical equations and geometric optics

Light particle-photon mixing in magnetised plasmas plays a vital role in constraining the existence of new physics, especially axions, dark photons, and ultra-high-frequency gravitational waves. Recently, we derived an expression for the resonant conversion of axions to photons in inhomogeneous media using kinetic theory to derive photon transport equations. In this work, we show how the same expression for the conversion probability can be obtained from the classical wave equations of axion-electrodynamics by deriving an equivalent transport equation along the photon worldline. This result provides further corroboration of this expression for the resonant production of photons from light particles, which has also recently been supported by independent numerical simulations of full axion-electrodynamics. In addition, this new approach provides a more general expression that accounts for mixing away from resonance, which is integrated along the whole worldline of the photon in a way that naturally incorporates a curved photon trajectory relevant to refractive media where the photon and light-particle worldlines differ.

Kinetics Parameters Estimation for the Coupled Neutron-Photon Point Kinetics Model in Monte Carlo Eigenvalue Calculations

The delayed photoneutron effect should be considered in the point kinetics equation (PKE) applied to D2O and beryllium-moderated or -reflected systems because of its importance on reactor kinetics. This paper proposes neutron-photon-coupled PKE with a clear definition of adjoint-weighted kinetics parameters after providing the mathematical derivation from the neutron and photon transport and precursor equations. The Monte Carlo algorithms to estimate the kinetics parameters are induced from their definition and implemented in the eigenvalue calculation module of McCARD. They are verified through homogeneous infinite-medium problems with few-group neutron and photon cross sections by comparing with analytic solutions. The proposed PKE and kinetics parameters estimation methods are applied for the kinetics analyses of the artificial control rod drop transient problem in the RB reactor. Photonuclear physics is also implemented in a time-dependent Monte Carlo simulation to calculate the reference data of neutron amplitude in the core to be compared with the PKE results. As good agreement is shown in the neutron amplitude, it is validated that the developed PKE is capable of predicting the reactor kinetics considering photoneutrons.

ESTIMATION OF THE GAMMA-RAY FIELD IN AIR FROM RADIOACTIVE SOURCES IN THE GROUND BY NUMERICAL SOLUTION OF THE BOLTZMANN TRANSPORT EQUATION.

Gamma-ray field in air from radioactive sources uniformly distributed in the ground is calculated by numerically solving the photon transport equation. The scattered flux is developed on the Legendre polynomials basis of the spherical harmonics method and a double P1 approximation is applied. The method is implemented in the Octave programming package. The calculation of the gamma-ray field is also done by Monte Carlo simulation using an optimised geometry model of the soil-air medium that is implemented in Geant4 simulation code. The results obtained by the two methods are in good agreement. The computing time for the spherical harmonics deterministic method is significantly less than the Monte Carlo simulation. Dose rate conversion factors in the air are calculated for the natural radioactive series of 238U and 232Th and for 40K nuclide and for soils contaminated by various radionuclides. The results are in agreement with the published theoretical and experimental studies.

Major and Minor Contributions to X-ray Characteristic Lines in the Framework of the Boltzmann Transport Equation

The emission of characteristic lines after X-ray excitation is usually explained as the consequence of two independent and consecutive physical processes: the photoelectric ionization produced by incoming photons and the successive spontaneous atomic relaxation. However, the photoelectric effect is not the only ionization mechanism driven by incoming photons. It has been recently shown that Compton ionization is another possible process that contributes not negligibly to the ionization of the L and M shells. In addition, the secondary electrons from these two interactions, photoelectric and Compton, are also able to ionize the atom by means of so-called impact ionization. Such a contribution has been recently described, showing that it can be relevant in cases of monochromatic excitation for certain lines and elements. A third mechanism of line modification is the so-called self-enhancement produced by absorption of the tail of Lorentzian distribution of the characteristic line, which mainly modifies the shape of the lines but also produces an intensity increase. The four effects contribute to the formation of the characteristic line and must be considered to obtain a precise picture in terms of the shell and the element. This work furnishes a review of these contributions and their formal theoretical descriptions. It gives a complete picture of the photon kernel, describing the emission of characteristic X-rays comprising the main photoelectric contribution and the three effects of lower extent. All four contributions to the characteristic X-ray line must be followed along successive photon interactions to describe multiple scattering using the Boltzmann transport equation for photons.

