Transport Of Energetic Particles Research Articles

Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields

This paper summarizes the results obtained by the team "Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields" supported by the International Space Science Institute in Bern, Switzerland. We focus on the physical processes occurring in the outer heliosphere, especially at its boundary called the heliopause (HP), and in the LISM. The importance of magnetic field, charge exchange between atoms and ions, and solar cycle on the heliopause topology and observed heliocentric distances to different heliospheric discontinuities are discussed. It is shown that time-dependent boundary conditions are necessary to describe the heliospheric asymmetries detected by the Voyager spacecraft. We also discuss the structure of the HP, especially due to its instability and magnetic reconnection. It is demonstrated that the Rayleigh-Taylor instability of the nose of the HP creates consecutive layers of the interstellar and heliospheric plasma which are magnetically connected to different sources. This may be a possible explanation of abrupt changes in the galactic and anomalous cosmic ray fluxes observed by Voyager 1 when it was crossing the HP structure for a period of about one month in the summer of 2012. This paper also discusses the plausibility of fitting simulation results to a number of observational data sets obtained by in situ and remote measurements. The distribution of magnetic field in the vicinity of the HP is discussed in the context of Voyager measurements. We discuss the transport of energetic particles in the inner and outer heliosheath, concentrating on the anisotropic spatial diffusion diffusion tensor and the pitch-angle dependence of perpendicular diffusion and demonstrate that the latter can explain the observed pitch-angle anisotropies of both the anomalous and galactic cosmic rays in the outer heliosheath.

Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification.

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

Perpendicular Diffusion of Solar Energetic Particles: Model Results and Implications for Electrons

Abstract The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations at energies of 55–105 keV, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy, and the onset time. By using transport coefficients that are derived from first principles, we limit the number of free parameters in the model to (i) the probability of SEPs following diffusing magnetic field lines, quantified by , and (ii) the broadness of the Gaussian injection function. It is found that the model solutions are extremely sensitive to the magnitude of the perpendicular diffusion coefficient and relatively insensitive to the form of the injection function as long as a reasonable value of a = 0.2 is used. We illustrate the effects of perpendicular diffusion on the model solutions and discuss the viability of this process as a dominant mechanism by which SEPs are transported in longitude. Lastly, we try to quantity the effectiveness of perpendicular diffusion as an interplay between the magnitude of the relevant diffusion coefficient and the SEP intensity gradient driving the diffusion process. It follows that perpendicular diffusion is extremely effective early in an SEP event when large intensity gradients are present, while the effectiveness quickly decreases with time thereafter.

Conceptual design of Dipole Research Experiment (DREX)**Supported by National Natural Science Foundation of China (Nos. 11505040, 11261140326 and 11405038), China Postdoctoral Science Foundation (Nos. 2016M591518, 2015M570283) and Project Supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. 2017008).

A new terrella-like device for laboratory simulation of inner magnetosphere plasmas, Dipole Research Experiment, is scheduled to be built at the Harbin Institute of Technology (HIT), China, as a major state scientific research facility for space physics studies. It is designed to provide a ground experimental platform to reproduce the inner magnetosphere to simulate the processes of trapping, acceleration, and transport of energetic charged particles restrained in a dipole magnetic field configuration. The scaling relation of hydromagnetism between the laboratory plasma of the device and the geomagnetosphere plasma is applied to resemble geospace processes in the Dipole Research Experiment plasma. Multiple plasma sources, different kinds of coils with specific functions, and advanced diagnostics are designed to be equipped in the facility for multi-functions. The motivation, design criteria for the Dipole Research Experiment experiments and the means applied to generate the plasma of desired parameters in the laboratory are also described.

Solar Energetic Particle Transport Near a Heliospheric Current Sheet

Abstract Solar energetic particles (SEPs), a major component of space weather, propagate through the interplanetary medium strongly guided by the interplanetary magnetic field (IMF). In this work, we analyze the implications that a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP release sites to the Earth. We simulate proton propagation by integrating fully 3D trajectories near an analytically defined flat current sheet, collecting comprehensive statistics into histograms, fluence maps, and virtual observer time profiles within an energy range of 1–800 MeV. We show that protons experience significant current sheet drift to distant longitudes, causing time profiles to exhibit multiple components, which are a potential source of confusing interpretations of observations. We find that variation of the current sheet thickness within a realistic parameter range has little effect on particle propagation. We show that the IMF configuration strongly affects the deceleration of protons. We show that in our model, the presence of a flat equatorial HCS in the inner heliosphere limits the crossing of protons into the opposite hemisphere.

THE IMPLICIT CONTRIBUTION OF SLAB MODES TO THE PERPENDICULAR DIFFUSION COEFFICIENT OF PARTICLES INTERACTING WITH TWO-COMPONENT TURBULENCE

ABSTRACT We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper, the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction of the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration.

