Transport Of Energetic Particles Research Articles

Gyrokinetic simulations of mesoscale energetic particle-driven Alfvénic turbulent transport embedded in microturbulence

Energetic particle (EP) transport from local high-n toroidal Alfvén eigenmodes (TAEs) and energetic particle modes (EPMs) is simulated with a gyrokinetic code. Linear and nonlinear simulations have identified a parameter range where the longwave TAE and EPM are unstable alongside the well-known ion-temperature-gradient (ITG) and trapped-electron-mode (TEM) instabilities. A new eigenvalue solver in GYRO facilitates this mode identification. States of nonlinearly saturated local TAE/EPM turbulent intensity are identified, showing a “soft” transport threshold for enhanced energetic particle transport against the TAE/EPM drive from the EP pressure gradient. The very long-wavelength (mesoscale) TAE/EPM transport is saturated partially by nonlinear interaction with microturbulent ITG/TEM-driven zonal flows. Fixed-gradient-length, nonlinearly saturated states are accessible over a relatively narrow range of EP pressure gradient. Within this range, and in the local limit employed, TAE/EPM-driven transport more closely resembles drift-wave microturbulent transport than “stiff” ideal MHD transport with a clamped critical total pressure gradient. At a higher, critical EP pressure gradient, fixed-gradient nonlinear saturation fails: EP transport increases without limit and background transport decreases. Presumably saturation is then obtained by relaxation of the EP pressure gradient to near this critical EP pressure gradient. If the background plasma gradients driving the ITG/TEM turbulence and zonal flows are weakened, the critical gradient collapses to the TAE/EPM linear stability threshold. Even at the critical EP pressure gradient there is no evidence that TAE/EPM instability significantly increases transport in the background plasma channels.

Magnetic Decreases (MDs) and mirror modes: two different plasma β changing mechanisms

Abstract. We discuss two different physical processes that create localized high β plasma regions. One is nonlinear wave-steepening, generating magnetic decreases (MDs) by a ponderomotive force. The other is the mirror instability generating alternating high and low β plasma regions. It is demonstrated that MDs and mirror modes are observationally quite different structures. MDs spatially occur in interplanetary space and mirror modes primarily in planetary magnetosheaths. MDs are characterized by: 1) variable (exponentially decreasing number with increasing) angular changes, 2) variable (exponentially decreasing) thicknesses, and 3) no characteristic inter-event spacings. In sharp contrast, mirror modes are characterized by: 1) little or no angular changes across the structures, 2) a characteristic scale size, and 3) are quasiperiodic in nature. Arguments are presented for the recently observed magnetic dips in the heliosheath being mirror mode structures. The sources of free energy for instability are discussed. Both structures are important for energetic particle transport in astrophysical and heliospheric plasmas.

Energetic particle acceleration and transport by Alfvén/acoustic waves in tokamak-like Solar flares

AbstractAlfven/acoustic waves are ubiquitous in astrophysical as well as in laboratory plasmas. Their interplay with energetic ions is of crucial importance to understanding the energy and particle exchange in astrophysical plasmas as well as to obtaining a viable energy source in magnetically confined fusion devices. In magnetically confined fusion plasmas, an experimental phase-space characterisation of convective and diffusive energetic particle losses induced by Alfven/acoustic waves allows for a better understanding of the underlying physics. The relevance of these results in the problem of the anomalous heating of the solar corona is checked by MHD simulations of Tokamak-like Solar flare tubes.

