Particle Transport Theory Research Articles

On the Relevance of Magnetic Correlation Functions in Energetic Particle Transport Theory

On the Relevance of Magnetic Correlation Functions in Energetic Particle Transport Theory

A weight Monte Carlo estimation of fluctuations in branching processes

Abstract It is well known that shortened modeling of particle trajectories with the use multiplicative statistical weights, as a rule, increases the efficiency of the program (in terms of accuracy/time ratio). This trick is often used in non-branching schemes simulating transfer processes without multiplication (for example, the transfer of X-ray radiation), in which it is sufficient to confine ourselves to studying only the average values of the field characteristics. With an increase in energy, however, multiplication processes begin to play a significant role (the production of electron-photon pairs by gamma quanta with energies above 1.022 MeV, etc.), when the resulting trajectory is not just a broken curve in the phase space, but a branched tree. This technique is also applicable to this process, but only if the study of statistical fluctuations and correlations is not the purpose of the calculation. The present review contains the basic concepts of the Monte Carlo method as applied to the theory of particle transport, demonstration of the weighting method in non-branching processes, and ends with a discussion of unbiased estimates of the second moment and covariance of additive functionals.

Response Matrix/Discrete Ordinates Solution of the 1D Fokker-Planck Equation

The Fokker-Planck equation (FPE) is one of the quintessential equations of particle transport theory. Representing small angle scattering characteristics of electron and photon transport by differential scattering indeed is a mathematical/numerical challenge. Here, we address the challenge with the method of response matrix applied to the Sn approximation to arrive at a nearly six-place-precision benchmark. Our approach aligns with the response matrix solution of the radiative transfer equation for anisotropic scattering published previously. We conclude with the comparison of the response matrix benchmark to a classical finite difference approximation.

Revisiting Airflow and Aerosol Transport Phenomena in the Deep Lungs with Microfluidics.

The dynamics of respiratory airflows and the associated transport mechanisms of inhaled aerosols characteristic of the deep regions of the lungs are of broad interest in assessing both respiratory health risks and inhalation therapy outcomes. In the present review, we present a comprehensive discussion of our current understanding of airflow and aerosol transport phenomena that take place within the unique and complex anatomical environment of the deep lungs, characterized by submillimeter 3D alveolated airspaces and nominally slow resident airflows, known as low-Reynolds-number flows. We exemplify the advances brought forward by experimental efforts, in conjunction with numerical simulations, to revisit past mechanistic theories of respiratory airflow and particle transport in the distal acinar regions. Most significantly, we highlight how microfluidic-based platforms spanning the past decade have accelerated opportunities to deliver anatomically inspired in vitro solutions that capture with sufficient realism and accuracy the leading mechanisms governing both respiratory airflow and aerosol transport at true scale. Despite ongoing challenges and limitations with microfabrication techniques, the efforts witnessed in recent years have provided previously unattainable in vitro quantifications on the local transport properties in the deep pulmonary acinar airways. These may ultimately provide new opportunities to explore improved strategies of inhaled drug delivery to the deep acinar regions by investigating further the mechanistic interactions between airborne particulate carriers and respiratory airflows at the pulmonary microscales.

Drift kinetic theory of alpha transport by tokamak perturbations

Upcoming tokamak experiments fuelled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alpha particles with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power and damage to device walls. Alpha interaction with these perturbations is often studied with single-particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.

Producing a Beam Model of the Varian ProBeam Proton Therapy System using TOPAS Monte Carlo Toolkit.

