Parallel Diffusion Coefficient Research Articles

A Study of the Coefficient a2 in the Extended Nonlinear Guiding Center Theory

The diffusion mechanism of charged particles is one of the very im- portant problems in astrophysics. Recently, Matthaeus et al. (2003) developed a nonlinear guiding center theory (NLGC) of the perpendicular diffusion of en- ergetic charged particles with the parallel diffusion coefficient as an input. This theory agrees with the results of numerical simulations very well. In addition, Qin (2007) developed a nonlinear parallel diffusion theory (NLPA) following the idea of NLGC. Combining the NLGC with the NLPA, a new theory, NLGC-E was developed to solve the parallel and perpendicular diffusion coefficients simultaneously. In the NLGC theory, there is a coefficient a2 which is selected to be 1/3 for the best agreement with the results of numerical simulations. In this work we tried the different values of a2 for the NLGC-E theory to determine the optimal value which fits best the results of numerical simulations.

ON THE DIFFERENT ANALYTICAL RESULTS OBTAINED FOR THE PARALLEL DIFFUSION COEFFICIENT OF COSMIC PARTICLES WITH ADIABATIC FOCUSING

A spatially varying mean magnetic field gives rise to so-called adiabatic focusing of energetic particles propagating through the universe. In the past, different analytical approaches have been proposed to calculate the particle diffusion coefficient along the mean field with focusing. In the present paper, we show how these different results are related to each other. New results for the parallel diffusion coefficient that are more general than previous results are also presented.

Coarse Grained Molecular Dynamics Simulation of Nanoconfined Water

A coarse-grained (CG) model for the simulation of nanoconfined water between graphene surfaces is developed. For this purpose, mixed-grained simulations are done, in which the two-site water model of Riniker and van Gunsteren [S. Riniker, W. F. van Gunsteren, J. Chem. Phys. 2011, 134, 084110] is simulated between atomistically resolved graphene surfaces. In the developed pure CG model, the two interaction sites of water and a combination of eight carbon atoms in the graphene surface are grouped together to construct water and surface CG beads. The pure CG potentials are constructed by iteratively matching the radial distribution functions and the density profiles of water beads in the pore with the corresponding mixed-grained distributions. The constructed potentials are shown to be pore-size transferable, capable of predicting structural properties of confined water over the whole range of pore sizes, ranging from extremely narrow pores to bulk water. The model is used to simulate a number of nanoconfined systems of a variety of pore sizes at constant temperature, constant parallel component of pressure, and constant surface area of the confining surfaces. The model is shown to predict the layering of water in contact with the surfaces, and the solvation force is in complete agreement with the mixed-grained model. It is shown that water molecules in the pore have smaller parallel diffusion coefficients compared to bulk water. Well-organized layers beside the surfaces are shown to have lower diffusion coefficients than diffuse layers. More information on the dynamics of water in the pore is obtained by calculating the rate of water exchange between slabs parallel to the surfaces. The time scale to achieve equilibrium for this process, depending on the pore width and on the degree of layering of water beside the surfaces, is a few nanoseconds in nanometric pores.

ENERGETIC PARTICLE DIFFUSION IN CRITICALLY BALANCED TURBULENCE

Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scale-dependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale-dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by \cite{GoSr1995}, and calculate energetic particle spatial diffusion coefficients using full-orbit simulations. The model uses an enveloped turbulence approach, where each 2-dimensional wave mode with wavenumber $k_\perp$ is packed into envelopes of length $L$ following the critical balance condition, $L\propto k_\perp^{-2/3}$, with the wave mode parameters changing between envelopes. Using full-orbit particle simulations, we find that both the parallel and perpendicular diffusion coefficients increase by a factor 2, compared to previous models with scale-independent anisotropy.

Controlling Anisotropic Drug Diffusion in Lipid-Fe3O4 Nanoparticle Hybrid Mesophases by Magnetic Alignment

We present a new strategy to control the anisotropic diffusion of hydrophilic drugs in lyotropic liquid crystals via the dispersion of magnetic nanoparticles in the mesophase, followed by reorientation of the mesophase domains via an external magnetic field. We select a lipid reverse hexagonal phase doped with magnetic iron oxide nanoparticles and glucose and caffeine as model hybrid mesophase and hydrophilic drugs, respectively. Upon cooling through the disorder-order phase transition of the hexagonal phase and under exposure to an external moderate magnetic field (1.1 T), both the nanoparticles and the hexagonal domains align with their columnar axes along the field direction. As a result, the water nanochannels of the inverted hexagonal domains also align parallel to the field direction, leading to a drug diffusion coefficient parallel to the field direction much larger than what was measured perpendicularly: in the case of glucose, for example, this difference in diffusion coefficients approaches 1 order of magnitude. Drug diffusion of the unaligned reverse hexagonal phase, which consists of randomly distributed domains, shows values in between the parallel and transversal diffusion values. This study shows that modifying the overall alignment of anisotropic mesophases via moderate external fields is a valuable means to control the corresponding transport tensor of the mesophase and demonstrates that the orientation of the domains plays an important role in the diffusion process of foreign hydrophilic molecules.

