Transport Of Energetic Particles Research Articles

Influence of large‐scale interplanetary structures on energetic particle propagation: September 2004 event at Ulysses and ACE

An intense solar energetic particle (SEP) event was detected in September 2004 by near‐Earth spacecraft and by Ulysses at 5.4 AU. Characteristics of the intensity and anisotropy time profiles at both heliospheric locations were determined by the presence of a corotating low‐density, low‐speed, and low‐proton‐beta βp solar wind stream. This low‐βp stream was followed by a faster and denser solar wind that formed a strong compression region. The bulk of energetic particles at 1 AU were observed downstream of this compression region. Only those particles either able to leak from behind the compression region, accelerated by the shock driven by the coronal mass ejection that generated the SEP event as it penetrated into the low‐βp region, or both were observed prior to the main component of the SEP event at 1 AU. Anisotropic ion intensity enhancements observed upstream of this shock resulted from both particle acceleration in a corrugated shock surface and particle propagation within the low‐βp region. The particle event at Ulysses had exceptionally large and long‐lasting (>4 days) field‐aligned anisotropies. These large anisotropies resulted from both leakage of energetic particles from behind the compression region and their propagation within the low‐βp region. We propose a scenario that explains the characteristics of the particle event at both 1 AU and Ulysses. The effects that large‐scale interplanetary structures have on the energetic particle transport determine the properties of the event at both spacecraft. These effects must be carefully considered by models of energetic particle transport in the heliosphere.

Basic physics of Alfvén instabilities driven by energetic particles in toroidally confined plasmas

Superthermal energetic particles (EP) often drive shear Alfvén waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfvén instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfvén waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfvén eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfvén eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfvén instabilities of all three types occur in every toroidal magnetic confinement device with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum Pζ is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.

Non-Thermal Processes in Cosmological Simulations

Non-thermal components are key ingredients for understanding clusters of galaxies. In the hierarchical model of structure formation, shocks and large-scale turbulence are unavoidable in the cluster formation processes. Understanding the amplification and evolution of the magnetic field in galaxy clusters is necessary for modelling both the heat transport and the dissipative processes in the hot intra-cluster plasma. The acceleration, transport and interactions of non-thermal energetic particles are essential for modelling the observed emissions. Therefore, the inclusion of the non-thermal components will be mandatory for simulating accurately the global dynamical processes in clusters. In this review, we summarise the results obtained with the simulations of the formation of galaxy clusters which address the issues of shocks, magnetic field, cosmic ray particles and turbulence.

Anisotropy Signatures of Solar Energetic Particle Transport in a Closed Interplanetary Magnetic Loop

Recent studies have stressed the importance of solar energetic particle (SEP) transport under disturbed interplanetary conditions, including the case of detection inside a closed interplanetary magnetic loop ejected by a preceding solar event. In this case, particles might be observed to arrive from the far leg of the loop, thus arriving at the detector while traveling sunward. We perform numerical simulations of the focused transport of SEPs along Archimedean spiral and magnetic loop configurations. For loop configurations, we consider injection along either the near leg or the far leg of the loop, either with or without compression at the leading edge. We show that there are specific anisotropy signatures of transport in a closed magnetic loop configuration. SEPs traveling sunward cannot have a high, sustained anisotropy due to the effect of inverse focusing. As an example, the relativistic SEP event of 2003 October 28 exhibited unusual directional distributions, with an early peak of particle flow ≈120° and a main peak ≈80° from the radial direction. However, quantitative fitting of data from the Spaceship Earth network of polar neutron monitors indicates that injection along the far leg of an interplanetary loop is not a good description; our analysis strongly favors transport from the Sun to the Earth over a short path length of ~1 AU.

Optical estimation of auroral ion upflow: Theory

This work presents a systematic analysis of optical emissions related to auroral ion upflow. Optical intensities and field‐aligned ion transport are computed for a set of monoenergetic incident electron beams using a combined fluid‐kinetic model. The kinetic portion models the energetic particle transport with a multiple stream approach and provides ionization, excitation, and heating rates to an eight‐moment fluid model of the ionosphere, which then calculates the resulting ion upflow. The analysis is used to develop a technique for estimating upward ion flux from photometric measurements at five discrete wavelengths: 427.8 nm, 557.7 nm, 630.0 nm, 732 nm, and 844.6 nm. The procedure involves (1) estimating the incident particle spectrum by inversion of multiwavelength optical measurements in the magnetic zenith, (2) applying this incident spectrum to the fluid‐kinetic model to estimate the upflow response. The robustness of the procedure is demonstrated by inverting brightnesses computed for a known electron spectrum and then comparing upflow directly calculated from the known spectrum to the upflow calculated from the estimated spectrum. The inversion is found to provide a reliable estimate of the precipitating electron spectrum and ion upflow, even in the presence of realistic uncertainties in brightness. The technique represents a new tool for studying mass coupling between the magnetosphere and ionosphere. Potential applications range from upflow event studies to estimating the total amount of plasma entering the transition region during a substorm surge via fusion of optical data from multiple sensors.

