On the universality of asymptotic limits in the theory of field line diffusion and perpendicular transport of energetic particles

We discuss the random walk of magnetic field lines in astrophysical plasmas. Based on the standard theory of field line diffusion we show that there are two asymptotic limits. In these limits field line wandering is universal because in both regimes the field line diffusion coefficient depends only on fundamental length scales and absolute magnetic field strengths. As examples we discuss the field line diffusion coefficient for different prominent turbulence models namely the slab model, the two-dimensional model, and the Goldreich–Sridhar model. We show that the field line diffusion coefficient for the latter model agrees with the results obtained for slab and two-dimensional turbulence in limiting cases. We also discuss the transport of energetic particles perpendicular with respect to the mean magnetic field. Based on the unified nonlinear transport theory we consider again asymptotic limits. It is shown that one can identify four different regimes in which the transport is again universal. In all four cases perpendicular transport only depends on fundamental length scales of turbulence, magnetic field values, and the parallel diffusion coefficient.     

Energetic particle transport in anisotropic magnetic turbulence

We study energetic particle transport in a magnetic field configuration which models the solar wind magnetic turbulence plus the background field. A power-law Fourier amplitude is used for the fully 3D turbulence model, and in order to model anisotropic turbulence, the constant amplitude surfaces in k space are ellipsoids. The turbulence correlation lengths parallel (perpendicular) to the background magnetic field l_∥ (l_⊥) are varied in a wide range, and proton energies from 1 MeV to 10 GeV are assumed. Considering propagation on a distance corresponding to 1 AU, it is found that transport parallel and perpendicular to the background field heavily depends on the turbulence anisotropy, that is on the ratio l_∥/l_⊥. The spatial distribution of energetic particle follows the shape of magnetic flux tube up to about 10 MeV, while for larger energies the structure of the magnetic flux tube is progressively washed out. The scatterplots of particle distribution show intermittent, non Gaussian structures for l_∥ ≪ l_⊥ (quasi slab turbulence), while a more diffusive, Gaussian structure is obtained for l_∥ ≫ l_⊥ (quasi 2D turbulence). The long time behavior of transport shows that anomalous (subdiffusive perpendicular and superdiffusive parallel) transport regimes are obtained for l_∥ ≪ l_⊥, while Gaussian diffusive transport is obtained for both l_∥ ≫ l_⊥ and the isotropic turbulence case.     

Particle transport in a vortex medium

We study numerically particle transport in a two-dimensional coherent vortex field. Reasonable agreement exists between previously derived radial transport coefficients for energetic particles (Verkhoglyadova, O.P., le Roux, J.A. Particle diffusion on vortices in nearly incompressible magnetohydrodynamics. Astrophys. J. 602, 1002–1005, 2004a; Verkhoglyadova, O.P., le Roux, J.A. Cosmic ray transport in a vortex flow. IGPP-UCR Conf. Physics of the Outer Heliosphere (Riverside), AIP Conf. Proc., pp. 243–248, 2004b) and results of numerical simulations. Different physical factors controlling particle momentum change and drifts are analysed. It is shown that the vortex electric field is the main cause of trapped particle motion. Drift due to magnetic field inhomogeneity predominantly disturbs free particle gyroorbit along background magnetic field in the vicinity of a vortex. Our simulations show the development of a subdiffusion regime.     

Acceleration and transport of energeticparticles at CME-driven shocks

Historically, solar energetic particle (SEP) events are classified in two classes as “impulsive” and “gradual”. Whether there is a clear distinction between the two classes is still a matter of debate, but it is now commonly accepted that in large “gradual” SEP events, Fermi acceleration, also known as diffusive shock acceleration, is the underlying acceleration mechanism. At shock waves driven by coronal mass ejections (CMEs), particles are accelerated diffusively at the shock and often reach > MeV energies (and perhaps up to GeV energies). As a CME-driven shock propagates, expands and weakens, the accelerated particles can escape ahead of the shock into the interplanetary medium. These escaping energized particles then propagate along the interplanetary magnetic field, experiencing only weak scattering from fluctuations in the interplanetary magnetic field (IMF). In this paper, we use a Monte-Carlo approach to study the transport of energetic particles escaping from a CME-driven shock. We present particle spectra observed at 1 AU. We also discuss the particle “crossing number” at 1AU and its implication to particle anisotropy. Based on previous models of particle acceleration at CME-driven shocks, our simulation allows us to investigate various characteristics of energetic particles arriving at various distances from the sun. This provides us an excellent basis for understanding the observations of high-energy particles made at 1 AU by ACE and WIND.     

Probing heliospheric diffusion coefficients with solar energetic particles

The dynamics of solar particle events provide a direct link to the understanding of properties of wave–particle interactions, and to the nature of the solar wind fluctuations. Depending on their energy, the often simultaneously observed electrons, protons and ions interact with different wavenumber ranges of the fluctuations, and are sensitive to various aspects of the dynamical nature of the solar wind turbulence. In general, the evolution of particle events is also sensitive to the spatial variation of the transport parameters between the Sun and a few AU. Together with in situ plasma and magnetic field observations this information can be used to extrapolate the properties of transport parameters into the more distant Heliosphere. Recent developments in the theory of parallel transport of energetic particles, and examples for the modelling of solar particle events and the derivation of transport parameters are considered. A dynamical quasi-linear theory is presented which gives special emphasis to the geometry and dynamic nature of the fluctuations, and which is able to provide particle mean free paths solely from observed plasma parameters, in good agreement with those derived by the modelling. Possibilities to apply the above results to the study of other energetic particle processes in the Heliosphere are discussed.     

