Transport Of Energetic Particles Research Articles

The latitudinal transport of energetic particles associated with corotating interaction regions

We investigate the effect of large‐scale magnetic turbulence in the solar wind on the transport of ∼1–10‐MeV protons associated with corotating interaction regions (CIRs). We develop a quantitative model of the heliospheric magnetic field which is determined by the motions of magnetic foot points near the solar photosphere. The trajectories of many test particles are numerically integrated in this field to examine the variation of the particle distribution function with latitude. The foot points of the magnetic field lines, which extend radially from the source surface, execute a random walk in latitude and longitude. We find that the resulting long‐wavelength magnetic fluctuations lead to significant latitudinal field line diffusion which simultaneously leads to significant latitudinal transport of CIR‐associated energetic particles. The results from our model are qualitatively consistent with recent Ulysses observations of recurrent energetic particle intensity enhancements at high heliographic latitudes.

The transport of energetic particles and cosmic rays in the heliosphere

Abstract We discuss recent observations of energetic particles and cosmic rays lending insight into how these particles are influenced by the interplanetary magnetic field and what can be learned about the field itself by using the energetic particles as probes. Two recent observations on which we focus attention are those by Ulysses at high heliographic latitudes and those by the Advanced Composition Explorer of impulsive solar flare events. The Ulysses observations of low-rigidity energetic particles at high latitudes associated with corotating interaction regions at lower latitudes are consistent with propagation in a stochastic field superimposed on a Parker spiral. These observations indicate that the particles undergo a significant cross-field diffusion. More-recent observation of energetic particles from impulsive solar flare events show structure on a fine scale which seems also to reflect the field-line meandering. Large small-scale gradients normal to the local magnetic field are shown to be completely consistent with significant cross-field diffusion on larger time scales.

ORIGIN OF THE SOLAR WIND: THEORY

A theory is presented for the origin of the solar wind, which is based on the behavior of the magnetic field of the Sun. The magnetic field of the Sun can be considered as having two distinct components: Open magnetic flux in which the field lines remain attached to the Sun and are dragged outward into the heliosphere with the solar wind. Closed magnetic flux in which the field remains entirely attached to the Sun, and forms loops and active regions in the solar corona. It is argued that the total open flux should tend to be constant in time, since it can be destroyed only if open flux of opposite polarity reconnect, a process that may be unlikely since the open flux is ordered into large-scale regions of uniform polarity. The behavior of open flux is thus governed by its motion on the solar surface. The motion may be due primarily to a diffusive process that results from open field lines reconnecting with randomly oriented closed loops, and also due to the usual convective motions on the solar surface such as differential rotation. The diffusion process needs to be described by a diffusion equation appropriate for transport by an external medium, which is different from the usual diffusion coefficient used in energetic particle transport. The loops required for the diffusion have been identified in recent observations of the Sun, and have properties, both in size and composition, consistent with their use in the model. The diffusive process, in which reconnection occurs between open field lines and loops, is responsible for the input of mass and energy into the solar wind.

Acceleration and Transport of Energetic Charged Particles in Space

Energetic charged particles or cosmic rays are found in space wherever the ambient matter density is small enough to allow them to exist. Their observed kinetic energies vary from just above the local thermal energies to in excess of 1020 eV. The energy spectrum is quite smooth, suggesting that a common mechanism is responsible for particles of all energies. Their arrival directions are distributed evenly in solid angle, with the observed anisotropies being quite small even at energies ∼ 1018 eV. Various scenarios for their acceleration are discussed, including 2nd-order Fermi acceleration, shocks and cosmic-ray viscosity. It is concluded that the most likely mechanism for the acceleration of most energetic particles to high energies is diffusive shock acceleration. This mechanism has the benefit of producing a power-law energy spectrum with a spectral index which is very insensitive to parameters and which is close in magnitude to that observed in a variety of contexts. It is also reasonably fast and efficient. Anomalous cosmic rays in the heliosphere are discussed as one example of the success of the shock-acceleration picture.