Rate of proton intensity decay in solar cosmic ray events as a generalized characteristic of the interplanetary space

[1] The transport of solar energetic particles in interplanetary space is determined by the structure and dynamics of the solar wind between the source and the observer. The intensity time profile, in particular the decay phase, is determined by the transport processes. In this paper we discuss the decay phases of solar energetic proton events in the energy range 1‐48 MeV for the period 1974‐2001. For events with exponential shape of decay, the dependence of the characteristic time on the exponent of the energetic spectrum , the solar wind velocity V , and the proton energy E assumed in a form (E) = CE n is given. Such presentation allows us to consider the action of three main mechanisms of propagation (diusion, convection, and adiabatic cooling) that determine the value. It is shown that approximately half of decays with the constant value of V is described quite satisfactorily within the frame of the model with predominant convection and adiabatic deceleration in comparison with particle diusion. The dependence of n on heliolongitude of the parent flare (the source of particles) is investigated. INDEX TERMS: 2104 Interplanetary Physics: Cosmic rays; 2114 Interplanetary Physics: Energetic particles; 2194 Interplanetary Physics: Instruments and techniques;

Simulations of coronal shock acceleration in self-generated turbulence

We have recently presented a numerical model to simulate the acceleration and transport of energetic particles at coronal shock waves, which includes the back-reaction of the energetic particles on the Alfvén waves responsible for their scattering in the ambient medium [Vainio, R., Laitinen, T., 2007. Monte Carlo simulations of coronal diffusive shock acceleration in self-generated turbulence. Astrophysical Journal 658, 622–630]. The model results imply that the acceleration of energetic protons to energies exceeding 100 MeV can occur in some minutes in parallel coronal shocks driven by fast CMEs. In this paper we give a detailed description of the numerical model and its foreseen extensions. We extend the parameter study presented in the first paper to cover (shorter and) longer time scales, and present the intensities observed in the interplanetary medium during the initial phases of an SEP event. We also study the scattering mean free path resulting from the self-consistent computations. Finally, the potential of the model to explain ion acceleration up to relativistic energies is discussed.

Acceleration and transport of energetic particles observed in the inner heliosphere

A number of distinct species of energetic particles—ranging from those accelerated at the Sun and heliosphere to galactic cosmic rays, are observed in the inner heliosphere. In turn, a number of different acceleration mechanisms—including stochastic fluctuations, shocks and more-gradual compressions—have been proposed to explain the various observations and each mechanism has its adherents. In this tutorial review, various popular mechanisms are introduced, and the differences between statistical acceleration and acceleration at shocks at quasi-perpendicular and quasi-parallel shocks and compressions are discussed. Spatial transport is an important part of the acceleration process, and the accelerated particles must propagate through the turbulent solar wind to the point of observation. Both the acceleration and the subsequent transport of the particles depend fundamentally on the nature of the ambient, generally turbulent, plasma and electromagnetic fields. New constraints imposed by recent in situ and remote observations of the energetic particles in the inner heliosphere will be discussed.

Comparing proton fluxes of central meridian SEP events with those predicted by SOLPENCO

We have developed an operational code, SOLPENCO, that can be used for space weather prediction schemes of solar energetic particle (SEP) events. SOLPENCO provides proton differential flux and cumulated fluence profiles from the onset of the event up to the arrival of the associated traveling interplanetary shock at the observer’s position (either 1.0 or 0.4 AU). SOLPENCO considers a variety of interplanetary scenarios where the SEP events develop. These scenarios include solar longitudes of the parent solar event ranging from E75 to W90, transit speeds of the associated shock ranging from 400 to 1700 km s −1, proton energies ranging from 0.125 to 64 MeV, and interplanetary conditions for the energetic particle transport characterized by specific mean free paths. We compare the results of SOLPENCO with flux measurements of a set of SEP events observed at 1 AU that fulfill the following four conditions: (1) the association between the interplanetary shock observed at 1 AU and the parent solar event is well established; (2) the heliolongitude of the active region site is within 30° of the Sun–Earth line; (3) the event shows a significant proton flux increase at energies below 96 MeV; (4) the pre-event intensity background is low. The results are discussed in terms of the transit velocity of the shock and the proton energy. We draw conclusions about both the use of SOLPENCO as a prediction tool and the required improvements to make it useful for space weather purposes.