A Geant4-based TOPAS Monte Carlo toolkit was utilized to model a Varian ProBeam proton therapy system, with the aim of providing an independent computational platform for validating advanced dosimetric methods. The model was tested for accuracy of dose and linear energy transfer (LET) prediction relative to the commissioning data, which included integral depth dose (IDD) in water and spot profiles in air measured at varying depths (for energies of 70 to 240MeV in increments of 10MeV, and 242MeV), and absolute dose calibration. Emittance was defined based on depth-dependent spot profiles and Courant-Snyder's particle transport theory, which provided spot size and angular divergence along the inline and crossline plane. Energy spectra were defined as Gaussian distributions that best matched the range and maximum dose of the IDD. The validity of the model was assessed based on measurements of range, dose to peak difference, mean point to point difference, spot sizes at different depths, and spread-out Bragg peak (SOBP) IDD and was compared to the current treatment planning software (TPS). Simulated and commissioned spot sizes agreed within 2.5%. The single spot IDD range, maximum dose, and mean point to point difference of each commissioned energy agreed with the simulated profiles generally within 0.07mm, 0.4%, and 0.6%, respectively. A simulated SOBP plan agreed with the measured dose within 2% for the plateau region. The protons/MU and absolute dose agreed with the current TPS to within 1.6% and exhibited the greatest discrepancy at higher energies. The TOPAS model agreed well with the commissioning data and included inline and crossline asymmetry of the beam profiles. The discrepancy between the measured and TOPAS-simulated SOBP plan may be due to beam modeling simplifications of the current TPS and the nuclear halo effect. The model can compute LET, and motivates future studies in understanding equivalent dose prediction in treatment planning, and investigating scintillation quenching.

Partial Range Completeness of Case Eigenfunctions and Numerical Solution of Singular Integral Equations of Particle Transport Problems

We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.

Bosonic superfluid transport in a quantum point contact

We present a microscopic theory of heat and particle transport of an interacting, low temperature Bose-Einstein condensate in a quantum point contact. We show that, in contrast to charged, fermionic superconductors, bosonic systems feature tunneling processes of condensate elements, leading to the presence of odd-order harmonics in the AC Josephson current. A crucial role is played by an anomalous tunneling process where condensate elements are coherently converted into phonon excitations, leading to even-order harmonics in the AC currents as well as a DC contribution. At low bias, we find dissipative components obeying Ohm's law, and bias-independent nondissipative components, in sharp contrast to fermionic superconductors. Analyzing the DC contribution, we find zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. These results highlight importance of the anomalous tunneling process inherent to charge neutral superfluids. The consequences could readily be observed in existing cold-atom transport setups.

ACR Proton Acceleration Associated with Reconnection Processes beyond the Heliospheric Termination Shock

Abstract One of the curious observations from the Voyagers is that the intensity of anomalous cosmic rays (ACRs) did not peak at the heliospheric termination shock (HTS) but instead a short distance (within ∼1 au) downstream of the HTS. One possible explanation is that the interaction of the wavy heliospheric current sheet with the HTS enhances magnetic reconnection and generates numerous small-scale magnetic flux ropes in the heliosheath immediately downstream of the HTS. Charged particles are accelerated in this region due to Fermi acceleration and the reconnection electric field. In this work, we provide observational evidence of the presence of magnetic flux ropes in the heliosheath region just downstream of the HTS using a wavelet analysis of the reduced magnetic helicity and Grad–Shafranov reconstruction techniques. The Zank et al. kinetic transport theory for particles propagating through the magnetic islands region is employed to fit the observed energetic proton intensities in the post-HTS region. Our modeling results agree reasonably well with the observations, which suggests that stochastic acceleration via reconnection processes can explain the ACR proton peak beyond the HTS.

Application of the Photometric Theory of the Radiance Field in the Problems of Electron Scattering

The physical model of the radiance field is similar in some aspects to the elementary particle transport theory under the assumptions of the classical mechanics. Disregarding the differences in the used nomenclatures, it can be shown that the transport equations for the radiance field are identical to those for the particle flux density. Since the end of the 19th century, both theories have been developing in parallel, thereby enriching each other. In other words, a breakthrough, which has been made in one theory, readily contributes to the significant progress in another one. Nowadays the accuracy achieved in the experiments with particles is close to the limit, which allows validating the relationships derived within the light scattering theory. Besides, the experiments with particles are free from uncertainties in the scattering medium, which are typical for atmospheric remote sensing applications. In this paper, a new algorithm is described, which is derived by analogies between these theories. It is applied for calculating the electron flux elastically scattered by plane-parallel layers of a solid with the strongly forward peaked phase functions. The calculations are compared against the experimental angular distributions of electrons, which are elastically reflected by the two-layer solid samples.

