Particle Transport Theory Research Articles

Momentum transfer theory of nonconservative charged particle transport in mixtures of gases: General equations and negative differential conductivity.

In this paper we develop general equations for the momentum transfer theory (MTT) for swarms of particles in mixtures of gases including the effect of nonconservative (reactive) collisions. MTT equations for mean energy, drift velocity, diffusion tensor components, and rate coefficients are derived for different degrees of approximation including the hydrodynamic limit and small swarm to gas particle mass ratio. Specific formulas were developed for the criteria for negative differential conductivity (NDC) in mixtures of gases with elastic collisions only and for a single gas with reactions. The criteria and the numerical calculations are in excellent agreement, showing that NDC can be induced by light atomic constituents in purely elastic collisions and also by ionization and attachment.

Remarks on stopping power: Its connections with particle transport and with the electronic structure of matter

This article presents remarks on the meaning of stopping power and of its magnitude. More precisely, the first set of remarks concerns the connection of stopping power with elements of particle-transport theory, which describes particle transport and its consequences in full detail, including its stochastic aspects. The second set of remarks concerns the magnitude of the stopping power of a material and its relation with the material's electronic structure and other properties. © 1996 John Wiley & Sons, Inc.

Transport of solar energetic particles

view Abstract Citations (36) References (46) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Transport of Solar Energetic Particles Droege, Wolfgang Abstract New developments in the understanding of the interplanetary transport of solar cosmic rays are reviewed. Based on carefully analyzed solar particle events observed on the Helios and International Sun Earth Explorer (ISEE) 3 spacecraft the relation of transport parameters to the structure of the interplanetary magnetic field is discussed. Special emphasis is given to a comparison of particle mean free paths determined from fits to intensity and anisotropy profiles with theoretical predictions derived from magnetic field spectra measured at the time of the solar particle event. Different aspects of the turbulence and wave models for the magnetic fluctuations are considered, including the effects resulting from the finite temperature of the plasma and of resonance broadening. It is found that a modified quasi-linear theory of particle scattering taking into account the effects of plasma waves propagating with respect to the average solar wind flow and the proper treatment of the dispersion relation at high wavenumber gives results which are in several cases in good agreement with particle observations in the interplanetary medium between 0.3 and 1 AU, indicating that quasi-linear theory is probably a good approximation to a full theory of solar particle transport. This has important implications for other astrophysical problems where quasi-linear theory is often used, such as the propagation and acceleration of Galactic cosmic rays and particle acceleration at shock waves. Publication: The Astrophysical Journal Supplement Series Pub Date: February 1994 DOI: 10.1086/191876 Bibcode: 1994ApJS...90..567D Keywords: Energetic Particles; Interplanetary Magnetic Fields; Interplanetary Medium; Particle Acceleration; Scatter Propagation; Solar Cosmic Rays; International Sun Earth Explorers; Transport Theory; Turbulence Models; Wave Propagation; Solar Physics; ACCELERATION OF PARTICLES; INTERPLANETARY MEDIUM; ISM: COSMIC RAYS; MAGNETOHYDRODYNAMICS: MHD; SUN: PARTICLE EMISSION; SUN: SOLAR WIND full text sources ADS |

On the dispersion function in particle transport theory

iz 1(3, #, ~0) + I(3, ~, e) =-~ -1 0 where c > 0 is the mean number of secondary particles per collision, p is the direction cosine of the propagating radiation and ~0 is the azimuthal angle. In addition O is the scattering angle, and we consider scattering laws that can be adequately represented by a finite Legendre expansion, i.e. L ;(cos O) = ~ (2l+ 1)fPl(cos O), 3~ = 1. (2) l=0 Using the addition theorem to write Eq. (2) as L l p(cos O) = ~ ~ (2 - 60,m) fit m P~ (/z) P~ (/.t') cos m(~0- ~0'),

On the Limitations of the Diffusion Equation

AbstractThis paper identifies the physical limitations inherent in the laws of Fickian diffusion by critically examining various derivations of the diffusion equation. Particle transport theory, statistical mechanics, and thermodynamic principles are utilized for this purpose. It is rigorously demonstrated that diffusion describes a quasi‐equilibrium and nearly isotropic process at regions away from external boundaries and sources or sinks of the transported quantity. It is also proven that the diffusion equation is not applicable to transport within a void, or when the vector flux changes rapidly with time.