Effects of interplanetary transport on derived energetic particle source strengths

We study the transport of solar energetic particles (SEPs) in the inner heliosphere in order to relate observations made by an observer at 1 AU to the number and total energy content of accelerated particles at the source, assumed to be near the Sun. We use a numerical simulation that integrates the trajectories of a large number of individual particles moving in the interplanetary magnetic field. We model pitch angle scattering and adiabatic cooling of energetic ions with energies from 50 keV nucleon−1 to 100 MeV nucleon−1. Among other things, we determine the number of times that particles of a given energy cross 1 AU and the average energy loss that they suffer because of adiabatic deceleration in the solar wind. We use a number of different forms of the interplanetary spatial diffusion coefficient and a wide range of scattering mean‐free paths and consider a number of different ion species in order to generate a wide range of simulation results that can be applied to individual SEP events. We apply our simulation results to observations made at 1 AU of the 20 February 2002 solar energetic particle event, finding the original energy content of several species. We find that estimates of the source energy based on SEP measurements at 1 AU are relatively insensitive to the mean‐free path and scattering scheme if adiabatic cooling and multiple crossings are taken into account.

Estimation of the fluence of high‐energy electron bursts produced by thunderclouds and the resulting radiation doses received in aircraft

Using recent X‐ray and gamma‐ray observations of terrestrial gamma‐ray flashes (TGFs) from spacecraft and of natural and rocket‐triggered lightning from the ground, along with detailed models of energetic particle transport, we calculate the fluence (integrated flux) of high‐energy (million electronvolt) electrons, X rays, and gamma rays likely to be produced inside or near thunderclouds in high electric field regions. We find that the X‐ray/gamma‐ray fluence predicted for lightning leaders propagating inside thunderclouds agrees well with the fluence calculated for TGFs, suggesting a possible link between these two phenomena. Furthermore, based on reasonable meteorological assumptions about the magnitude and extent of the electric fields, we estimate that the fluence of high‐energy runaway electrons can reach biologically significant levels at aircraft altitudes. If an aircraft happened to be in or near the high‐field region when either a lightning discharge or a TGF event is occurring, then the radiation dose received by passengers and crew members inside that aircraft could potentially approach 0.1 Sv (10 rem) in less than 1 ms. Considering that commercial aircraft are struck by lightning, on average, one to two times per year, the risk of such large radiation doses should be investigated further.

Scalings of energetic particle transport by ion temperature gradient microturbulence

Transport scaling of energetic particles by ion temperature gradient microturbulence in magnetized plasmas is studied in massively paralleled gyrokinetic particle-in-cell simulations. It is found that the diffusivity decreases drastically at high particles energy (E) to plasma temperature (T) ratio because of the averaging effects of the large gyroradius and drift-orbit width, and the fast wave-particle decorrelation. At high energy, the diffusivity follows a (E/T)−1 scaling for purely passing particles, a (E/T)−2 scaling for deeply trapped particles and a (E/T)−1 scaling for particles with an isotropic velocity distribution since the diffusivity therein is contributed mostly by the passing particles.

Electric and magnetic field observations of Pc4 and Pc5 pulsations in the inner magnetosphere: A statistical study

Ultralow frequency (ULF) waves in the Pc4 and Pc5 bands are ubiquitous in the inner magnetosphere and have significant influence on energetic particle transport. Investigating the source and characteristics of ULF waves also helps us better understand the interaction processes between the solar wind and the magnetosphere. However, owing to the limitation in instrumentation and spatial coverage, the distribution of ULF waves in local time and L shell in the inner magnetosphere has not been completely studied. The recent Time History of Events and Macroscale Interactions During Substorms (THEMIS) mission provides unique opportunities to investigate the spatial distribution of ULF pulsations across different L shells with full local time coverage in the inner magnetosphere during solar minimum, with both electric and magnetic field measurements. Pc4 and Pc5 pulsations in the electric field observations are identified throughout 13 months of measurements, covering 24 h in local time. The pulsations are characterized as either toroidal or poloidal (including compressional) mode, depending on the polarization of the electric field. Subsequently, the pulsations' occurrence rate and wave power distributions in radial distance and local time are recorded. While the distributions of both Pc4 and Pc5 events vary greatly with radial distance and local time, Pc4 events are more frequently observed in the inner region around 5–6 RE and Pc5 events are more frequently observed in the outer region around 7–9 RE, which suggests that the field line resonance is an important source of the ULF waves. In the flank regions, the wave power is dominated by the toroidal mode, likely associated with the Kelvin‐Helmholtz (KH) instability. In the noon sector, the Pc5 ULF wave power is dominated by the poloidal mode, likely associated with the solar wind dynamic pressure disturbance. The KH instability plays an important role, suggested by our observations, during the solar minimum when the solar wind dynamic pressure is relatively weak. We also find that the contributions to the Pc5 ULF wave power from the external sources are larger than the contributions from the internal sources. These statistical results are important in characterizing Pc4 and Pc5 waves and also important for any efforts to model the transport of energetic particles in the magnetosphere.