Transport of energetic charged particles in a radial magnetic field. Part 1. Large-angle scattering

A new approach, the propagating-source method, is introduced to solve the time-dependent Boltzmann equation. The method relies on the decomposition of the particle distribution function into scattered and unscattered particles. It is assumed in this paper that the particles are transported in a constant-velocity spherically expanding supersonic flow (such as the solar wind) in the presence of a radial magnetic field. Attention too has been restricted to very fast particles. The present paper addresses only large-angle scattering, which is modelled as a BGK relaxation time operator. A subsequent paper (Part 2) will apply the propagating-source method to a small-angle quasilinear scattering operator. Initially, we consider the simplest form of the BGK Boltzmann equation, which omits both adiabatic deceleration and focusing, to re-derive the well-known telegrapher equation for particle transport. However, the derivation based on the propagating-source method yields an inhomogeneous form of the telegrapher equation; a form for which the well-known problem of coherent pulse solutions is absent. Furthermore, the inhomogeneous telegrapher equation is valid for times t much smaller than the ‘scattering time’ τ, i.e. for times t [Lt ] τ, as well as for t > τ. More complicated forms of the BGK Boltzmann equation that now include focusing and adiabatic deceleration are solved. The basic results to emerge from this new approach to solving the BGK Boltzmann equation are the following. (i) Low-order polynomial expansions can be used to investigate particle propagation and transport at arbitrarily small times in a scattering medium. (ii) The theory of characteristics for linear hyperbolic equations illuminates the role of causality in the expanded integro-differential Fokker–Planck equation. (iii) The propagating-source approach is not restricted to isotropic initial data, but instead arbitrarily anisotropic initial data can be investigated. Examples using different ring-beam distributions are presented. (iv) Finally, the numerical scheme can include both small-angle and large-angle particle scattering operators (Part 2). A detailed discussion of the results for the various Boltzmann-equation models is given. In general, it is found that particle beams that experience scattering by, for example, interplanetary fluctuations are likely to remain highly anisotropic for many scattering times. This makes the use of the diffusion approximation for charged-particle transport particularly dangerous under many reasonable solar-wind conditions, especially in the inner heliosphere.

Robustness and flexibility in compact quasiaxial stellarators: Global ideal magnetohydrodynamic stability and energetic particle transport

Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic (MHD) stability and energetic particle transport are evaluated. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the nonperiodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.

Multiple scattering and the BGK Boltzmann equation

A multiple scattering formalism is developed for the BGK Boltzmann equation. The formalism is equivalent to constructing the Neumann series for the corresponding integral equation. By using Laplace and Fourier transform methods, the distribution of unscattered particles f0, and the distribution of particles that have undergone n-scatters, fn (n≥1), are determined for the initial value problem in a uniform background medium. The relationship between the Green function solutions obtained by Fedorov and Shakhov (Fedorov Yu I and Shakhov B A 1993 Proc. 23rd Int. Cosmic Ray Conf. (Calgary) vol 3 p 215), Kota (Kota J 1994 Astrophys. J. 427 1035) and Fedorov et al (Fedorov Yu I et al Astron. Astrophys. 302 623-34), in studies of coherent and diffusive transport of energetic charged particles in the interplanetary medium and the multiple scattering series is elucidated. The multiple scattering approach yields results on the number of particles that have done n-scatters (n≥1). This information is not accessible in the Green function solutions given by Fedorov and Shakhov and Fedorov et al in references given above.

Physics of the Space Environment

This book, one in the Cambridge Atmospheric and Space Science Series, joins a growing list of advanced‐level textbooks in a field of study and research known under a variety of names: space plasma physics, solar‐terrestrial or solar‐planetary relations, space weather, or (the official name of the relevant AGU section) space physics and aeronomy. On the basis of graduate courses taught by the author in various departments at the University of Michigan, complete with problems and with appendices of physical constants and mathematical identities, this is indeed a textbook, systematic and severe in its approach.The book is divided into three parts, in length ratios of roughly 6:4:5. Part I, “Theoretical Description of Gases and Plasmas,” starts by writing down Maxwell's equations and the Lorentz transformation (no nonsense about any introductory material of a descriptive or historical nature) and proceeds through particle orbit theory, kinetics, and plasma physics with fluid and MHD approximations to waves, shocks, and energetic particle transport. Part II, “The Upper Atmosphere,” features chapters on the terrestrial upper atmosphere, airglow and aurora, and the ionosphere. Part III, “Sun‐Earth Connection,” deals with the Sun, the solar wind, cosmic rays, and the terrestrial magnetosphere. The book thus covers, with two exceptions, just about all the topics of interest to Space Physics and Aeronomy scientists, and then some (the chapter on the Sun, for instance, briefly discusses also topics of the solar interior: thermonuclear energy generation, equilibrium structure, energy transfer, with a page or two on each). One exception reflects a strong geocentric bias: there is not one word in the main text on magnetospheres and ionospheres of other planets and their interaction with the solar wind (they are mentioned in a few problems). The other exception: the chapter on the terrestrial magnetosphere lacks a systematic exposition of the theory of magnetosphereionosphere coupling.

Coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks and Earth's bow shock revisited

A revised version of the self‐consistent theory of ion diffusive shock acceleration and the associated generation of hydromagnetic waves is presented. The theory generalizes and corrects the theory of Lee [1982, 1983]. Lee assumed a linear dependence of the anisotropic part of the ion distribution function on the cosine of the ion pitch angle. Here the wave growth or damping rate is again calculated using linear theory, but a more general ion anisotropy is calculated using the pitch angle diffusion equation. The wave intensity satisfies a wave kinetic equation, and the ion omnidirectional distribution function satisfies the energetic particle transport equation. These coupled equations are solved numerically and compared with an analytical approximation similar to that derived by Lee. The analytical approximation provides an accurate representation of both the proton distribution and the wave intensity. A comparison is made between the predicted wave magnetic power spectral density adjacent to the shock as a function of frequency and the wave spectrum measured by ISEE 3 at the November 11–12, 1978, interplanetary traveling shock. There is excellent agreement between the predicted and measured power spectral density in the frequency range of 0.03–0.3 Hz. A comparison is also made between the predicted total wave energy density and that observed upstream of Earth's bow shock by the AMPTE/IRM satellite for a statistical survey of ∼400 near‐to nose events from late 1984 and 1985. This comparison revises the result presented by Trattner et al. [1994]. The correlation between the observed wave power and that predicted, based on the observed energetic proton energy density, is very good with a correlation coefficient of 0.92. However, the average observed wave magnetic energy density is ∼63% of that predicted, suggesting possible wave dissipation which is not included in the theory.

Populating of the cusp and boundary layers by energetic (hundreds of keV) equatorial particles

We examine the dynamics of charged particles in the frontside magnetosphere. We show that the existence of a magnetic field minimum in the outer cusp region has significant implications for the large‐scale transport of energetic (a few hundreds of keV) particles that are trapped near the equator. Upon approach (within a few Earth radii) of the magnetopause in the day side sector, these particles are subjected to a mirror force pointing away from the equator and may escape toward high latitudes. We demonstrate that via this process, energetic electrons and ions from the outer radiation belts and ring current may leak into the outer cusp and be scattered back into the nightside plasma sheet. During transport, the particle behavior critically depends upon gradient drift timescale as compared with convection timescale. We show that by diverting energetic equatorial particles toward the frontside magnetopause, dynamical reconfiguration of the magnetospheric field lines during substorms may favor such injections toward high latitudes and loading of the outer cusp. At a given energy, equatorial particles with higher charge state (i.e., larger drift timescale) reside longer in the dayside magnetosphere and are thus more susceptible to transport toward the field minimum.

Energetic particle transport and alpha driven instabilities in advanced confinement DT plasmas on TFTR

The article reviews the physics of fusion alpha particles andenergetic neutral beam ions studied in the final phase of TFTRoperation, with an emphasis on observations in reversed magnetic shear(RS) and enhanced reversed shear (ERS) DT plasmas. Energy resolvedmeasurements of the radial profiles of confined, trapped alphas in RSplasmas exhibit reduced core alpha density with increasing alphaenergy, in contrast to plasmas with normal monotonic shear. Themeasured profiles are consistent with predictions of increased alphaloss due to stochastic ripple diffusion and increased first orbit lossin RS plasmas. In experiments in which a short tritium beam pulse isinjected into a deuterium RS plasma, the measured DT neutron emissionis lower than standard predictions assuming first orbit loss andstochastic ripple diffusion of the beam ions. A microwavereflectometer measured the spatial localization of low toroidal modenumber (n), alpha driven toroidal Alfvén eigenmodes (TAEs) in DTRS discharges. Although the observed ballooning character of the n = 4mode is consistent with predictions of a kinetic MHD stability code,the observed antiballooning nature of the n = 2 mode isnot. Furthermore, the modelling does not show the observed strongdependence of mode frequency on n. These alpha driven TAEs do notcause measurable alpha loss in TFTR. Other Alfvén frequency modeswith n = 2-4 seen in both DT and DD ERS and RS discharges arelocalized to the weak magnetic shear region near qmin. In 10-20% ofDT discharges, normal low n MHD activity causes alpha loss at levelsabove the first orbit loss rate.