The physics of particle acceleration at the heliospheric termination shock

Cosmic rays are ubiquitous in space, and the essential similarity of their energy spectra in many different regions places significant general constraints on the mechanisms for their acceleration and confinement. Diffusive shock acceleration is at present the most successful acceleration mechanism proposed, and, together with transport in Kolmogorov turbulence, can account for the universal specta. A unique laboratory for studying the acceleration and transport of charged particles is the outer heliosphere, including the solar wind termination shock and heliosheath. A widely accepted paradigm for the transport and acceleration of energetic particles in the heliosphere has evolved over the last few decades. This picture has successfully explained many features of the modulation of galactic cosmic rays and the transport and acceleration of anomalous cosmic rays at the solar-wind termination shock. Recent Voyager observations near and beyond the termination shock have revealed new, and in some cases, unexpected phenomena which have led to questions concerning the established paradigm. The physical interpretation of the observations requires a blunt termination shock, rapid inward motion of the shock and temporal variations over time scales ranging from hours to 22 years. Incorporation of these into the physics has promise of explaining most, if not, all of the observed phenomena while retaining the advantages of the termination shock paradigm for both galactic and anomalous cosmic rays.

Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence

The transport of energetic particles in a mean magnetic field and in the presence of anisotropic magnetic turbulence is studied numerically, for parameter values relevant to astrophysical plasmas. A numerical realization of magnetic turbulence is set up, in which the degree of anisotropy is varied by changing the correlation lengths lx, ly, and lz. The ratio ρ∕λ of the particle Larmor radius ρ over the turbulence correlation length λ is also varied. It is found that for lx,ly⪢lz, and for ρ∕λ≲10−2 transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. In addition, the spatial distribution of particles is clearly non-Gaussian. Such regimes are characterized by a Levy statistics, with diverging second-order moments. Decreasing the ratio lx∕lz, nearly Gaussian (normal) diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for 10−2≲ρ∕λ≲1 because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when ρ∕λ≳1 showing that the interaction between particles and turbulence decreases in these cases. A new regime, called generalized double diffusion, is proposed for the cases when particles are able to trace back field lines. A summary of the physical conditions which lead to non-Gaussian transport is given.

Radial dependence of proton peak intensities and fluences in SEP events: Influence of the energetic particle transport parameters

We study the radial dependence of peak intensities and fluences of solar energetic particle (SEP) events in the framework of the focused transport theory. We solve the focused-diffusion transport equation that includes the effects of solar wind convection, adiabatic deceleration and pitch-angle scattering. We assume a Reid–Axford time profile for the particle injection at the base of a flux tube described by an Archimedean spiral magnetic field whose cross section A( r) expands as r 2 cos( ψ), where r is the radial distance and ψ( r) is the angle between the magnetic field line and the radial direction. We assume that energetic particles propagate along the field line. We locate several observers along the flux tube at radial distances ranging from 0.3 to 1.6 AU. Both peak intensities and event fluences decrease with increasing radial distance. We deduce functional forms to extrapolate peak fluxes and fluences with radial distance that depend on the energy of the particles, the pitch-angle scattering conditions, and the duration of the particle injection. The smaller the mean free path of the particles, the larger the decrease of both peak intensities and fluences with radial distance. The smaller the energy of the particles, the larger the decrease of both peak intensities and fluences with radial distance. Extended particle injections contribute to soften the decrease of the peak intensities with the radial distance but have no influence on the event fluence. We note that mobile particle sources (i.e. traveling interplanetary shocks) may vary the radial dependences deduced in this work.

