Particle Mean Free Path Research Articles

DETAILED NUMERICAL INVESTIGATION OF THE BOHM LIMIT IN COSMIC RAY DIFFUSION THEORY

A standard model in cosmic ray diffusion theory is the so-called Bohm limit in which the particle mean free path is assumed to be equal to the Larmor radius. This type of diffusion is often employed to model the propagation and acceleration of energetic particles. However, recent analytical and numerical work has shown that standard Bohm diffusion is not realistic. In the present paper, we perform test-particle simulations to explore particle diffusion in the strong turbulence limit in which the wave field is much stronger than the mean magnetic field. We show that there is indeed a lower limit of the particle mean free path along the mean field. In this limit, the mean free path is directly proportional to the unperturbed Larmor radius like in the traditional Bohm limit, but it is reduced by the factor δB/B 0 where B 0 is the mean field and δB the turbulent field. Although we focus on parallel diffusion, we also explore diffusion across the mean field in the strong turbulence limit.

Studying Validity of Single-Fluid Model in Inertial Confinement Fusion

The validity of single-fluid model in inertial confinement fusion simulations is studied by comparing the results of the multi- and single-fluid models. The multi-fluid model includes the effects of collision and interpenetration between fluid species. By simulating the collision of fluid species, steady-state shock propagation into the thin DT gas and expansion of hohlraum Au wall heated by lasers, the results show that the validity of single-fluid model is strongly dependent on the ratio of the characteristic length of the simulated system to the particle mean free path. When the characteristic length L is one order larger than the mean free path λ, the single-fluid model's results are found to be in good agreement with the multi-fluid model's simulations, and the modeling of single-fluid remains valid. If the value of L/λ is lower than 10, the interpenetration between fluid species is significant, and the single-fluid simulations show some unphysical results; while the multi-fluid model can describe well the interpenetration and mix phenomena, and give more reasonable results.

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

We introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Our code combines advantages of the DSMC and the Point of Closest Approach techniques for solving the collision integral. With that, it achieves high spatial accuracy in simulations of large particle systems while maintaining computational feasibility. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we reproduce hydrodynamic behavior. To demonstrate that our code can retrieve continuum solutions, we perform a test-suite of classic hydrodynamic shock problems consisting of the Sod, the Noh, and the Sedov tests. We find that the results of our simulations which apply millions of test-particles match the analytic solutions well. In addition, we take advantage of the ability of kinetic codes to describe matter out of the continuum regime when applying large particle mean free paths. With that, we study and compare the evolution of shock waves in the hydrodynamic limit and in a regime which is not reachable by hydrodynamic codes.

THE EFFICIENCY OF SECOND-ORDER FERMI ACCELERATION BY WEAKLY COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE

We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scattering rates, the interaction between particles and turbulent fluctuations becomes non-resonant, governed by particles heating and cooling adiabatically as they encounter turbulent density fluctuations. Rapid pitch-angle scattering can produce a power-law tail in the proton distribution function but this requires fine-tuning of parameters. Moreover, in the near-Earth solar wind, a significant power-law tail cannot develop by this mechanism because the particle acceleration timescales are longer than the adiabatic cooling timescale set by the expansion of the solar wind. Our results thus imply that MHD-scale turbulent fluctuations are unlikely to be the origin of the v^{-5} tail in the proton distribution function observed in the solar wind.

The scattering mean free path of cosmic ray particles in isotropic damped plasma wave turbulence

An analytical expression for the mean free path of single-charged cosmic ray particles, especially for positrons, is derived in isotropic plasma wave turbulence, where the crucial scattering of cosmic ray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with oblique magnetosonic waves. In this calculation, viscous damping effects are included, which results in broadening of the resonance function. It is demonstrated that including resonance function broadening ensures a finite mean free path for cosmic ray energies, for which previously reported types of turbulence predicted an infinitely large mean free path.