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 >100 MeV/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 θ_BN, where θ_BN 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 1 AU for five θ_BN’s are calculated for an example shock.     

The structure and dynamics of the Jovian energetic particle distribution

We review the recent progress made in unravelling the properties of the energetic particle population in the magnetosphere of Jupiter. The importance of the findings with respect to mechanisms driving the dynamics of the Jovian system is addressed. We concentrate on the implications of phase space density variations for particle loss and source mechanism. Systematic local time and radial dependencies observed in the characteristics of the energetic ion and electron distributions, specifically the particle pitch angle distributions and particle flow pattern are discussed. They possibly bear important information for disentangling those mechanisms responsible for driving the Jovian aurora and for identifying the magnetospheric source populations. Furthermore, we discuss transient particle events in the tail which point to the importance of reconnection for the tail dynamics.     

Shock acceleration of energetic particles in wave heated corona

The solar wind wave heating models require substantial amount of wave power in order to efficiently heat and accelerate solar wind. The level of fluctuations is however limited by energetic particle observations. The simplest cyclotron sweep models result in convection-dominated transport, contradicting observations. However, models incorporating wave-wave -interactions, which cause wave energy to cascade in wavenumber, allow more reasonable energetic particle transport in the interplanetary space. The mean free path of the energetic particles remains still relatively short in the corona, providing favorable conditions for coronal mass ejection (CME) related shock acceleration. We study the consequences of this scenario on the energetic particle production related to CMEs. The role of self-generated waves is also discussed.     

Cosmic-ray diffusion in the inner heliosphere

For about the last 40 years, we have been trying to understand the propagation of cosmic rays and other energetic charged particles through the interplanetary medium. Identification of the basic processes affecting the propagation, namely diffusion, convection by the solar wind, adiabatic deceleration, and gradient and curvature drifts, was attained early on, but reaching detailed physical understanding, particularly of the roles of diffusion and gradient and curvature drifts, continues as an active topic of research to this day. Particularly unclear is the nature of the cross-field propagation. Many observations seem to require more efficient cross-field propagation than theoretical propagation models can easily produce. At the same time, there are other observations that seem to show strong guidance of the particles by the interplanetary magnetic field. With current measurements from spacecraft near Earth and from the Ulysses spacecraft, which samples nearly the complete range of heliographic latitudes in the inner heliosphere, critical tests of the ways in which cosmic rays and other energetic charged particles propagate through the interplanetary medium are possible. I briefly review the status of observations that are relevant to the characterization of diffusive propagation in the inner heliosphere and will present evidence for a possibly previously overlooked contribution from transport along magnetic flux tubes that deviate dramatically from the average interplanetary spiral configuration.     

Temporal profiles of solar energetic particle events from SOHO/EPHIN data

Temporal profiles of energetic ions and electrons observed at 1 AU during solar energetic particle events are mainly determined by particle injection features, the observer location relative to the source region at the Sun, and the interplanetary space plasma and field conditions during particle transport. In this work, temporal profiles of 18 solar energetic particle events have been analyzed by fitting a pulse function to them in order to find a set of parameters which can be used to characterize the events.     

Energetic particle signatures of geoeffective coronal mass ejections

We have studied statistically associations of moderate and intense geomagnetic storms with coronal mass ejections (CMEs) and energetic particle events. The goal was to identify specific energetic particle signatures, which could be used to improve the predictions of the geoeffectiveness of full and partial halo CMEs. Protons in the range 1–110 MeV from the ERNE experiment onboard SOHO are used in the analysis. The study covers the time period from August 1996 to July 2000. We demonstrate the feasibility of energetic particle observations as an additional source of information in evaluating the geoeffectiveness of full and partial halo CMEs. Based on the observed onset times of solar energetic particle (SEP) events and energetic storm particle (ESP) events, we derive a proxy for the transit times of shocks driven by the interplanetary counterparts of coronal mass ejections from the Sun to the Earth. For a limited number of geomagnetic storms which can be associated to both SEP and ESP signatures, we found that this transit time correlates with the strength of geomagnetic storms.     

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.     

Why should the latitude of the observer be considered when modeling gradual proton events? An insight using the concept of cobpoint

The shape of flux profiles of gradual solar energetic particle (SEP) events depends on several not well-understood factors, such as the strength of the associated shock, the relative position of the observer in space with respect to the traveling shock, the existence of a background seed particle population, the interplanetary conditions for particle transport, as well as the particle energy. Here, we focus on two of these factors: the influence of the shock strength and the relative position of the observer. We performed a 3D simulation of the propagation of a coronal/interplanetary CME-driven shock in the framework of ideal MHD modeling. We analyze the passage of this shock by nine spacecraft located at ∼0.4 AU (Mercury’s orbit) and at different longitudes and latitudes. We study the evolution of the plasma conditions in the shock front region magnetically connected to each spacecraft, that is the region of the shock front scanned by the “cobpoint” (Heras et al., 1995), as the shock propagates away from the Sun. Particularly, we discuss the influence of the latitude of the observer on the injection rate of shock-accelerated particles and, hence, on the resulting proton flux profiles to be detected by each spacecraft.     