Diffusion Coefficients, Short-Term Cosmic Ray Modulation, and Convected Magnetic Structures

Three cases of large-amplitude, small spatial-scale interplanetary particle gradients observed by the anticoincidence shield (ACS) aboard the INTEGRAL spacecraft in 2006 are investigated. The high data rates provided by the INTEGRAL ACS allow an unprecedented ability to probe the fine structure of GCR propagation in the inner Heliosphere. For two of the three cases, calculating perpendicular and parallel cosmic ray diffusion coefficients based on both field and particle data results in parallel diffusion appearing to satisfy a convection gradient current balance, provided that the magnetic scattering of the particles can be described by quasi-linear theory. In the third case, perpendicular diffusion seems to dominate. The likelihood of magnetic flux rope topologies within solar ejecta affecting the local modulation is considered, and its importance in understanding the field-particle interaction for the astrophysics of nonthermal particle phenomena is discussed.

Diffusion mechanisms in smectic ionic liquid crystals: insights from coarse-grained MD simulations

We present the results of MD simulations, using a coarse grained force field, concerning the mechanism of diffusion in ionic liquid crystals. The dynamical properties of the recently characterized (G. Saielli, Soft Matter, 2012, 8, 10279) model system of 1-hexadecyl-3-methylimidazolium nitrate in the smectic A phase are analysed in detail. Comparison is made with the dynamical behaviour of thermotropic non-ionic smectic liquid crystals (LCs) and with that of lamellar phases of surfactant–water mixtures. The self-diffusion anisotropy, that is the ratio between the parallel and perpendicular diffusion coefficients, is consistent with that of non-ionic smectic LCs, though a significant contribution to the parallel diffusion is given by “pore” defects, similarly to what was observed in lamellar phases.

White matter abnormalities revealed by DTI correlate with interictal grey matter FDG‐PET metabolism in focal childhood epilepsies

For patients with focal epilepsy scheduled for surgery, including MRI-negative cases, (18)FDG-PET was shown to disclose hypometabolism in the seizure onset zone. However, it is not clear whether grey matter hypometabolism is informative of the integrity of the surrounding white matter cerebral tissue. In order to study the relationship between metabolism of the seizure onset zone grey matter and the integrity of the surrounding white matter measured by diffusion tensor imaging (DTI), we performed a monocentric prospective study (from 2006 to 2009) in 15 children with pharmacoresistant focal epilepsy, suitable for interictal (18)FDG-PET, T1-, T2-, FLAIR sequence MRI and DTI. Children had either positive or negative MRI (eight with symptomatic and seven with cryptogenic epilepsies, respectively). Seven children subsequently underwent surgery. Standardised uptake values of grey matter PET metabolism were compared with DTI indices (fractional anisotropy [FA], apparent diffusion coefficient [ADC], parallel diffusion coefficient [PDC], and transverse diffusion coefficient [TDC]) in grey matter within the seizure onset zone and adjacent white matter, using regions of interest automatically drawn from individual sulcal and gyral parcellation. Hypometabolism correlated positively with white matter ADC, PDC, and TDC, and negatively with white matter FA. In the cryptogenic group of children, hypometabolism correlated positively with white matter ADC. Our results demonstrate a relationship between abnormalities of grey matter metabolism in the seizure onset zone and adjacent white matter structural alterations in childhood focal epilepsies, even in cryptogenic epilepsy. This relationship supports the hypothesis that microstructural alterations of the white matter are related to epileptic networks and has potential implications for the evaluation of children with MRI-negative epilepsy.

Analytical description of nonlinear particle transport in slab turbulence: High particle energies and stochastic acceleration

Pitch-angle scattering, parallel spatial diffusion, and stochastic acceleration of cosmic rays are investigated analytically. Based on a second-order quasilinear theory, we derive analytical expressions for the aforementioned transport parameters for all possible magnetic field strengths and particle energies. This work complements previous work where only parallel diffusion for low energetic particles was considered. Furthermore, we compute the first time the momentum diffusion coefficient. It is also shown that the relation between the momentum diffusion coefficient and the parallel spatial diffusion coefficient is more complicated than assumed in previous work.