SU‐E‐T‐490: A Geant4 Implementation of the Generalized Boltzmann Fokker‐Plank Method

Purpose: A geant4 implementation of the Generalized Boltzmann Fokker‐Plank (GBFP) method, an advanced, computationally efficient Monte Carlo method for charged particle transport, is studied. Methods: The GBFP method is a systematic approach for extending the mean free path (MFP) of particles while exactly preserving moments of the true differential cross section (DCS) to some order, $N$, and approximating higher order moments by the exact moments of the approximate DCS. The approximate DCS preserves important physical quantities like mean scattering cosine, stopping power, and energy straggling. The GBFP method is a single event method, so transport mechanics are restored and step size and boundary crossing limitations inherent to condensed history methods are a non‐issue. A geant4 application with GBFP physics was developed for testing speed and accuracy of the GBFP method dose calculations. Results: Initial testing revealed that speed‐ups for the discrete GBFP model are consistent with previous work on the GBFP method. Computed dose profiles using the discrete GBFP method are in agreement with benchmarks within statistical uncertainty (in most cases < 1$\%) for sufficiently sampled regions. This indicates that the geant4 implementation was successful. A framework for further testing is now established. Conclusion: The GBFP method provides systematic control of calculation speed and accuracy for electron transport calculations. The GBFP method is single event Monte Carlo so pre‐existing production code transport algorithms are all that are needed for the implementation. Therefore, no major changes are necessary for incorporation of the GBFP method into production code systems.

TURBULENT SHEAR ACCELERATION

We consider particle acceleration by large-scale incompressible turbulence with a lengthscale larger than the particle mean free path. We derive an ensemble-averaged transport equation of energetic charged particles from an extended transport equation which contains the shear acceleration. The ensemble-averaged transport equation describes particle acceleration by incompressible turbulence (turbulent shear acceleration). We find that for Kolmogorov turbulence, the turbulent shear acceleration becomes important in small scale. Moreover, by Monte Carlo simulations, we confirm that the ensemble-averaged transport equation describes the turbulent shear acceleration.

Analysis of the [formula omitted] model: Well-posedness and diffusion asymptotics

This paper is devoted to the analysis of the M1 model which arises in radiative transfer theory. The derivation of the model is based on the entropy minimization principle, which leads to a hyperbolic system of balance laws with relaxation. In the multi-dimensional case, we establish the existence–uniqueness of a globally defined smooth solution under a suitable smallness condition on the initial data. In the one-dimensional case we show that the smallness condition does not depend on the particles mean free path so that we can also rigorously justify the consistency of the model with the diffusion asymptotics. The result extends the analysis of Coulombel et al. [J.-F. Coulombel, F. Golse T. Goudon, Diffusion approximation and entropy-based moment closure for kinetic equations, Asymptotic Analysis, 45 (2005) 1–39] to the case where the entropy functional accounts for relaxation towards the Planckian state, which is physically more relevant.

Leaky-box approximation to the fractional diffusion model

Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.

Measurement of the proton-air cross-section with the Pierre Auger Observatory

We present the procedure to measure the proton-air cross-section at a center-of-mass energy per nucleon of 57TeV developed by the Pierre Auger Collaboration. The conversion from proton-air to inelastic proton-proton cross-section with an extended Glauber calculation is discussed. The systematic uncertainties of the analysis are summarized and the final result compared to accelerator data and model predictions. The growth of hadronic cross-sections towards ultra-high energies reflects changes in the internal structure of the colliding particles. Due to the nature of QCD it is still not possible to calculate hadronic cross-sections at ultra-high energies from first principles. It is thus of paramount importance to measure hadronic cross-sections in order to guide the development of phenomenological models needed to describe secondary multiparticle production at ultra-high energies. Such models are crucial, for example, for a detailed interpretation of available cosmic-ray air-shower data in terms of the primary mass composition. Without a better understanding of the cosmic-ray mass composition it will be very difficult to distinguish between different scenarios of cosmic-ray acceleration and propagation. We present the measurement of the proton-air cross-section with data of the Pierre Auger Observatory (1). The Pierre Auger Observatory is located close to the town of Malargue in Argentina. It consist of about 1660 water Cherenkov particle detector spread over a surface area of 3000km 2 .D uring clear and moonless nights the atmosphere on top of the surface array is overlooked by 27 fluorescence telescopes. This analysis is based on the observation of the longitudinal air-shower development with the telescopes. By combining the timing data of the surface detectors with that of the fluorescence telescopes a very precise reconstruction of the geometry is achieved (2). This technique is called hybrid reconstruction. It allows us a very accurate measurement of Xmax, the position at which an air-shower deposits the maximum energy per unit of mass of atmosphere traversed (3). With the precise observation of longitudinal air-shower fluctuations it is possible to achieve high sensitivity to the mean free path of the primary cosmic-ray particles and thus to the cross-section. This technique is well known and has been first applied by the Fly's Eye experiment (4). We also discuss systematic uncertainties and limitations of the cross-section measurement. In a last step, the proton-air cross-section measurement is converted into a proton-proton cross-section. This conversion makes use of a Glauber calculation, which has been extended to account for inelastic screening effects.