Body size and tube voltage dependent corrections for Hounsfield Unit in medical X-ray computed tomography: theory and experiments

The purpose of this work is to present a body size and tube voltage dependent correction scheme for the Hounsfield Unit, HU, in medical X-ray Computed Tomography imaging. Boltzmann photon transport equation was employed to study X-ray interaction with bulk water in CT imaging. Experimentally measured X-ray output in body of phantoms and attenuation cross sections of water were employed in the derivation of beam intensity in X-ray imaging. A Somatom Emotion CT scanner from Siemens and electron density phantoms from CIRS were employed to acquire CT images of different body sizes and different tissue materials located at different depths from body’s surface. Tube voltage and depth dependent effective attenuation of bulk water was found from theoretical analysis in agreement with measured size-specific correction factors for CTDIvol under different tube voltages. A size and tube voltage dependent correction scheme for the Hounsfield Unit is established. For the same tissue material, body size has much larger impact on the CT number variations than that of depth from the body surface in phantom measurements. Good results were achieved by applying the established correction scheme on the experimentally measured CT number variations under different tube voltages and body sizes.

Numerical simulation of short laser pulse amplification

Within this work, the numerical solution of the photon transport equation for pulse amplification is presented. Several discretization schemes are introduced that enable the calculation of the coupling between the transport equation and population inversion. It is demonstrated that the presented discretization schemes are convergent with respect to the analytic Frantz–Nodvik solution. Specifically, the application of a prediction-correction approach based on Heun’s method leads to an improvement in accuracy compared to the pure explicit approach. Finally, novel discretization schemes are applied to simulate different regenerative amplifiers based on Ti:Sapphire and Ho:YAG. Moreover, bifurcation of the Ho:YAG system is analyzed, which results in the determination of stable operating regimes for pulsed amplification.

An inversion formula for the transport equation in ℝ3 using complex analysis in several variables

Abstract In this paper, the stationary photon transport equation has been extended by analytical continuation from ℝ 3 {\mathbb{R}^{3}} to ℂ 3 {\mathbb{C}^{3}} . A solution to the inverse problem posed by this equation is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transforms, respectively. We show that these results can be transformed into each other, and they agree with known results. Numerical reconstructions of a three-dimensional Shepp–Logan head phantom using the obtained inverse formula illustrate the analytical results obtained in this manuscript.

Performance prediction of p-i-n HgCdTe long-wavelength infrared HOT photodiodes.

Recently, an enhanced computer program was applied to explain in detail the influence of different recombination mechanisms (Auger, radiative, and Shockley-Read-Hall) on the performance of high-operation-temperature, long-wavelength, infrared p-i-n HgCdTe heterojunction photodiodes. It is shown that the photon recycling effect drastically limits the influence of radiative recombination on the performance of small pixel HgCdTe photodiodes. The computer program is based on a solution of the carrier transport equations, as well as the photon transport equations for semiconductor heterostructures. Both the distribution of thermal carrier generation and recombination rates, and spatial photon density distribution in photodiode structures have been obtained. In comparison with two previously published papers in the Journal of Electronics Materials [J. Electron. Mater.45, 4587 (2016)JECMA50361-523510.1007/s11664-016-4566-6 and J. Electron. Mater.46, 6295 (2017)JECMA50361-523510.1007/s11664-017-5736-x], our paper provides an additional insight on the ultimate performance of long-wavelength infrared, high-operation-temperature HgCdTe arrays with pixel densities that are fully consistent with background- and diffraction-limited performance due to system optics.

Dynamical and Radiative Properties of X-Ray Pulsar Accretion Columns: Phase-averaged Spectra

Abstract The availability of the unprecedented spectral resolution provided by modern X-ray observatories is opening up new areas for study involving the coupled formation of the continuum emission and the cyclotron absorption features in accretion-powered X-ray pulsar spectra. Previous research focusing on the dynamics and the associated formation of the observed spectra has largely been confined to the single-fluid model, in which the super-Eddington luminosity inside the column decelerates the flow to rest at the stellar surface, while the dynamical effect of gas pressure is ignored. In a companion paper, we have presented a detailed analysis of the hydrodynamic and thermodynamic structure of the accretion column obtained using a new self-consistent model that includes the effects of both gas and radiation pressures. In this paper, we explore the formation of the associated X-ray spectra using a rigorous photon transport equation that is consistent with the hydrodynamic and thermodynamic structure of the column. We use the new model to obtain phase-averaged spectra and partially occulted spectra for Her X-1, Cen X-3, and LMC X-4. We also use the new model to constrain the emission geometry, and compare the resulting parameters with those obtained using previously published models. Our model sheds new light on the structure of the column, the relationship between the ionized gas and the photons, the competition between diffusive and advective transport, and the magnitude of the energy-averaged cyclotron scattering cross-section.