RADIAL DEPENDENCE OF PEAK PROTON AND IRON ION FLUXES IN SOLAR ENERGETIC PARTICLE EVENTS: APPLICATION OF THE PATH CODE

The radial dependence of particle peak fluxes in large solar energetic particle (SEP) events is important in determining the potential impact of space weather hazards on space missions. Using the Particle Acceleration and Transport in the Heliosphere code, we model the acceleration and transport of protons and iron ions at evolving coronal mass ejection shocks propagating throughout the inner heliosphere from about 0.1 to 2.5 AU. An example shock with a compression ratio of 3.9 and a speed of 1000 km s{sup -1} close to the Sun is modeled using a two-dimensional MHD ZEUS code. The compression ratio and shock speed weakened to 2.3 and 630 km s{sup -1}, correspondingly, at 2 AU. Shocks with 15 Degree-Sign , 45 Degree-Sign , and 75 Degree-Sign angles between the upstream magnetic field and the shock normal were studied. The shock angle was kept constant throughout the simulation. Both gradual and impulsive events are studied. Diffusive shock acceleration is assumed at the shock and we use a total diffusion coefficient that includes a parallel diffusion coefficient which takes into account the upstream wave amplification, and a perpendicular diffusion coefficient which is based on the NonLinear Guiding Center theory. The transport of particles escapingmore » from the shock is modeled using a Monte Carlo approach. Time-intensity profiles for protons and iron ions are obtained. We analyzed the radial dependence of peak fluxes (J) for both protons and iron ions from 0.5 to 2 AU. We find that the functional dependence is softer than R {sup -3} and is about R {sup -2.9} to R {sup -1.8} in the energy range of 0.3-5 MeV nuc{sup -1}. Quasi-perpendicular shock showed a steeper radial dependence than a quasi-parallel shock. Mixed events show a softer radial dependence at energies above 500 keV nuc{sup -1} for iron ions and above 1 MeV for protons. The values of J(R) depend on seed particle composition, particle energy, shock obliquity, and the interplanetary turbulence level. Consequently, we advocate using SEP event-specific computer modeling rather than empirical formulae for future forecasting of the radiation environment throughout the heliosphere during large SEP events.« less

Parallel transport of cosmic rays for non-diffusive pitch-angle scattering: I. Using the standard Fokker–Planck equation

Diffusion along a mean magnetic field is one of the most important transport processes of cosmic rays and solar energetic particles. Parallel spatial diffusion is controlled by pitch-angle scattering. In the literature, one can find a relation between the pitch-angle scattering coefficient and the parallel spatial diffusion coefficient. The latter relation is a consequence of a pitch-angle isotropization process and provides a powerful tool for computing the parallel spatial diffusion coefficient. In recent years, researchers have discussed non-diffusive pitch-angle scattering as well as non-diffusive parallel transport. In this paper, we discuss the relation between pitch-angle scattering and parallel spatial diffusion for the non-diffusive cases.

THE LONGITUDINAL TRANSPORT OF ENERGETIC IONS FROM IMPULSIVE SOLAR FLARES IN INTERPLANETARY SPACE

We present a study of the longitudinal spread of energetic charged particles from a localized instantaneous compact source on the Sun. Our study utilizes a diffusive-transport model for the propagation of energetic ions in interplanetary space. We show that even for very small values of the ratio of perpendicular to parallel diffusion coefficients—a few percent—the particles spread significantly in longitude. Spatial diffusion and adiabatic energy loss of ions in the interplanetary plasma cause impulsive particle events at Earth's orbit to last a few days. In this time, the combination of transport both along and across the local Parker-spiral magnetic field and the longitudinal motion of the magnetic lines of forces rooted at the Sun as it rotates leads to substantial longitudinal transport of the particles. We show that spacecraft separated by as much as 180° or more may observe events associated with compact solar sources, such as those from impulsive solar flares. Our results are qualitatively consistent with recent multi-spacecraft observations.

CROSS-FIELD TRANSPORT OF SOLAR ENERGETIC PARTICLES IN A LARGE-SCALE FLUCTUATING MAGNETIC FIELD

The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) exhibiting large-scale fluctuations due to footpoint motions originating in the photosphere, are simulated using a full-orbit test-particle code. The cross-field transport experienced by the particles in three propagation conditions (scatter-free, with scattering mean free path lambda=0.3 AU and lambda=2 AU) is characterized in the Parker spiral geometry. The role of expansion of the magnetic field with radial distance from the Sun is taken into consideration in the calculation of particle displacements and diffusion coefficients from the output of the simulations. It is found that transport across the magnetic field is enhanced in the lambda=0.3 AU and lambda=2 AU cases, compared to the scatter-free case. Values of the ratios of perpendicular to parallel diffusion coefficients vary between 0.01 and 0.08. The ratio of latitudinal to longitudinal diffusion coefficient perpendicular to the magnetic field is typically 0.2, suggesting that transport in latitude may be less efficient.