Dispersion and Transport of Energetic Particles due to the Interaction of Intense Laser Pulses with Overdense Plasmas

We study the angular distribution of relativistic electrons generated through laser-plasma interaction with pulse intensity varying from 10(18) W/cm2 up to 10(21) W/cm2 and plasma density ranging from 10 times up to 160 times critical density with the help of 2D and 3D particle-in-cell simulations. This study gives clear evidence that the divergence of the beam is an intrinsic property of the interaction of a laser pulse with a sharp density gradient. It is entirely due to the excitation of large static magnetic fields in the layer of interaction. The energy deposited in this layer increases drastically the temperature of the plasma independently of the initial temperature. This makes the plasma locally collisionless and the simulation relevant for the current experiments.

High energy particle transport in stochastic magnetic fields in the solar corona

Aims. We study energetic particle transport in the solar corona in the presence of magnetic fluctuations by analyzing the motion of protons injected at the center of a model coronal loop. Methods. We set up a numerical realization of magnetic turbulence, in which the magnetic fluctuations are represented by a Fourier expansion with random phases. We perform test particle simulations by varying the turbulence correlation length λ, the turbulence level, and the proton energy. Coulomb collisions are neglected. Results. For large A, the ratio ρ/λ (with ρ the Larmor radius) is small, and the magnetic moment is conserved. In this case, a fraction of the injected protons, which grow with the fluctuation level, are trapped at the top of the magnetic loop, near the injection region, by magnetic mirroring due to the magnetic fluctuations. The rest of the protons propagate freely along B, corresponding to nearly ballistic transport. Decreasing A, that is, increasing the ratio ρ/λ, the magnetic moment is no longer well conserved, and pitch angle diffusion progressively sets in. Pitch angle diffusion leads to a decrease in the trapped population and progressively changes proton transport from ballistic to superdiffusive, and finally, for small λ, to diffusive. Conclusions. Particle mirroring by magnetic turbulence makes for compact trapping regions. The particle dynamics inside the magnetic loop is non-Gaussian and the statistical description of transport properties requires the use of such ideas as the Levy random walk.

Simulating radial diffusion of energetic (MeV) electrons through a model of fluctuating electric and magnetic fields

Abstract. In the present work, a test particle simulation is performed in a model of analytic Ultra Low Frequency, ULF, perturbations in the electric and magnetic fields of the Earth's magnetosphere. The goal of this work is to examine if the radial transport of energetic particles in quiet-time ULF magnetospheric perturbations of various azimuthal mode numbers can be described as a diffusive process and be approximated by theoretically derived radial diffusion coefficients. In the model realistic compressional electromagnetic field perturbations are constructed by a superposition of a large number of propagating electric and consistent magnetic pulses. The diffusion rates of the electrons under the effect of the fluctuating fields are calculated numerically through the test-particle simulation as a function of the radial coordinate L in a dipolar magnetosphere; these calculations are then compared to the symmetric, electromagnetic radial diffusion coefficients for compressional, poloidal perturbations in the Earth's magnetosphere. In the model the amplitude of the perturbation fields can be adjusted to represent realistic states of magnetospheric activity. Similarly, the azimuthal modulation of the fields can be adjusted to represent different azimuthal modes of fluctuations and the contribution to radial diffusion from each mode can be quantified. Two simulations of quiet-time magnetospheric variability are performed: in the first simulation, diffusion due to poloidal perturbations of mode number m=1 is calculated; in the second, the diffusion rates from multiple-mode (m=0 to m=8) perturbations are calculated. The numerical calculations of the diffusion coefficients derived from the particle orbits are found to agree with the corresponding theoretical estimates of the diffusion coefficient within a factor of two.

Experimental observations of enhanced radial transport of energetic particles with Alfvén eigenmode on the LHD

Clump and hole creations are observed with TAE bursts in energetic neutral spectra at low-magnetic field configurations of the LHD. Energy slowing down of the clump and the hole are also observed, experimentally. From the slowing down time analysis of the clump and/or hole, the location of each orbit is identified. The drift surface of each orbit has its maximum or second maximum close to the gap location of the TAE burst. The simultaneous observations of clump and hole creations in the energetic spectra reveal the enhanced radial transport of energetic particles by TAE bursts on the LHD.