High‐order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

SummaryThe nonlocal theory of the radiative energy transport in laser‐heated plasmas of arbitrary ratio of the characteristic inhomogeneity scale length to the photon mean free paths is applied to define the closure relations of a hydrodynamic system. The corresponding transport phenomena cannot be described accurately using the Chapman–Enskog approach, that is, with the usual fluid approach dealing only with local values and derivatives. Thus, we directly solve the photon transport equation allowing one to take into account the effect of long‐range photon transport. The proposed approach is based on the Bhatnagar–Gross–Krook collision operator using the photon mean free path as a unique parameter. Such an approach delivers a calculation efficiency and an inherent coupling of radiation to the fluid plasma parameters in an implicit way and directly incorporates nonequilibrium physics present under the condition of intense laser energy deposition due to inverse bremsstrahlung. In combination with a higher order discontinuous Galerkin scheme of the transport equation, the solution obeys both limiting cases, that is, the local diffusion asymptotic usually present in radiation hydrodynamics models and the collisionless transport asymptotic of free‐streaming photons. In other words, we can analyze the radiation transport closure for radiation hydrodynamics and how it behaves when deviating from the conditions of validity of Chapman–Enskog method, which is demonstrated in the case of exact steady transport and approximate multigroup diffusion numerical tests. As an application, we present simulation results of intense laser‐target interaction, where the radiative energy transport is controlled by the mean free path of photons. Copyright © 2016 John Wiley & Sons, Ltd.

An Evaluation of an Improper Integral Arises from an Analytic Solution of a Model Boltzmann Equation for Photon Transport

In this article we adopted the Mathematical model of solution of an improper integral which is created from the solution of the Boltzmann Transport equation (BTE) for photons. For the dose calculation of radiotherapy for cancer treatment, we need to solve the Boltzmann Transport equation. This improper integral is the important part of the BTE. Also the calculating time of the dose calculation is mostly dependent on the calculating time of this improper integral. For reducing the calculating time we need the minimum integrating area which is explained in this paper.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 87-94

Optimizing canopy photosynthetic rate through PAR modeling in cotton (Gossypium spp.) crops

A study of the distribution of photosynthetically active radiation (PAR) within cotton (Gossypium spp.) canopies of varying architecture is presented. Based on this study, a computer model is formulated to estimate PAR distribution and photosynthetic rates of cotton canopies. The model is developed from photon flux densities (PFD) measured at several stages of development in row-planted cotton canopies. The photon transport equation is implemented into the model along with an algorithm to calculate canopy photosynthetic rates. The resulting model is then used to generate different scenarios of plant architecture to identify the canopy architecture with optimal canopy photosynthetic rates.The results demonstrate that the differences in light distribution within the different cotton canopies were successfully captured. The model reproduces PAR distributions successfully for the cotton cultivars included in the study (R2>0.9 for most cultivars).Photosynthetic rate estimations showed that the structure of the DP-50 canopy is the most efficient canopy architecture by allowing PAR penetration throughout its canopy. This cultivar also uses the available sunlight more efficiently by enhancing PAR interception. The optimization process suggests that a cotton plant could increase its photosynthetic rate by 10% by distributing leaves within the canopy similarly to that of DP-50, and with leaves shaped like small-to-medium PS-6 leaves.

New insights into the numerical solution of the Boltzmann transport equation for photons

This paper has been thought to describe a numerical algorithm, basedon the expansion in orders of scattering, for solving the steadyBoltzmann transport equation for photons, and to show somesubsequent numerical results which have been obtained by developingan own Matlab® code. Thespatial domain is assumed to be a rectangular-shaped containerwith air and a water phantom inside, albeit the method can beextended to arbitrarily shaped convex domains filled with some otherheterogeneous material. High energy x-rays enter the domainthrough a small rectangle located on its upper face.

Generalized coupled photon transport equations for handling correlated photon streams with distinct frequencies

A generalized form of coupled photon transport equations that can handle correlated light beams with distinct frequencies is introduced. The derivation is based on the principle of energy conservation. For a single frequency, the current formulation reduces to a standard photon transport equation, and for fluorescence and phosphorescence, the diffusion models derived from the proposed photon transport model match for homogenous media. The generalized photon transport model is extended to handle wideband inputs in the frequency domain.

Anisotropic light propagation in paper

Abstract We investigate anisotropic light propagation in paper using both a theoretical model and experiments. The theoretical model utilizes the Monte Carlo method to solve the photon transport equation numerically. It is assumed that wood fibres are represented by infinitely long, homogeneous and straight cylinders. The layer-like microstructure and anisotropic orientation of the fibres is considered in the model. The conical scattering by cylindrical objects, the wood fibres, is argued as the main source of anisotropic scattering. Simulations revealed that laterally resolved transmittance exhibits directional dependence. Experiments on light transmitted through a standard kraft liner product confirmed that light in fact do propagate more in the machine direction than in the cross direction. Reasonably good agreement was obtained between experimentally and numerically obtained iso-intensity patterns.