Perpendicular Transport in the Inner Heliosphere: A Quick and Dirty Approach

In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ⊥/κ‖ between 0.02 and 0.1 at 1 AU scaled with r2 as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.

Major Solar Energetic Particle Events of Solar Cycles 22 and 23: Intensities Close to the Streaming Limit

It has been argued that the highest intensities measured near 1 AU during large solar energetic particle events occur in association with the passage of interplanetary shocks driven by coronal mass ejections, whereas the intensities measured early in the events (known as the prompt component) are bounded by a maximum intensity plateau known as the streaming limit. A few events in Solar Cycle 23 showed prompt components with intensities above the previously determined streaming limit. One of the scenarios proposed to explain intensities that exceed this limit in these events invokes the existence of transient plasma structures beyond 1 AU able to confine and/or mirror energetic particles. We study whether other particle events with prompt-component intensities close to the previously determined streaming limit are similarly affected by the presence of interplanetary structures. Whereas such structures were observed in four out of the nine events studied here, we conclude that only the events on 22 October 1989, 29 October 2003, and 17 January 2005 show interplanetary structures that can have modified the transport conditions in a way similar to those events with prompt components exceeding the previously determined streaming limit. The other six events with prompt components close to the previously determined streaming limit were characterized by either a low level of pre-event solar activity and/or the absence of transient interplanetary structures able to modify the transport of energetic particles.

Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Aims. We investigate pitch-angle scattering, which is a fundamental process in the physics of cosmic rays. Methods. By employing the second-order quasilinear theory, the pitch-angle Fokker-Planck coefficient is calculated analytically for the first time. Results. We demonstrate that for sufficiently strong turbulence the pitch-angle Fokker-Planck coefficient is isotropic. The derived results can be used to compute the parallel mean free path for all forms of the turbulence spectrum. We also consider applications, namely the transport of solar energetic particles and the propagation of cosmic rays in the Galaxy. Conclusions. The previously used assumption of isotropic pitch-angle diffusion is indeed correct for sufficiently strong turbulence. An analytical description of nonlinear particle scattering is possible.

ANOMALOUS COSMIC RAYS AS PROBES OF MAGNETIC CLOUDS

Abstract : We report, for the first time, the observation near the Earth of anomalous cosmic ray (ACR) particles throughout the interiors of interplanetary magnetic clouds (MCs) at the same intensity as outside the MCs. ACRs, accelerated in the outer heliosphere, have unique elemental abundances making their identity unambiguous as they probe these clouds from the outside. Thus, MCs, carried out from the sun by coronal mass ejections (CMEs), are seen to contain no structures that are magnetically closed to the penetration of ions with energies above a few MeV per amu . As the MCs expand outward they must fill their increasing volume with ACRs dynamically, to the same degree as neighboring open field lines. These observations cast doubt on conventional ideas about the closed field topologies of MCs and the cross-field transport of energetic particles. The ACR observations conflict with some reports of significant exclusion from MCs of solar energetic particles (SEPs) of comparable energy and rigidity. A process that allows cross-field transport of ACRs may also allow similar transport of SEPs late in events, causing the large spatial extent and uniformity of SEPs in invariant spectral regions extending far behind the CME-driven shock waves.