Field line random walk, field line separation, and particle transport in turbulence with weak transverse complexity

We study the random walk of magnetic field lines as well as field line separation in a magnetized plasma such as the solar wind or the interstellar medium. By doing so we focus on turbulence with small Kubo numbers. For field line random walk this allows us to employ an approach based on a Taylor expansion which is essentially an expansion in the Kubo number. Compared to previous non-linear descriptions, no assumption concerning the field line distribution or diffusivity has to be made. Based on this approach, we compute corrections to the quasi-linear formula allowing us also to test assumptions usually made in non-linear theories of field line random walk. We show that up to the considered order, the assumption of Gaussian statistics does not alter the diffusion coefficient whereas the diffusion approximation provides a correction term which is a factor two too large. We also discuss the separation of two magnetic field lines. We develop a quasi-linear theory for field line separation and introduce a fundamental scale of turbulence describing its transverse structure. Furthermore, we discuss applications of our results in the theory of energetic particle transport. Besides quasi-linear diffusion we also discuss compound sub-diffusion as well as the recovery of diffusion due to transverse complexity. Furthermore, we derive a formula for the perpendicular diffusion coefficient of energetic particles similar compared to the famous Rechester & Rosenbluth result. Applications in astrophysics are also discussed.

Where do the ultra-high energy cosmic rays come from?

Cosmic rays are the only sample of matter coming from outer space. They carry rich information about particle physics, high-energy astrophysics, composition and evolution of the Universe. The highest energy of cosmic rays detected so far is about 3×10 20 eV. How are the cosmic rays accelerated?What kind of astronomic sources do the cosmic rays originate from?Are the fundamental physics laws still valid in such high-energy scales? are all important scientific problems waiting to be addressed. To answer these questions, various space and ground experiments have been carried out to explore the nature of cosmic rays in a multi-messenger approach. The past few decades have witnessed great achievements in high-energy cosmic ray, gamma ray, neutrino observations, and detection of gravitational wave. (1) The cosmic ray spectra, composition, and anisotropy have been measured with unprecedented precision leading to better understanding of cosmic ray acceleration and transport and stricter constraints on properties of potential candidates of dark matter particles, and the dipole anisotropy of ultrahigh energy cosmic rays indicates that they have an extragalactic origin. (2) Space borne experiments have discovered more than 3000 sources in the GeV range, and the ground based experiments have uncovered more than 200 sources at TeV energies. Most of these sources are high-energy electron accelerators, and a few of them are identified as the accelerators of cosmic ray nuclei. Diffuse gamma-ray emission associated with galactic disks and jets and/or outbursts of Active Galactic Nuclei is also measured with better spatial and energy resolutions, which can be used to study cosmic ray transport in the interstellar/galactic/cluster medium. (3) With the IceCube experiment, about 100 high-energy neutrino events have been recorded and their isotropic distribution suggests an extragalactic origin. (4) The first gravitational wave event with simultaneous multi-wavelength observations has been detected opening the epoch of gravitational wave astronomy. Strong gravitational wave events represent the most catastrophic energy release in the Universe and can be important cosmic ray sources. These new results established the foundation to address the origin of cosmic rays and to develop theories of particle acceleration and transport. The study of cosmic ray transport has gone beyond the diffusion approximation to study the effect of magnetic field fluctuations on small scale anisotropy of cosmic rays and comprehensive numerical modelings of cosmic ray transport in the Galaxy are advanced with multi-wavelength observations. Diffusive particle acceleration by strong shocks of supernova remnants (SNRs) is also advanced based on multi-wavelength observations and cosmic ray measurements. The scenario of SNR origin of Galactic cosmic rays is being quantified with testable predictions. Although there are still uncertainties in amplification of magnetic field by cosmic rays and cosmic ray scattering by turbulent plasmas, sophisticated numerical codes are being developed to address these issues. Successful construction and operation of new generation cosmic ray and gamma-ray experiments will open a new chapter of the astro-particle physics study.