Energetic particle transport in compact quasi-axisymmetric stellarators

Hamiltonian coordinate, guiding center code calculations of the confinement of suprathermal ions in quasi-axisymmetric stellarator (QAS) designs have been carried out to evaluate the attractiveness of compact configurations which are optimized for ballooning stability. A new stellarator particle following code is used to predict the confinement of thermal and neutral beam ions in a small experiment with R=145 cm, B=1–2 T and for alpha particles in a reactor size device. As for tokamaks, collisional pitch angle scattering drives ions into ripple wells and stochastic field regions, where they are quickly lost. In contrast, however, such losses are enhanced in QAS so that high edge poloidal flux has limited value in improving ion confinement. The necessity for reduced stellarator ripple fields is emphasized.

Summary talk: The transport of galactic and anomalous cosmic rays in the heliosphere

The field of the transport of galactic and anomalous cosmic rays in the heliosphere shows great vitality, as evidenced by the many excellent papers presented in this symposium. It seems now that the basic transport of energetic charged particles is well understood. The Parker equation is adequate, and what remains is the important and nontrivial task of determining the transport coefficients and the structure of the heliosphere well enough to interpret the cosmic-ray observations. This will permit a better understanding of the physics of cosmic rays, and also lead to more use of cosmic rays as probes of the heliosphere in regions not yet directly explored.

Cosmic-Ray Momentum Diffusion in Magnetosonic versus Alfvénic Turbulent Field

Energetic particle transport in a finite amplitude magnetosonic and Alfvenic turbulence is considered using the Monte Carlo particle simulations, which involve integration of particle equations of motion. We show that in the low-β plasma the cosmic-ray acceleration can be the most important damping process for magnetosonic waves. Assuming such conditions we derive the momentum diffusion coefficient Dp, for relativistic particles in the presence of anisotropic finite-amplitude turbulent wave fields, for flat and Kolmogorov-type turbulence spectra, respectively. We confirm the possibility of larger values of Dp occurring due to transit-time damping resonance interaction in the presence of isotropic fast-mode waves in comparison to the Alfven waves of the same amplitude (cf. Schlickeiser and Miller, 1997). The importance of quasi-perpendicular fast-mode waves is stressed for the acceleration of high velocity particles.

Transport and Acceleration of Energetic Charged Particles near an Oblique Shock

We have developed a numerical simulation code that treats the transport and acceleration of charged particles crossing an idealized oblique, non-relativistic shock within the framework of pitch angle transport using a finite-difference method. We consider two applications: 1) to study the steady-state acceleration of energetic particles at an oblique shock, and 2) to explain observed precursors of Forbush decreases of galactic cosmic rays before the arrival of an interplanetary shock induced by solar activity. For the former, we find that there is a jump in the particle intensity at the shock, which is stronger for more oblique shocks. Detailed pitch angle distributions are also presented. The simple model of a Forbush decrease explains the key features of observed precursors, an enhanced diurnal anisotropy extending several mean free paths upstream of the shock and a depletion of particles in a narrow loss cone at ~0.1 mean free path from the shock. Such precursors have practical applications for space weather prediction.

Imaging Saturns dust rings using energetic neutral atoms

The intense populations of magnetically trap- ped, energetic charged particles that constitute the radiation belts of Saturn’s inner magnetosphere are slowly transported towards the planet by radial diffusion processes. Many of these energetic particles interact with the rings of Saturn and ultimately are lost to the magnetospheric system. Energetic protons with energies greater than ∼ 50 keV will completely penetrate ring particulates with diameters in the sub-micron regime, such as those that are key constitutents of the F, G, and E rings of Saturn. A substantial fraction of those penetrating protons (∼ 60% at 50 keV) will emerge neutralized by the interaction, ending up as hydrogen Energetic Neutral Atoms (ENAs). In this paper we document the ion⧹dust neutralization process as applied to Saturn’s inner magnetosphere and show that it is an important mechanism by which ions are lost to the magnetosphere on interacting with dust. We also show that because the dust particulates emit ENAs, the interactions between the trapped energetic particles and the ring particulates may be observed remotely by an ENA camera that measures the energy, mass species, and the arrival direction of ENAs. Such a camera, the Ion and Neutral Camera (INCA), will fly to Saturn on the Cassini spacecraft as part of the Magnetospheric Imaging Instrument (MIMI). We document the ability of the INCA sensor to use ENAs to measure the energetic-particle⧹ring particulate interactions within Saturn’s inner megnetosphere during the Saturn Orbit Insertion (SOI) phase of the Cassini mission. With such ENA images we can obtain new diagnostics of magnetospheric radial transport of energetic charged particles because the ENA intensities are proportional to these rates. Also, the impact rates for the consideration of sputtering and erosion will be better constrained, and the relative importance of the rings as a sink of radiation belt particles will be determined. Finally, the energy spectra of the ENA emissions will provide a new type of constraint on the size distribution of the ring particulates.