On the east–west longitudinally asymmetric distribution of solar proton events

A large data set of 78 solar proton events observed near the Earth's orbit during 1996-2011 is investigated. An East-West longitudinal (azimuthal) asymmetry is found to exist in the distribution of flare sources of solar proton events. With the same longitudinal separation between the flare sources and the magnetic field line footpoint of observer, the number of the solar proton events originating from solar sources located on the eastern side of the nominal magnetic footpoint of observer is larger than the number of the solar proton events from solar sources located on the western side. We emphasize the importance of this statistical investigation in two aspects. On the one hand, this statistical finding confirms our previous simulation results obtained by numerically solving five-dimensional Fokker-Planck equation of solar energetic particle (SEP) transport. On the other hand, the East-West longitudinally (azimuthally) asymmetric distribution of solar proton events accumulated over a long time period provides an observational evidence for the effects of perpendicular diffusion on the SEP propagation in the heliosphere. We further point out that, in the sense of perpendicular diffusion, our numerical simulations and statistical results of SEP events confirm each other. We discuss in detail the important effects of perpendicular diffusion on the formation of the East-West azimuthal (longitudinal) asymmetry of SEP distribution in two physical scenarios, i.e., 'multiple SEP events with one spacecraft' and 'one SEP event with multiple spacecraft'. A functional relation I_{max}(r)=kr^{-1.7} quantifying the radial dependence of SEP peak intensities is obtained and utilized in the analysis of physical mechanism. The relationship between our results and those of Dresing et al. is also discussed.

The influence of the Kubo number on the transport of energetic particles

We discuss the interaction between charged energetic particles and magnetized plasmas by using analytical theory. Based on the unified nonlinear transport (UNLT) theory we compute the diffusion coefficient across a large scale magnetic field. To achieve analytical tractability we use a simple Gaussian approach to model the turbulent magnetic fields. We show that the perpendicular diffusion coefficient depends only on two parameters, namely the Kubo number and the parallel mean free path. We combine the aforementioned turbulence model with the UNLT theory and we solve the corresponding integral equation numerically to show how these two parameters control the perpendicular diffusion coefficient. Furthermore, we consider two extreme cases, namely the case of strong and suppressed pitch-angle scattering, respectively. For each case we consider small and large Kubo numbers to achieve a further simplification. All our analytical findings are compared with formulas which are known in diffusion theory.

Superposed epoch study of ICME sub-structures near Earth and their effects on Galactic cosmic rays

Interplanetary coronal mass ejections (ICMEs) are the interplanetary manifestations of solar eruptions. The overtaken solar wind forms a sheath of compressed plasma at the front of ICMEs. Magnetic clouds (MCs) are a subset of ICMEs with specific properties (e.g. the presence of a flux rope). When ICMEs pass near Earth, ground observations indicate that the flux of galactic cosmic rays (GCRs) decreases. The main aims of this paper are to find: common plasma and magnetic properties of different ICME sub-structures, and which ICME properties affect the flux of GCRs near Earth. We use a superposed epoch method applied to a large set of ICMEs observed \insitu\ by the spacecraft ACE, between 1998 and 2006. We also apply a superposed epoch analysis on GCRs time series observed with the McMurdo neutron monitors. We find that slow MCs at 1 AU have on average more massive sheaths. We conclude that it is because they are more effectively slowed down by drag during their travel from the Sun. Slow MCs also have a more symmetric magnetic field and sheaths expanding similarly as their following MC, while in contrast, fast MCs have an asymmetric magnetic profile and a compressing sheath in compression. In all types of MCs, we find that the proton density and the temperature, as well as the magnetic fluctuations can diffuse within the front of the MC due to 3D reconnection. Finally, we derive a quantitative model which describes the decrease of cosmic rays as a function of the amount of magnetic fluctuations and field strength. The obtained typical profiles of sheath/MC/GCR properties corresponding to slow, mid, and fast ICMEs, can be used for forecasting/modelling these events, and to better understand the transport of energetic particles in ICMEs. They are also useful for improving future operative space weather activities.