Random Walk of Magnetic Field Lines in Nonaxisymmetric Turbulence

The random walk of turbulent magnetic field lines strongly affects transport of energetic particles in astrophysical plasmas, but is not well understood for general configurations that lack rotational symmetry. Here we derive nonperturbative field-line diffusion coefficients for magnetic fluctuations that are nonaxisymmetric with respect to the mean magnetic field. We consider a superposition of slab plus two-dimensional fluctuations, a model that has proven useful in heliospheric studies. Two independent parameters are introduced to allow polarization of the slab component and stretching of the two-dimensional component. With the assumptions of homogeneity, the diffusion approximation, and Corrsin's independence hypothesis, we derive two coupled biquadratic equations for the diffusion coefficients. The results and underlying assumptions are confirmed by numerical simulations. Special cases of interest include the counterintuitive results that enhanced fluctuations in one direction lead to decreased diffusion in the other direction, and that extreme nonaxisymmetry leads to diffusion coefficients proportional to the rms two-dimensional fluctuation.

Particle acceleration at perpendicular shock waves: Model and observations

On the basis of a recently developed nonlinear guiding center theory for the perpendicular spatial diffusion coefficient κ⊥ used to describe the transport of energetic particles, we construct a model for diffusive particle acceleration at highly perpendicular shocks, i.e., shocks whose upstream magnetic field is almost orthogonal to the shock normal. We use κ⊥ to investigate energetic particle anisotropy and injection energy at shocks of all obliquities, finding that at 1 AU, for example, parallel and perpendicular shocks can inject protons with equal facility. It is only at highly perpendicular shocks that very high injection energies are necessary. Similar results hold for the termination shock. Furthermore, the inclusion of self‐consistent wave excitation at quasiparallel shocks in evaluating the particle acceleration timescale ensures that it is significantly smaller than that for highly perpendicular shocks at low to intermediate energies and comparable at high energies. Thus higher proton energies are achieved at quasiparallel rather than highly perpendicular interplanetary shocks within 1 AU. However, both injection energy and the acceleration timescale at highly perpendicular shocks are sensitive to assumptions about the ratio of the two‐dimensional (2‐D) correlation length scale to the slab correlation length scale λ2D/λ∥. Model proton spectra and intensity profiles accelerated by a highly perpendicular interplanetary shock are compared to an identical but parallel interplanetary shock, revealing important distinctions. Finally, we present observations of highly perpendicular interplanetary shocks that show that the absence of upstream wave activity does not inhibit particle acceleration at a perpendicular shock. The accelerated particle distributions closely resemble those expected of diffusive shock acceleration, and observed at oblique shocks, an example of which is shown.

Dispersion and transport of energetic particles created during the interaction of intense laser pulses with overdense plasma

We present the results of a parametric study of the interaction of intense laser pulse of intensity varying from 10 18 W/cm 2 up to 10 21 W/cm 2 with plasmas of density ranging from 10 times up to 160 times critical density. This study has been performed with the help of large 2D and 3D PIC simulations. It gives clear evidences that the divergence of the beam is an intrinsic property of the interaction of a laser pulse with a sharp density gradient. This divergence is related to the excitation of large static magnetic fields in the layer of interaction. The effective spread is a complex balance between the intensity of the beam and the plasma density.

Theory of energetic particle transport in the magnetosphere: A noncanonical approach

This paper presents a new transport theory suitable for the study of energetic particles in the magnetospheric environment. A Fokker‐Planck diffusion equation governing the variation of the particle distribution function, along with its isotropic and bounce average approximations, is established in the phase space of location and momentum, which is similar to how cosmic rays are treated by the heliospheric community. The equation includes essentially all the particle transport mechanisms: streaming, convection, drift, adiabatic energy change, acceleration by parallel electric field, focusing, and diffusions in location, momentum, and pitch angle. All the coefficients of the equation are directly linked to plasma and magnetic configurations including electromagnetic fluctuations. The theory can form a base for developing full‐scale numerical models of energetic particle transport including acceleration in the magnetosphere. Unlike the conventional theory using canonical variables which is only applicable to the radiation belt of the inner magnetosphere, this theory includes the effects of nonuniform magnetospheric convection and thus is valid for the entire magnetosphere. The derivation of the transport equation has identified some important particle transport mechanisms that have not received careful study by the magnetospheric community. It is found that the compression of magnetospheric plasma can play a significant role in particle acceleration and trapping. The compressional acceleration is the first‐order particle acceleration mechanism, very similar to particle acceleration at shock waves in other space plasma environments. This acceleration mechanism is operable to both electrons and ions. A model map of magnetospheric convection flow shows that the compressional particle acceleration is a large‐scale phenomenon and it is the strongest in the near‐Earth nightside plasma sheet. Magnetospheric compression can also drive particles toward the 90° equatorial pitch angle, which is ideal for trapping them in the geomagnetic field.