Particle simulation of energetic particle driven Alfvén modes in NBI heated DIII-D experiments

The mutual nonlinear interactions of shear Alfvén modes and alpha particles can enhance their transport in burning plasmas. Theoretical and numerical works have shown that rapid transport of energetic ions can take place because of fast growing Alfvén modes (e.g. energetic particle driven modes, EPMs). This kind of transport has been observed in experiments as well as in numerical simulations. Hybrid MHD-gyrokinetic codes can investigate linear and nonlinear dynamics of energetic particle (EP) driven modes, retaining the mutual interaction between waves and EPs self-consistently. Self-consistent nonlinear wave–particle interactions (both in configuration and velocity space) are crucial for a correct description of the mode dynamics in the case of strongly driven modes; thus, a non-perturbative approach is mandatory. The knowledge of the threshold characterizing the transition from weakly to strongly driven regimes is of primary importance for burning plasma operations (e.g. for ITER), in order to avoid EPM enhanced EP transport regimes. The hybrid MHD-gyrokinetic code (HMGC) has been applied to the interpretation of phenomena observed in present experiments with neutral beam (NB) heating. In reversed-shear beam-heated DIII-D discharges, a large discrepancy between the expected and measured EP radial density profiles has been observed in the presence of large Alfvénic activity. HMGC simulations with EP radial profiles expected from classical NB deposition as input give rise to strong EPM activity, resulting in relaxed EP radial profiles at saturation level close to experimental measurements. The frequency spectra obtained from several simulations with different toroidal mode numbers, as calculated during the saturated phase when the strong EPMs transform in weak reversed-shear Alfvén modes, are quite close to experimental observations both in absolute frequency and in radial localization. In this work, we discuss in particular the effects of nonlinear coupling between different toroidal mode numbers.

Compound and perpendicular diffusion of cosmic rays and random walk of the field lines: II. Non-parallel particle transport and drifts

Compound transport of energetic charged particles across the mean magnetic field due to field line random walk is investigated by means of a Chapman–Kolmogorov equation. The probability distribution function (pdf) for the particle transport across the field P⊥ is given as a convolution of the pdf for random walk of the magnetic field, PFRW, with the pdf Pp, for particle transport relative to the random walking field. The particle propagator Pp includes the effects of advection, drift, parallel diffusion and local perpendicular diffusion of particles relative to the random walking field. At early times, the particles sub-diffuse across the field due to field line random walk. At late times, the effective cross-field diffusion coefficient has the form κ⊥e = κ⊥ + κF. The diffusion coefficient κ⊥ is the local cross-field diffusion coefficient due to particle scattering in the random magnetic field. The diffusion coefficient κF is due to coherent particle advection parallel to the mean magnetic field B0 coupled with transverse random walk of the magnetic field. Estimates of cross-field diffusion due to field line random walk, advection and drift are obtained both near to the heliospheric current sheet at Earth and at higher helio-latitudes. Cross-field diffusion due to field line random walk and advection is shown to be an important transport mechanism for low-energy particles near the current sheet, where the effects of drifts are negligible. Drift effects and field line random walk are also assessed at higher helio-latitudes off the current sheet, for a model interplanetary magnetic field, with a flat current sheet in the helio-equatorial plane.

A unified model of solar energetic particle transport in structured solar wind

Solar energetic particle (SEP) fluxes, after their propagation from the particles' source to the Earth's orbit, depend on the state of solar wind, which is known to be highly variable in both time and space. Commonly used SEP transport models are based on the assumption of the standard interplanetary magnetic field, which would be the case for a uniform, steady state expansion of solar wind. Modeling of SEP transport in the standard solar wind can be facilitated by the use of a corotating reference frame, wherein the solar wind speed is parallel to interplanetary magnetic field at each point and the magnetic field is static. However, this approach is not possible in the realistic solar wind. This necessitates development of a more general SEP model applicable to particle transport in arbitrarily structured solar wind and in interplanetary coronal mass ejections, magnetic clouds, and shocks. In the framework of focused transport theory, we formulate a practical model of SEP transport in an evolving, structured solar wind. This unified model accommodates the results of three‐dimensional MHD modeling of solar wind based on observations of the sun, solar wind, and SEPs in a particular event. A relation between the generalized focused transport model and the diffusion‐convection equation of cosmic ray transport is discussed.