Numerical Estimations of Carrier Generation–Recombination Processes and the Photon Recycling Effect in HgCdTe Heterostructure Photodiodes

An enhanced computer program has been applied to explain in detail the photon recycling effect which drastically limits the influence of radiative recombination on the performance of p-on-n HgCdTe heterostructure photodiodes. The computer program is based on a solution of the carrier transport equations, as well as the photon transport equations for semiconductor heterostructures. We distinguish photons in two energy ranges according to p+ and n region with unequal band gaps. As a result, both the distribution of thermal carrier generation and recombination rates and spatial photon density distribution in photodiode structures have been obtained. The general conclusion, similar to our earlier work concerning 3-μm n-on-p HgCdTe heterostructure photodiodes, confirms the previous assertion by Humphreys that radiative recombination does not limit HgCdTe photodiode performance.

Jacobian transformed and detailed balance approximations for photon induced scattering

Photon emission and scattering are enhanced by the number of photons in the final state, and the photon transport equation reflects this in scattering–emission kernels and source terms. This is often a complication in both theoretical and numerical analyzes, requiring approximations and assumptions about background and material temperatures, incident and exiting photon energies, local thermodynamic equilibrium, plus other related aspects of photon scattering and emission. We review earlier schemes parameterizing photon scattering–emission processes, and suggest two alternative schemes. One links the product of photon and electron distributions in the final state to the product in the initial state by Jacobian transformation of kinematical variables (energy and angle), and the other links integrands of scattering kernels in a detailed balance requirement for overall (integrated) induced effects. Compton and inverse Compton differential scattering cross sections are detailed in appropriate limits, numerical integrations are performed over the induced scattering kernel, and for tabulation induced scattering terms are incorporated into effective cross sections for comparisons and numerical estimates. Relativistic electron distributions are assumed for calculations. Both Wien and Planckian distributions are contrasted for impact on induced scattering as LTE limit points. We find that both transformed and balanced approximations suggest larger induced scattering effects at high photon energies and low electron temperatures, and smaller effects in the opposite limits, compared to previous analyzes, with 10–20% increases in effective cross sections. We also note that both approximations can be simply implemented within existing transport modules or opacity processors as an additional term in the effective scattering cross section. Applications and comparisons include effective cross sections, kernel approximations, and impacts on radiative transport solutions in 1D geometry. The additional computing time for processing opacities (cross sections) within these approximations is negligible as induced terms are merely added (multipliers) to cross sections at the end of the processing cycle.

Numerical estimations of carrier generation-recombination processes and photon recycling effect in 3-<inline-formula><tex-math>${\bm \mu}$</tex-math><math altimg="m1.gif" overflow="scroll"><mrow><mi mathvariant="bold-italic">μ</mi></mrow></math></inline-formula>m n-on-p HgCdTe photodiodes

An enhanced original computer program is applied to explain in detail the influence of the photon recycling effect on carrier lifetime in a selected 3-μm n-on-p HgCdTe photodiode structure. The computer program is based on solution of carrier and photon transport equations for practical photodiode design. As a result, both distribution of thermal carrier generation and recombination rates and spatial photon density distribution in photodiode structures have been obtained. It is clearly shown that the photon recycling effect drastically limits the influence of radiative recombination on performance of HgCdTe photodiodes. A general conclusion confirms previous Humpreys' ascertainment that the radiative recombination, although of fundamental nature, does not limit the ultimate performance of HgCdTe photodiodes.

Derivation of the Frantz-Nodvik Equation for Diode-Side-Pumped Zigzag Slab Laser Amplifiers With Gaussian Laser Mode and Pump Beam Shapes

The theory for Gaussian beam pulse propagation in a zigzag slab amplifier with a Gaussian pump distribution is detailed. Provisions are made for amplification of an input signal with an elliptical Gaussian spatial mode by modifying the time-dependent photon transport equations as described by Eggleston Frantz, and Injeyan. A comparison is made with experimental results of a diode-side-pumped zigzag slab amplifier element amplifying a near-Gaussian beam.

Eigen decomposition solution to the one-dimensional time-dependent photon transport equation

The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique based on eigen decomposition of the vectorized version of the photon transport equation. Using clever transformations, the four variable integro-differential equation is reduced to a set of first order ordinary differential equations using a combination of a spectral method and the discrete ordinates method. An eigen decomposition approach is then utilized to obtain the closed-form solution of this reduced set of ordinary differential equations.