Transport of Solar Energetic Particles

AbstractNew developments in the understanding of the interplanetary transport of solar cosmic rays are reviewed. Based on carefully analyzed solar particle events observed on the Helios and ISEE 3 spacecraft, the relation of transport parameters to the structure of the interplanetary magnetic field is discussed. Special emphasis is given to a comparison of particle mean free paths determined from fits to intensity and anisotropy profiles with theoretical predictions derived from magnetic field spectra measured at the time of the solar particle event. Different aspects of the turbulence and wave models for the magnetic fluctuations are considered, including the effects resulting from the finite temperature of the plasma and of resonance broadening. It is found that a modified quasi-linear theory of particle scattering taking into account the effects of plasma waves propagating with respect to the average solar wind flow and the proper treatment of the dispersion relation at high wavenumber gives results which are in several cases in good agreement with particle observations in the interplanetary medium between 0.3 and 1 AU, indicating that quasi-linear theory is probably a good approximation to a full theory of solar particle transport. This has important implications for other astrophysical problems where quasi-linear theory is often used, such as the propagation and acceleration of Galactic cosmic rays and particle acceleration at shock waves.Subject headings: acceleration of particles — cosmic rays — interplanetary medium — MHD — solar wind — Sun: particle emission

Two novel applications of bootstrap currents: Snakes and jitter stabilization

Both neoclassical theory and certain turbulence theories of particle transport in tokamaks predict the existence of bootstrap (i.e., pressure-driven) currents. Two new applications of this form of noninductive current are considered in this work. In the first, an earlier model of the nonlinearly saturated m=1 tearing mode is extended to include the stabilizing effect of a bootstrap current inside the island. This is used to explain several observed features of the so-called ‘‘snake’’ reported in the Joint European Torus (JET) [R. D. Gill, A. W. Edwards, D. Pasini, and A. Weller, Nucl. Fusion 32, 723 (1992)]. The second application involves an alternating current (ac) form of bootstrap current, produced by pressure-gradient fluctuations. It is suggested that a time-dependent (in the plasma frame), radio-frequency (rf) power source can be used to produce localized pressure fluctuations of suitable frequency and amplitude to implement the dynamic stabilization method for suppressing gross modes in tokamaks suggested in a recent paper [A. Thyagaraja, R. D. Hazeltine, and A. Y. Aydemir, Phys. Fluids B 4, 2733 (1992)]. This method works by ‘‘detuning’’ the resonant layer by rapid current/shear fluctuations. Estimates made for the power source requirements both for small machines such as COMPASS and for larger machines like JET suggest that the method could be practically feasible. This ‘‘jitter’’ (i.e., dynamic) stabilization method could provide a useful form of active instability control to avoid both gross/disruptive and fine-scale/transportive instabilities, which may set severe operating/safety constraints in the reactor regime. The results are also capable, in principle, of throwing considerable light on the local properties of current generation and diffusion in tokamaks, which may be enhanced by turbulence, as has been suggested recently by several researchers.

Parameter‐dependent operator equations of the Riccati type with application to transport theory

AbstractWe obtain an existence result for global solutions to initial‐value problems for Riccati equations of the form R′(t) + TR(t) + R(t)T = Tρ A(t)T1−ρ + Tρ B(t)T1−ρ R(t) + R(t)TρC(t) T1−ρ + R(t)TρD(t)T1−ρ R(t), R(0)=R0, where 0 ⩽ ρ ⩽ 1 and where the functions R and A through D take on values in the cone of non‐negative bounded linear operators on L1 (0, W; μ). T is an unbounded multiplication operator. This problem is of particular interest in case ρ = 1 since it arisess in the theories of particle transport and radiative transfer in a slab. However, in this case there are some serious difficulties associated with this equation, which lead us to define a solution for the case ρ = 1 as the limit of solutions for the cases 0 < ρ < 1.

Turbulence, particle transport and flow-driven currents in tokamaks

Six different theories of particle transport and flow-driven currents are discussed. These include the classical, neoclassical and four phenomenological models based on turbulence. The theoretical results are compared and contrasted. In particular, two different, turbulence-based, equivalent versions of the toroidal Ohm's law are obtained. The possibility of experimentally distinguishing between the phenomenological models is discussed. In two of the phenomenological models the anomalous particle transport is necessarily related to anomalous flow-driven currents (i.e. enhanced above the neoclassical bootstrap current), and to anomalous inward pinches.

An overview of the transport theory of charged particles

An unified description of the transport theory for charged particles including electrons, ions and atoms has been formulated and is presented. The main content of the paper includes: the Boltzmann equation and its different approximations, the theory of electron slowing down spectra, multiple scattering theory, the theory of deep penetration and the theory of secondary particle emission. The scaling properties of the transport of charged particles are also presented. Although some discussion of stochastic (Monte Carlo) methods is included, the main focus of this review is on analytical approaches. Finally, some important unsolved problems in the transport theory for charged particles are discussed.