Perpendicular Transport of Energetic Charged Particles in Nonaxisymmetric Two‐Component Magnetic Turbulence

We examine energetic charged particle diffusion perpendicular to a mean magnetic field B0 due to turbulent fluctuations in a plasma, relaxing the common assumption of axisymmetry around B0 and varying the ratio of two fluctuation components, a slab component with parallel wavenumbers and a two-dimensional (2D) component with perpendicular wavenumbers. We perform computer simulations mostly for 80% 2D and 20% slab energy and a fluctuation amplitude on the order of B0. The nonlinear guiding center (NLGC) theory provides a reasonable description of asymptotic perpendicular diffusion as a function of the nonaxisymmetry and particle energy. These values areroughlyproportionaltotheparticlespeedtimesthefieldlinediffusioncoefficient,withaprefactorthatismuchlower than in the classical field line random walk model of particle diffusion. NLGC predicts a prefactor in closer agreement with simulations. Next we consider extreme fluctuation anisotropy and the approach to reduced dimensionality. For 99% slab fluctuation energy, field line trajectories are diffusive, but the particle motion is subdiffusive. For 99% 2D fluctuation energy, both field lines and particle motions are initially subdiffusive and then diffusive, but NLGC gives unreliable results. The time dependence of the running particle diffusion coefficient shows that in all cases asymptotic diffusionisprecededbyfreestreamingandsubdiffusion,but thelatterdiffersfromstandardcompoundsubdiffusion.We can model the time profiles in terms of a decaying negative correlation of the perpendicular velocity due to the possibility of backtracking along magnetic field lines.

Transport of Energetic Particles by Microturbulence in Magnetized Plasmas

Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves.

Effect of Flux Tubes in the Solar Wind on the Diffusion of Energetic Particles

Current sheets are common structures in the solar wind and possibly the boundaries of individual flux tubes. Observations show that magnetic field directions often change abruptly upon crossing these structures. The presence of these structures introduces a new source of solar wind turbulence intermittency and can affect the transport of energetic particles. Previous studies of energetic-particle transport in the solar wind often assume a uniform large-scale background magnetic field, with a turbulent field superposed. With the existence of flux tubes in the solar wind, this picture needs to be changed. In this Letter, we study the effects of flux tubes on the transport of energetic particles in the solar wind. We construct a model turbulence of the solar wind by including explicitly flux-tube-like structures. In our model, the solar wind is composed of many individual cells with a local uniform mean magnetic field chosen randomly. The turbulence in each cell is modeled by either a slab and/or 2D type. We then calculate numerically the particle diffusion coefficients by following single particle trajectories. Our results show that flux tubes in the solar wind can lead to stronger scatterings of particles in directions both parallel and perpendicular to the large-scale background magnetic field. In particular, a true diffusion in the large-scale perpendicular direction (with respect to B0) is obtained even when the local intrinsic turbulence in individual cells is of pure slab type.

A New Approach to Interplanetary Transport of Solar Energetic Particles in Impulsive Events

Impulsive,3He-rich events originate close to the interface between slow solar wind overlying active regions and a faster solar wind coming from small coronal holes. This causes large-scale magnetic compressions to be an interplanetary environment for solar energetic particle (SEP) transport in impulsive events, which is typically ignored by SEP modelers. We have modeled SEP transport in a simplified corotating solar wind structure to estimate the possible effect of the rising wind speed on particle anisotropy and spectra at 1 AU. Along with traditional modeling of SEP transport in the static magnetic field and the field-aligned solar wind flow of the corotating frame of reference, we have formulated and tested a new model that is the first model of focused transport applicable to a general case of SEP propagation in realistic, dynamic, and structured solar wind. Numerical modeling shows that a fast increase of the wind speed by only 200 km s−1 can strongly affect the SEP flux anisotropy at 1 AU. Accurate analysis of impulsive SEP events can be done with the use of solar wind data, SEP flux anisotropy measurements, and the new approach that accounts for the solar wind structures associated with the sources of impulsive events and uses the general solution of the focused transport problem applicable to SEPs in realistic solar wind.