The influence of non-Gaussian distribution functions on the time-dependent perpendicular transport of energetic particles

In the current paper we explore the influence of the assumed particle statistics on the transport of energetic particles across a mean magnetic field. In previous work the assumption of a Gaussian distribution function was standard, although there have been known cases for which the transport is non-Gaussian. In the present work we combine a kappa distribution with the ordinary differential equation provided by the so-called unified non-linear transport theory. We then compute running perpendicular diffusion coefficients for different values of κ and turbulence configurations. We show that changing the parameter κ slightly increases or decreases the perpendicular diffusion coefficient depending on the considered turbulence configuration. Since these changes are small, we conclude that the assumed statistics is less significant in particle transport theory. The results obtained in the current paper support to use a Gaussian distribution function as usually done in particle transport theory.

The Roles of Fluid Compression and Shear in Electron Energization during Magnetic Reconnection

Abstract Particle acceleration in space and astrophysical reconnection sites is an important unsolved problem in studies of magnetic reconnection. Earlier kinetic simulations have identified several acceleration mechanisms that are associated with particle drift motions. Here, we show that, for sufficiently large systems, the energization processes due to particle drift motions can be described as fluid compression and shear, and that the shear energization is proportional to the pressure anisotropy of energetic particles. By analyzing results from fully kinetic simulations, we show that the compression energization dominates the acceleration of high-energy particles in reconnection with a weak guide field, and the compression and shear effects are comparable when the guide field is 50% of the reconnecting component. Spatial distributions of those energization effects reveal that reconnection exhausts, contracting islands, and island-merging regions are the three most important regions for compression and shear acceleration. This study connects particle energization by particle guiding-center drift motions with that due to background fluid motions, as in the energetic particle transport theory. It provides foundations for building particle transport models for large-scale reconnection acceleration such as those in solar flares.

Numerical assessment of particle dispersion and exposure risk in an underground parking lot

The transient air flow, particle dispersion, and particle exposure risk during and after transient vehicle exhaust in an underground parking lot was investigated in the present study. The Realizable k-ε model together with particle transport theory was employed and a parking space with two cars idling and emitting exhaust and four cars at rest was established. A three-dimensional model was validated by comparing the simulated results with measured data in a residential underground parking lot of Harbin, China. Particle exposure risk during and after transient vehicle exhaust was also evaluated using the index of intake fraction. The simulation results showed that the stream of vehicle exhaust and particles dispersed from the space between two opposite cars in the upward direction during the first 30s after vehicle exhaust was emitted. A remarkable downward dispersion of particles from the roof to the ground was observed after the vehicle stopped emitting exhaust. Intake fraction of particles increased linearly with time since exhaust and grew to approximately 1.4×10−3 for adult and 1.2×10−3 for child at 300s after the vehicle exhaust stopped, respectively.

Transport theory for energetic alpha particles in finite aspect ratio tokamaks with broken symmetry

Transport theory for the energetic alpha particles in finite aspect ratio tokamaks with broken symmetry is developed for the case where the slowing down collision operator dominates. The transport fluxes in the 1/ν and superbanana plateau regimes are derived. Here, ν is the typical collision frequency. They can be used in modeling the energy loss of the alpha particles in thermonuclear fusion reactors. Numerical realizations of the superbanana orbits of alpha particles in tokamaks with broken symmetry are also presented. The existence of the superbananas corroborates the predictions of the theories presented here and elsewhere.