A DIRECT APPROACH FOR DETERMINING THE PERPENDICULAR MEAN FREE PATH OF SOLAR ENERGETIC PARTICLES IN A TURBULENT AND SPATIALLY VARYING MAGNETIC FIELD

A direct approach for explicitly determining the perpendicular mean free path of solar energetic particles (SEPs) influenced by parallel diffusion and composite dynamical turbulence in a spatially varying magnetic field is presented. As theoretical applications of the direct approach, we investigate the inherent relations between the perpendicular mean free path and various parameters concerning physical properties of SEPs as well as those of interplanetary conditions such as the solar wind and the turbulent magnetic field. Comparisons of the perpendicular mean free paths with and without adiabatic focusing are also presented. The direct method shows encouraging agreement with spacecraft observations, suggesting it is a reliable and useful tool for use in theoretical investigations and space weather forecasting.

Fermi I particle acceleration in converging flows mediated by magnetic reconnection

Context. Converging flows with strong magnetic fields of different polarity can accelerate particles through magnetic reconnection. If the particle mean free path is longer than the reconnection layer is thick, but much shorter than the entire reconnection structure, the particle will mostly interact with the incoming flows potentially with a very low escape probability. Aims. We explore, in general and also in some specific scenarios, the possibility of particles to be accelerated in a magnetic reconnection layer by interacting only with the incoming flows. Methods. We characterize converging flows that undergo magnetic reconnection, and derive analytical estimates for the particle energy distribution, acceleration rate, and maximum energies achievable in these flows. We also discuss a scenario, based on jets dominated by magnetic fields of changing polarity, in which this mechanism may operate. Results. The proposed acceleration mechanism operates if the reconnection layer is much thinner than its transversal characteristic size, and the magnetic field has a disordered component. Synchrotron losses may prevent electrons from entering in this acceleration regime. The acceleration rate should be faster, and the energy distribution of particles harder than in standard diffusive shock acceleration. The interaction of obstacles with the innermost region of jets in active galactic nuclei and microquasars may be suitable sites for particle acceleration in converging flows.

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.

Photoelectron Mean Free Path on the EXAFS Analyses for Nanoparticles

We calculate the inelastic mean free path (IMFP) for small metal particles based on the plasmon model for free electron gas confined in small sphere with radius a. The IMFP decreases with the radius a smaller than about 100 ˚ and the rate of the decrease depends on the bulk plasmon energy !p. We furthermore discuss the coordination numbers obtained from the EXAFS curve fitting method for small Ag particles. We find the importance of the size dependent IMFP for EXAFS analyses in order to obtain reliable coordination numbers in nanoparticles. [DOI: 10.1380/ejssnt.2012.565]

ORIGIN OF ULTRA-HIGH-ENERGY GALACTIC COSMIC RAYS: THE ISOTROPY PROBLEM

We study the propagation of ultra-high-energy cosmic rays (UHECR) in the Galaxy, concentrating on the energy range below the ankle in the spectrum at 4 EeV. A Monte-Carlo method, based on analytical solutions to the time-dependent diffusion problem, is used to account for intermittency by placing sources at random locations. Assuming a source population that scales with baryon mass density or star formation (e.g. long GRB), we derive constraints arising from intermittency and the observational limits on the composition and anisotropy. It is shown that the composition and anisotropy at 1e18 eV are difficult to reproduce and require that either a) the particle mean free path is much smaller than a gyroradius, implying the escape time is very long, b) the composition is heavier than suggested by recent Auger data, c) the ultrahigh-energy sub-ankle component is mostly extragalactic, or d) we are living in a rare lull in the ultrahigh-energy cosmic-ray production, and the current ultrahigh-energy cosmic-ray intensity is far below the Galactic time average. We therefore recommend a strong observational focus on determining the UHECR composition around 1e18 eV.