Open magnetic flux tubes in the corona and the transport of solar energetic particles

We investigate how magnetic fields guide energetic particles through the corona into interplanetary space and eventually to a spacecraft near the Earth. A set of seven simple particle events is studied, where energetic electrons (30–500 keV; Wind spacecraft) or protons (5–55 MeV; SoHO) were released together with low-energy electron beams producing metric-to-kilometric type III emission. Imaging of the coronal (metre-wave) part of this emission with the Nancay Radioheliograph is used to identify the open flux tubes that guide these electrons – and by inference all particles detected at 1 AU. Open coronal field lines are also computed using potential magnetic field extrapolations, constrained by a source surface and by SoHO/MDI measurements in the photosphere (code by Schrijver and DeRosa). We find that in all events the type III radio sources lie in open flux tubes in the potential magnetic field extrapolations. The open flux tubes are rooted in small parts of the parent active region, covering a heliocentric angle of a few degrees in the photosphere. But they expand rapidly above the neighbouring closed magnetic structures and cover several tens of degrees in longitude on the source surface. Some of these open field lines are found to connect the parent active region to the footpoint of the nominal Parker spiral on the source surface, within the uncertainty of about ±10 ◦ inherent to the evaluation of its connection longitude. This is so even when the parent active region is as far as 50 ◦ away. In two cases where the coronal flux tubes point to high heliolatitudes, the detection of Langmuir waves at the Wind spacecraft in the ecliptic plane suggests that the interplanetary field lines curve down to the ecliptic before reaching 1 AU. We conclude that non-radial open flux tubes in the corona can transport particles over several tens of degrees in longitude even in simple impulsive particle events. In all events we studied, potential magnetic field models give an adequate description of these structures.

Are there Kronian electrons in the inner heliosphere?

Context. As the largest in our solar system the Jovian magnetosphere is treated in the literature as the dominant source of a fewMeV electrons, which have been measured by various spacecraft. In particular, observations obtained with Ulysses have significantly broadened the available data base. Aims. We simulated the transports of MeV electrons in the heliosphere on the basis of a time-dependent, three-dimensional modulation model. For this purpose the cosmic rays, the Jovian and the Saturnian electron sources have been, for the first time, considered together in the simulation of electron fluxes. The simulated electron intensities are discussed along the Ulysses and Cassini trajectories. The Ulysses spacecraft already passed by the planet Jupiter twice (1992, 2004), and Cassini passed by Jupiter in 2001 and reached Saturn in the year 2004. The strength of the electron source at Jupiter is relatively well known and well modelled. To determine the source strength of Saturn in comparison to that of Jupiter, we compared all available spacecraft measurements at Jupiter/Saturn in the overlapping energy range. We study the general distribution of Kronian electrons by successively using three different strengths of the Saturn source in our simulations. In addition, the effects of the solar activity are taken into account by varying the velocity field of the solar wind and the anisotropic diffusion tensor. Methods. Studying the particle diffusion is particularly relevant, because the really unknown function in the used transport equation is the diffusion tensor. The Jovian and/or Kronian electrons are suitable for studying the transport of energetic particles because the source locations are well known. Results. At 1 MeV the intensities along the Ulysses and the Cassini trajectories are clearly influenced by the presence of Kronian electrons. Conclusions. Our results reveal that the electrons from the Kronian magnetosphere, as the second largest, cannot be neglected in the very-low MeV energy range.