Rates of particle deposition from aqueous suspensions in turbulent flow: a comparison of theory with experiment

Particle transport velocities have been determined from published data for aqueous suspensions and dimensionless particle relaxation times ( t + p ) ranging from 10 −4 to 5. These were compared to predictions from several theories of particle transport. There is reasonably good agreement between measured and predicted transport velocities for diffusion-limited particle transport ( t + p → 0.001). The particle transport rate is dominated by the contribution from inertial forces for t + p ⩾ 0.02, in contrast to aerosol systems, where diffusion dominates up to t + p = 0.20. The theories of Beal and Davies are in much better agreement with the experimental data in the inertial regime than is the theory of Cleaver and Yates. For t + p ⩾ 0.2, the particle transport rate is no longer dominated by inertia but appears to be controlled by a diffusion process. None of the theories examined account for the magnitude of the particle transport rate in this regime.

On the density dependence of the self-diffusion coefficient of interacting Brownian particles

A brief summary is given of our theoretical approach to the statistical description of interacting Brownian particles. For the discussion of particle transport processes on the Smoluchowski level a hierarchy of coupled diffusion-like equations in configuration space for the reduced particle density functions and the corresponding particle flows is derived. Non-equilibrium processes are taken into account by means of linear perturbation theory. Applying the direct correlation force formalism, the hierarchy is cut off by replacing the three-particle density function nabc ( r 1, r 2, r 3, t). Here closure relations between the direct correlation force and nab ( r 1, r 2, t) have to be added. Specializing the brownons to hard spheres and neglecting the hydrodynamic interaction, the two-particle density function is evaluated from the well-known equilibrium PY approximation and (as a first step) from the low-density limit of the non-equilibrium closure. Using a linear response theory of particle transport, the self-diffusion coefficient in a one-component hard sphere system of Brownian particles is calculated through a formal non-equilibrium picture based on tracer diffusion.

Towards a quantum pump of electric charges.

Here we give a critical examination of the possibility of realizing a quantum pump of electric charges. The physics is based on the theory of quantum adiabatic particle transport initially due to Thouless. We present theoretical guidelines on the experimental conditions for observing this phenomenon. We argue that potentially very accurate quantization of charge transport or electron current can be achieved, once these conditions are approximately satisfied. An example of experimental setup is outlined to demonstrate the practical possibilities. Some comments are also made on the scientific significance of such a quantum device.

L1 -stability of the solutions to an integral evolution equation of the non-linear particle transport theory

The problem ofL1-stability of the solutions to a non linear integral equation arising in particles transport theory is studied. This equation can represent the standard spatially homogeneous Boltzmann equation in the case of Maxwellium particles with “cut off”.

Space-dependent forces and current density transients in particle transport theory

Transients of current density, that are induced by spatial discontinuities of both electric and magnetic field as applied to a mixture of two different species of particles, are investigated via an application of the linear integral transport equation.

Spatial effects in the study of nonlinear evolution problems of particle transport theory

Explicit analytical solutions to a nonlinear spatially inhomogeneous model Boltzmann equation are presented for a physical situation of reference, characterized by constant collision frequencies and scattering probability distributions depending only on the velocity after collision. The results obtained are approximately commented on physical grounds.

Lateral migration mechanisms in capillary hydrodynamic chromatography

In all chromatographic systems that achieve separation of colloidal particles based on the particles' hydrodynamic behavior, there are partitioning mechanisms that promote lateral migration of particles across solvent streamlines. In this work, solvent inertia and particle electrostatics are incorporated in Brenner & Gaydos' general diffusive transport theory for particles and solvent flowing in a capillary, yielding the mean axial velocity of particles as a function of particle size. A comparison is made with capillary hydrodynamic chromatography results. The lateral migration of small particles is primarily due to diffusion, while large particles are focused by the inertial force at one equilibrium radial position, as observed in “tubular pinch” experiments. The transition from diffusion- to inertia-controlled lateral migration can be tuned to specific particle size ranges through variation of solvent ionic strength, flowrate and capillary radius. Poor prediction of the separation behavior of large particles is attributed to inaccuracy in the calculation of the inertial radial velocity, suggesting the need for further theoretical analysis and experimental study of inertial migration.

Numerical solution of singular integral equations of neutron transport problems

Abstract A new numerical method is developed for solving singular integral equations of particle transport theory. The singular integral equations are of index -1 and their solution exists if and only if their source terms satisfy certain orthogonality condition. The method exploits this condition for existence in a practical way.

On the stability of the solutions to an integral evolution equation of the non linear particle transport theory

On the stability of the solutions to an integral evolution equation of the non linear particle transport theory

Recent trends in particle transport theory

A review of some recent trends and methods in describing neutron and photon transport in a host medium via the stationary linear integrodifferential Boltzmann equation is presented. Specific applications and numerical results are also illustrated for some benchmark problems of recent formulation.