Solar particle precipitation into the polar atmosphere and their dependence on hemisphere and local time

The precipitation of solar energetic particles, protons as well as electrons, at high latitudes is commonly assumed to be homogeneous across both polar caps. Using Low-Earth Orbit POES (Polar Orbiting Environmental Satellites) we determine particle penetration ratios into the polar atmosphere for protons ranging from about 0.1 MeV to 500 MeV and for electrons spanning about one order of magnitude in energy with a maximum of 0.3 MeV. Based on power law fits for the POES spectrum we show, that for energies interesting for middle and lower atmosphere chemistry, particle flux over the poles is comparable in magnitude to flux at the geostationary orbit or at L1 in interplanetary space. The time period under study are the solar energetic particle (SEP) event series of October/November 2003 and January 2005.     

Advances in modeling gradual solar energetic particle events

Solar energetic particles pose one of the most serious hazards to space probes, satellites and astronauts. The most intense and largest solar energetic particle events are closely associated with fast coronal mass ejections able to drive interplanetary shock waves as they propagate through interplanetary space. The simulation of these particle events requires knowledge of how particles and shocks propagate through the interplanetary medium, and how shocks accelerate and inject particles into interplanetary space. Several models have appeared in the literature that attempt to model these energetic particle events. Each model presents its own simplifying assumptions in order to tackle the series of complex phenomena occurring during the development of such events. The accuracy of these models depends upon the approximations used to describe the physical processes involved in the events. We review the current models used to describe gradual solar energetic particle events, their advances and shortcomings, and their possible applications to space weather forecasting.     

Non-linear diffusion of cosmic rays

The propagation of cosmic rays in the interstellar medium after their release from the sources – supernova remnants – can be attended by the development of streaming instability. The instability creates MHD turbulence that changes the conditions of particle transport and leads to a non-linear diffusion of cosmic rays. We present a self-similar solution of the equation of non-linear diffusion for particles ejected from a SNR and discuss how obtained results may change the physical picture of cosmic ray propagation in the Galaxy.     

Combining MHD and kinetic modelling of solar flares

Solar flares are explosive events in the solar corona, representing fast conversion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely difficult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging the gap between fluid and kinetic modelling of solar flares. Two types of approaches are discussed: combined MHD/test-particle (MHDTP) models, which can be used for modelling the flaring corona with relatively small numbers of energetic particles, and hybrid fluid-kinetic methods, which can be used for modelling stronger events with higher numbers of energetic particles. Two specific examples are discussed in more detail: MHDTP models of magnetic reconnection and particle acceleration in kink-unstable twisted coronal loops, and a novel reduced-kinetic model of particle transport in converging magnetic fields.     

MONITORING OF ENERGETIC PARTICLE ENVIRONMENT INSIDE THE CHINA-BRAZIL EARTH RESOURCE SATELLITE

On 14 October 1999, the Chinese-Brazil earth resource satellite (CBERS-1) was launched in China. On board of the satellite there was an instrument designed at Peking University to detect the energetic particle radiation inside the satellite so the radiation fluxes of energetic particles in the cabin can be monitored continuously. Inside a satellite cabin, radiation environment consists of ether penetrated energetic particles or secondary radiation from satellite materials due to the interactions with primary cosmic rays.Purpose of the detectors are twofold, to monitor the particle radiation in the cabin and also to study the space radiation environment The data can be used to study the radiation environment and their effects on the electronics inside the satelhte cabin. On the other hand, the data are useful in study of geo-space energetic particle events such as solar proton events, particle precipitation and variations of the radiation belt since there should be some correlation between the radiation situation inside and outside the satellite.The instrument consists of two semi-conductor detectors for protons and electrons respectively. Each detector has two channels of energy ranges. They are 0.5-2MeV and ≥2MeV for electrons and 5-30MeV and 30-60MeV for protons. Counting rate for all channels are up to 104/(cm2@s)and power consumption is about 2.5 W. There are also the additional functions of CMOS TID (total integrated dose) effect and direct SEU monitoring. The data of CBMC was first sent back on Oct. 17 1999 and it's almost three years from then on. The detector has been working normally and the quality of data is good.The preliminary results of data analysis of CBMC not only reveal the effects of polar particle precipitation and radiation belt on radiation environment inside a satellite, but also show some important features of the geo-space energetic particle radiation.As one of the most important parameters of space weather, the energetic charged particles have great influences on space activities and ground tech nology. CBMC is perhaps the first long-term on-board special equipment to monitor the energetic particle radiation environment inside the satellite and the data it accnmulated are very useful in both satellite designing and space research.