Monte Carlo calculation of electron diffusion coefficient in wurtzite indium nitride

This paper presents the theoretical analysis of the diffusivity of electrons in wurtzite (WZ) indium nitride (InN) using an ensemble Monte Carlo (EMC) method. The electron diffusion coefficient D(E,d,ω) as the functions of the electric field (E), doping concentration (d), and frequency (ω) is investigated in detail. The research results show that the maximum zero-field diffusion coefficient is about 250 cm2/s. The diffusion coefficient parallel to the electric field is smaller than that of perpendicular to the electric field. Further investigation shows that the diffusion coefficient decreases greatly at high frequency. Using Einstein equation, we obtain the zero-field mobility and make comparisons with the references.

Numerical investigation of the influence of large turbulence scales on the parallel and perpendicular transport of cosmic rays

In recent analytical investigations it has been demonstrated that the turbulence behavior at large scales has a very strong influence on the perpendicular diffusion coefficient of charged particles. In the present paper we use computer simulations to investigate numerically cross field transport and particle propagation along the mean magnetic field for different turbulence models at large scales. Our results are compared with quasilinear theory and nonlinear diffusion theories. We show that for different forms of the turbulence spectrum at large scales, the perpendicular mean free paths obtained numerically are in agreement with recent predictions made by analytical theory. It is also shown that the parallel diffusion coefficient contains always a strong nonlinear contribution which is, however, independent of the assumed spectrum at large scales.

A DIRECT METHOD TO DETERMINE THE PARALLEL MEAN FREE PATH OF SOLAR ENERGETIC PARTICLES WITH ADIABATIC FOCUSING

The parallel mean free path of solar energetic particles (SEPs), which is determined by physical properties of SEPs as well as those of solar wind, is a very important parameter in space physics to study the transport of charged energetic particles in the heliosphere, especially for space weather forecasting. In space weather practice, it is necessary to find a quick approach to obtain the parallel mean free path of SEPs for a solar event. In addition, the adiabatic focusing effect caused by a spatially varying mean magnetic field in the solar system is important to the transport processes of SEPs. Recently, Shalchi presented an analytical description of the parallel diffusion coefficient with adiabatic focusing. Based on Shalchi's results, in this paper we provide a direct analytical formula as a function of parameters concerning the physical properties of SEPs and solar wind to directly and quickly determine the parallel mean free path of SEPs with adiabatic focusing. Since all of the quantities in the analytical formula can be directly observed by spacecraft, this direct method would be a very useful tool in space weather research. As applications of the direct method, we investigate the inherent relations between the parallel mean free path and various parameters concerning physical properties of SEPs and solar wind. Comparisons of parallel mean free paths with and without adiabatic focusing are also presented.

COSMIC-RAY TRANSPORT THEORY IN PARTIALLY TURBULENT SPACE PLASMAS WITH COMPRESSIBLE MAGNETIC TURBULENCE

Recently a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here we generalize the approach to the important physical case of a compressible plasma. As previously obtained in the case of an incompressible plasma we allow arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field. For the case of quasi-stationary and spatially homogeneous magnetic turbulence we derive in the small Larmor radius approximation gyro-phase averaged cosmic ray Fokker-Planck coefficients. Upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients and for the perpendicular and parallel spatial diffusion coefficients are presented.

Scaling of Langevin and molecular dynamics persistence times of nonhomogeneous fluids

The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics.

Particle acceleration and transport at an oblique CME-driven shock

In gradual solar energetic particle (SEP) events, protons and heavy ions are often accelerated to >100MeV/nucleon at a CME-driven shock. In this work, we study particle acceleration at an oblique shock by extending our earlier particle acceleration and transport in heliosphere (PATH) code to include shocks with arbitrary θBN, where θBN is the angle between the upstream magnetic field and the shock normal. Instantaneous particle spectra at the shock front are obtained by solving the transport equation using the total diffusion coefficient κ, which is a function of the parallel diffusion coefficient κ∥ and the perpendicular diffusion coefficient κ⊥. In computing κ∥ and κ⊥, we use analytic expressions derived previously. The particle maximum energy at the shock front as a function of time, the time intensity profiles and particle spectra at 1AU for five θBN’s are calculated for an example shock.

Diffusion in a Strongly Coupled Magnetized Plasma

A first-principles study of diffusion in a strongly coupled one-component plasma in a magnetic field B is presented. As in a weakly coupled plasma, the diffusion coefficient perpendicular to the field exhibits a Bohm-like 1/B behavior in the strong-field limit but its overall scaling is substantially different. The diffusion coefficient parallel to the field is strongly affected by the field as well and also approaches a 1/B scaling, in striking contrast to earlier predictions.