Linear benchmarks between the hybrid codes HYMAGYC and HMGC to study energetic particle driven Alfvénic modes

Resonant interaction between energetic particles (EPs), produced by fusion reactions and/or additional heating systems, and shear Alfvén modes can destabilize global Alfvénic modes enhancing the EP transport. In order to investigate the EP transport in present and next generation fusion devices, numerical simulations are recognized as a very important tool. Among the various numerical models, the hybrid MHD gyrokinetic one has shown to be a valid compromise between a sufficiently accurate wave-particle interaction description and affordable computational resource requirements. This paper presents a linear benchmark between the hybrid codes HYMAGYC and HMGC. The HYMAGYC code solves the full, linear MHD equations in general curvilinear geometry for the bulk plasma and describes the EP population by the nonlinear gyrokinetic Vlasov equation. On the other side, HMGC solves the nonlinear, reduced , pressureless MHD equations ( being the inverse aspect ratio) for the bulk plasma and the drift kinetic Vlasov equation for the EPs. The results of the HYMAGYC and HMGC codes have been compared both in the MHD limit and in a wide range of the EP parameter space for two test cases (one of which being the so-called TAE n = 6 ITPA Energetic Particle Group test case), both characterized by . In the first test case (test case A), good qualitative agreement is found w.r.t. real frequencies, growth rates and spatial structures of the most unstable modes, with some quantitative differences for the growth rates. For the so-called ITPA test case (test case B), at the nominal energetic particle density value, the disagreement between the two codes is, on the contrary, also qualitative, as a different mode is found as the most unstable one.

Effects of energetic particle phase space modifications by instabilities on integrated modeling

Tokamak plasmas can feature a large population of energetic particles (EP) from neutral beam injection or fusion reactions. In turn, energetic particles can drive instabilities, which affect the driving EP population leading to a distortion of the original EP distribution function and of quantities that depend on it. The latter include, for example, neutral beam (NB) current drive and plasma heating through EP thermalization. Those effects must be taken into account to enable reliable and quantitative simulations of discharges for present devices as well as predictions for future burning plasmas. Reduced models for EP transport are emerging as an effective tool for long time-scale integrated simulations of tokamak plasmas, possibly including the effects of instabilities on EP dynamics. Available models differ in how EP distribution properties are modified by instabilities, e.g. in terms of gradients in real or phase space. It is therefore crucial to assess to what extent different assumptions in the transport models affect predicted quantities such as EP profile, energy distribution, NB driven current and energy/momentum transfer to the thermal populations. A newly developed kick model, which includes modifications of the EP distribution by instabilities in both real and velocity space, is used in this work to investigate these issues. Coupled to TRANSP simulations, the kick model is used to analyze NB-heated NSTX and DIII-D discharges featuring unstable Alfvén eigenmodes (AEs). Results show that instabilities can strongly affect the EP distribution function, and modifications propagate to macroscopic quantities such as NB-driven current profile and NB power transferred to the thermal plasma species. Those important aspects are only qualitatively captured by simpler fast ion transport models that are based on radial diffusion of energetic ions only.

Mixed Diffusive-Convective Relaxation of a Warm Beam of Energetic Particles in Cold Plasma

This work addresses the features of fast particle transport in the bump-on-tail problem for varying the width of the fluctuation spectrum, in the view of possible applications to studies of energetic particle transport in fusion plasmas. Our analysis is built around the idea that strongly-shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are convective (ballistic-like). We cast this idea in the form of a self-consistent nonlinear dynamical model, which extends the classic equations of the quasi-linear theory to “broad” beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport essentially depending on nonlinear wave-particle interactions and phase-space structures. Taking into account the modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution function and the fluctuation intensity spectrum.

Energetic particle transport in the presence of magnetic turbulence: influence of spectral extension and intermittency

Energetic particle transport in the presence of magnetic turbulence: influence of spectral extension and intermittency

Phase space effects on fast ion distribution function modeling in tokamaks

Integrated simulations of tokamak discharges typically rely on classical physics to model energetic particle (EP) dynamics. However, there are numerous cases in which energetic particles can suffer additional transport that is not classical in nature. Examples include transport by applied 3D magnetic perturbations and, more notably, by plasma instabilities. Focusing on the effects of instabilities, ad-hoc models can empirically reproduce increased transport, but the choice of transport coefficients is usually somehow arbitrary. New approaches based on physics-based reduced models are being developed to address those issues in a simplified way, while retaining a more correct treatment of resonant wave-particle interactions. The kick model implemented in the tokamak transport code TRANSP is an example of such reduced models. It includes modifications of the EP distribution by instabilities in real and velocity space, retaining correlations between transport in energy and space typical of resonant EP transport. The relevance of EP phase space modifications by instabilities is first discussed in terms of predicted fast ion distribution. Results are compared with those from a simple, ad-hoc diffusive model. It is then shown that the phase-space resolved model can also provide additional insight into important issues such as internal consistency of the simulations and mode stability through the analysis of the power exchanged between energetic particles and the instabilities.