DIFFUSIVE SHOCK ACCELERATION AND RECONNECTION ACCELERATION PROCESSES

Shock waves, as shown by simulations and observations, can generate high levels of downstream vortical turbulence, including magnetic islands. We consider a combination of diffusive shock acceleration (DSA) and downstream magnetic-island-reconnection-related processes as an energization mechanism for charged particles. Observations of electron and ion distributions downstream of interplanetary shocks and the heliospheric termination shock (HTS) are frequently inconsistent with the predictions of classical DSA. We utilize a recently developed transport theory for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets. Particle energization associated with the anti-reconnection electric field, a consequence of magnetic island merging, and magnetic island contraction, are considered. For the former only, we find that (i) the spectrum is a hard power law in particle speed, and (ii) the downstream solution is constant. For downstream plasmoid contraction only, (i) the accelerated spectrum is a hard power law in particle speed; (ii) the particle intensity for a given energy peaks downstream of the shock, and the distance to the peak location increases with increasing particle energy, and (iii) the particle intensity amplification for a particular particle energy, f(x,c/c_0)/f(0,c/c_0), is not 1, as predicted by DSA, but increases with increasing particle energy. The general solution combines both the reconnection-induced electric field and plasmoid contraction. The observed energetic particle intensity profile observed by Voyager 2 downstream of the HTS appears to support a particle acceleration mechanism that combines both DSA and magnetic-island-reconnection-related processes.

The dynamic adjoint as a Green’s function

The concept of the dynamic adjoint was introduced by Hugo van Dam for calculating the in-core neutron noise in boiling water reactors in the mid-70’s. This successful approach found numerous applications for calculating the neutron noise in both PWRs and BWRs since then. Although the advantages and disadvantages of using the direct (forward) or the adjoint (backward) approach for the calculation of the neutron noise were analysed in a number of publications, the direct relationship between the forward Green’s function and the dynamic adjoint has not been discussed. On the other hand, in particle transport theory the relationship between the direct and adjoint Green’s function has been discussed in detail, in which Mike Williams has had many seminal contributions. In this note we analyse the relationship between the direct Green’s function and the dynamic adjoint in the spirit of Mike’s work in neutron transport and radiation damage theory. The paper is closed with some personal remarks and reminiscences.

Aggregate particles in the plumes of Enceladus

Estimates of the total particulate mass of the plumes of Enceladus are important to constrain theories of particle formation and transport at the surface and interior of the satellite. We revisit the calculations of Ingersoll and Ewald (Ingersoll, A.P., Ewald, S.P. [2011]. Icarus 216(2), 492–506), who estimated the particulate mass of the Enceladus plumes from strongly forward scattered light in Cassini ISS images. We model the plume as a combination of spherical particles and irregular aggregates resulting from the coagulation of spherical monomers, the latter of which allows for plumes of lower particulate mass. Though a continuum of solutions are permitted by the model, the best fits to the ISS data consist either of low mass plumes composed entirely of small aggregates or high mass plumes composed of mostly spheres. The high particulate mass plumes have total particulate masses of (166±42)×103kg, consistent with the results of Ingersoll and Ewald (Ingersoll, A.P., Ewald, S.P. [2011]. Icarus 216(2), 492–506). The low particulate mass plumes have masses of (25±4)×103kg, leading to a solid to vapor mass ratio of 0.07±0.01 for the plume. If indeed the plumes are made of such aggregates, then a vapor-based origin for the plume particles cannot be ruled out. Finally, we show that the residence time of the monomers inside the plume vents is sufficiently long for Brownian coagulation to form the aggregates before they are ejected to space.

Comprehensive understanding of nano-sized particle separation processes using nanoparticle tracking analysis.

The understanding of nano-sized particle separation processes has been limited by difficulties of nanoparticle characterization. In this study, nanoparticle tracking analysis (NTA) was deployed to evaluate the absolute particle size distributions in laboratory scale flocculation and filtration experiments with silver nanoparticles. The results from NTA were consistent with standard theories of particle destabilization and transport. Direct observations of changes in absolute particle size distributions from NTA enhance both qualitative and quantitative understanding of particle separation processes of nano-sized particles.