Numerical investigation of the cosmic-ray scattering anisotropy and Bohm diffusion in space plasmas

We employ a recently developed test-particle simulation code to explore the Bohm diffusion and the scattering anisotropy of charged particles interacting with magnetic turbulence. By computing parallel and perpendicular mean free paths, it is shown that a dominant mean magnetic field and a large particle mean free path along the mean magnetic field break the scattering symmetry. In such cases, a strong scattering anisotropy is found, which is in good agreement with recent analytical calculations. It is also shown that the assumption of the Bohm diffusion in isotropic turbulence is only valid for some special cases.

A SIMPLE ANALYTICAL METHOD TO DETERMINE SOLAR ENERGETIC PARTICLES’ MEAN FREE PATH

To obtain the mean free path of solar energetic particles (SEPs) for a solar event, one usually has to fit time profiles of both flux and anisotropy from spacecraft observations to numerical simulations of SEPs' transport processes. This method can be called a simulation method. But a reasonably good fitting needs a lot of simulations, which demand a large amount of calculation resources. Sometimes, it is necessary to find an easy way to obtain the mean free path of SEPs quickly, for example, in space weather practice. Recently, Shalchi et al. provided an approximate analytical formula of SEPs' anisotropy time profile as a function of particles' mean free path for impulsive events. In this paper, we determine SEPs' mean free path by fitting the anisotropy time profiles from Shalchi et al.'s analytical formula to spacecraft observations. This new method can be called an analytical method. In addition, we obtain SEPs' mean free path with the traditional simulation methods. Finally, we compare the mean free path obtained with the simulation method to that of the analytical method to show that the analytical method, with some minor modifications, can give us a good, quick approximation of SEPs' mean free path for impulsive events.

Physical Parameters Related to Quantify Quality of Effectiveness of Charged Particles at Lower Doses

Quality factors for protons and helium particles has determined for cell inactivation using linear energy transfer. The quality has also been investigated as a function for other physical parameters, such as mean free path and effective charge for protons and helium particles, for a better interpretation to the effectiveness of these charged particles in V79 cells. Explanation of quality is clearly illustrated in terms of the average dis-tance of energy deposition events in biological systems.

PERPENDICULAR DIFFUSION OF COSMIC RAYS FOR A GOLDREICH-SRIDHAR SPECTRUM

Perpendicular diffusion coefficients and mean free paths of cosmic particles are computed for an anisotropic Alfvenic turbulence spectrum corresponding to the Goldreich-Sridhar model by employing an enhanced nonlinear guiding center theory. The calculations are important for understanding cosmic ray propagation in the Galaxy and in the solar system. In addition, the knowledge of diffusion coefficients is also useful for modeling charged particles which experience diffusive shock acceleration in supernova remnants and at interplanetary shock waves. To replace the parallel diffusion coefficient in our equation for the perpendicular diffusion coefficient, we employ different models such as quasilinear results and phenomenological models. The results are compared with those derived earlier. We demonstrate that the choice of the turbulence model as well as the choice of the model for the parallel diffusion coefficient has a strong influence on the perpendicular diffusion coefficient.

THE INFLUENCE OF DISSIPATION RANGE POWER SPECTRA AND PLASMA-WAVE POLARIZATION ON COSMIC-RAY SCATTERING MEAN FREE PATH

The influence of the polarization state and the dissipation range spectral steepening of slab plasma waves on the scattering mean free path of single-charged cosmic-ray particles is investigated in a turbulence model, where the crucial scattering of cosmic-ray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with slab plasma waves. Analytical expressions for the mean free path of protons, antiprotons, negatrons, and positrons are derived for the case of constant frequency-independent magnetic helicity values ? and different values of the dissipation range spectral index k for characteristic interplanetary and interstellar plasma conditions. The positron mean free path is not affected by the dissipation range spectral index k as these particles can only cyclotron-resonate for rigidity values larger than R 0 = mpc = 938?MV. Proton and antiproton mean free paths are only slightly affected by the dissipation range spectral index k at small rigidities R < R 0. The negatron mean free path is severely affected by the dissipation range spectral index k at rigidities smaller than R 0. At high rigidities R R 0, all particle species approach the same power-law dependence R 2?s determined by the inertial range spectral index s = 5/3. The magnetic helicity value ? affects the value of the mean free path. At all rigidities, the ratio of the antiproton to proton mean free paths equals the constant (1 + ?)/(1 ? ?), which also agrees with the ratio of the negatron to the proton and positron mean free paths at relativistic rigidities. At relativistic rigidities the positron and proton mean free paths agree, as do the negatron and antiproton mean free paths.