Kinetic transport simulation of energetic particles

A kinetic transport code (EPtran) is developed for the transport of the energetic particles (EPs). The EPtran code evolves the EP distribution function in radius, energy, and pitch angle phase space (r, E, λ) to steady state with classical slowing down, pitch angle scattering, as well as radial and energy transport of the injected EPs (neutral beam injection (NBI) or fusion alpha). The EPtran code is illustrated by treating the transport of NBI fast ions from high-n ITG/TEM micro-turbulence and EP driven unstable low-n Alfvén eigenmodes (AEs) in a well-studied DIII-D NBI heated discharge with significant AE central core loss. The kinetic transport code results for this discharge are compared with previous study using a simple EP density moment transport code ALPHA (R.E. Waltz and E.M. Bass 2014 Nucl. Fusion 54 104006). The dominant EP-AE transport is treated with a local stiff critical EP density (or equivalent pressure) gradient radial transport model modified to include energy-dependence and the nonlocal effects EP drift orbits. All previous EP transport models assume that the EP velocity space distribution function is not significantly distorted from the classical ‘no transport’ slowing down distribution. Important transport distortions away from the slowing down EP spectrum are illustrated by a focus on the coefficient of convection: EP energy flux divided by the product of EP average energy and EP particle flux.

Monte Carlo simulations of intensity profiles for energetic particle propagation

Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used to critically judge the applicability of diffusion to the stochastic transport of energetic particles in magnetized turbulence. Methods. A Monte-Carlo simulation code is extended to allow for the generation of intensity profiles as well as anisotropy-time profiles. Due to the relatively low number density of computational particles, a kernel function has to be used to describe the spatial extent of each particle. Results. The obtained intensity profiles are interpreted as solutions of the diffusion equation by inserting the diffusion coefficients that have been directly determined from the mean-square displacements. The comparison shows that the time dependence of the diffusion coefficients needs to be considered, in particular the initial ballistic phase and the often sub-diffusive perpendicular coefficient. Conclusions. It is argued that the perpendicular component of the distribution function is essential if agreement between the diffusion solution and the simulated flux is to be obtained. In addition, time-dependent diffusion can provide a better description than the classic diffusion equation only after the initial ballistic phase.

Cross-field transport and pitch-angle anisotropy of solar energetic particles in MHD turbulence

Abstract. Recent modelling of solar energetic particles (SEPs) propagation through the heliospheric turbulence, also discussed in this workshop, has investigated the role of the pitch-angle scattering and the perpendicular transport in spreading particles in heliolongitude, as shown by multi-spacecraft measurements (STEREO A/B, ACE, SOHO, etc.) at 1 AU in various energy ranges. In some events the first-order pitch-angle anisotropy of the particles distribution is not-negligible. We calculate the average perpendicular displacement due to the gradient/curvature drift in an inhomogeneous turbulence accounting for pitch-angle dependence for two MHD turbulence models: (a) 3-D isotropic, (b) anisotropic as conjectured by Goldreich-Sridhar. We find in both cases that the drift scales as (1 − μ2)2 with the cosine of pitch-angle μ, in contrast with previous models for transport of SEPs. This result can impact the models of propagation of SEPs through the heliosphere.

Modeling transport of energetic particles in corotating interaction regions: A case study

AbstractWe investigate energetic particle transport in corotating interaction regions (CIRs) through a case study. The CIR event we study occurred on 8 February 2008 and was observed by both the Advanced Composition Explorer (ACE) and the twin Solar TErrestrial RElations Observatory (STEREO) B spacecraft. An in situ reverse shock was observed by STEREO B (1.0 AU) but not ACE (0.98 AU). Using STEREO B observations and assuming the CIR structure does not vary significantly in the corotating frame, we estimate the shock location at later times for both the STEREO B and ACE observations. Further assuming the accelerated particle spectral shape at the shock does not vary with shock location, we calculate the particle differential intensities as observed by ACE and STEREO B at two different times by solving the focused transport equation using a Monte Carlo simulation. We assume that particles move along Parker's field and experience no cross‐field diffusion. We find that the modulation of sub‐MeV/nucleon particles is significant. To obtain reasonable comparisons between the simulations and the observations by both ACE and STEREO B, one has to assume that the CIR shock can accelerate more particles at a larger heliocentric distance than at a smaller heliocentric distance.

Deterministic model for the transport of energetic particles: Application in the electron radiotherapy

A new deterministic method for calculating the dose distribution in the electron radiotherapy field is presented. The aim of this work was to validate our model by comparing it with the Monte Carlo simulation toolkit, GEANT4. A comparison of the longitudinal and transverse dose deposition profiles and electron distributions in homogeneous water phantoms showed a good accuracy of our model for electron transport, while reducing the calculation time by a factor of 50. Although the Bremsstrahlung effect is not yet implemented in our model, we propose here a method that solves the Boltzmann kinetic equation and provides a viable and efficient alternative to the expensive Monte Carlo modeling.