Deconvolution of interplanetary transport of solar energetic particles

We address the problem of deconvolving the effects of interplanetary transport on observed intensity and anisotropy profiles of solar energetic particles with the goal of determining the time profile and spectrum of particle injection near the Sun as well as the interplanetary scattering mean free path. Semi‐automated techniques have been developed to quantitatively determine the best fit injection profile, assuming (1) a general piecewise linear profile or (2) a Reid profile of the form [C/(t − t0)] exp[−A/(t − t0) − (t − t0)/B]. The two assumptions for the form of the injection profile yielded similar results when we tested the techniques using ISEE 3 proton data from the solar flare events of July 20, 1981 (gradual flare), and January 2, 1982 (impulsive flare). For the former event, the duration of injection was much shorter for protons of higher energy (75–147 MeV), which may be interpreted as indicating that the coronal mass ejection‐driven shock lost the ability to accelerate protons to ∼100 MeV after traveling beyond a certain distance from the Sun.

Perpendicular Transport of Low-Energy Corotating Interaction Region–associated Nuclei

We present compelling observational evidence for substantial transport of energetic charged particles across the local average magnetic field. Using data from the STEP/EPACT instrument on board the Wind spacecraft, we find that during three intense corotating interaction region (CIR) events, for periods greater than 12 hr, the observed anisotropy of the particle intensity at 1 AU is often directed at a significant angle to the measured magnetic field direction, which implies significant transport across the local magnetic field. A simple diffusion model is found to fit the three events very well with a large inferred κ/κ. For example, for 80-154 keV nucleon-1 helium, we find that κ/κ=1.47±0.07, κ/κ=0.13±0.02, and κ/κ=0.45±0.05 for the most intense periods of the three events. We believe that this is the first direct, quantitative measurement in space of large cross-field particle transport, utilizing simultaneous measurements of the streaming particle flux, the solar wind velocity and the magnetic field direction.

Monte Carlo simulation of the variation of a binary alloy film composition due to intrinsic resputtering using different working gases

Intrinsic resputtering is inherently associated with the sputtering process. It is caused by energetic neutral particles resulting from primary sputtering events at the target. These energetic particles are target material atoms with energies up to tens of electronvolts and sputter gas neutrals backscattered from the target with energies exceeding 100 eV. To calculate the gas phase transport of energetic particles and the resputtering effects from the vacuum chamber walls and the substrate, we employed the Monte Carlo technique. The yield for each kind of sputtering event (and also the resputtering process) depends on the mass of the impinging particle and the mass and surface binding energy of the sputtered atom. To study the effect of various working gas atoms on the intrinsic resputtering processes, we simulated the deposition of a Cu-Pb film. Cu and Pb atoms have very different surface binding energies and masses. The variation of the working gas influences the energy of the primary sputtered target atoms and the reflected neutrals. Hence the composition of the deposited binary alloy film due to intrinsic resputtering varies with the pressure due to the different energy transfer from the target to the substrate and the surrounding chamber walls. To check the validity of the simulation results, we also performed experiments with an identical geometry with sputtering from a Cu-2.05at.%Pb target using He, Ne, Ar and Xe as the sputter gases.

Energetic particle investigation using the ERNE instrument

Abstract. During solar flares and coronal mass ejections, nuclei and electrons accelerated to high energies are injected into interplanetary space. These accelerated particles can be detected at the SOHO satellite by the ERNE instrument. From the data produced by the instrument, it is possible to identify the particles and to calculate their energy and direction of propagation. Depending on variable coronal/interplanetary conditions, different kinds of effects on the energetic particle transport can be predicted. The problems of interest include, for example, the effects of particle properties (mass, charge, energy, and propagation direction) on the particle transport, the particle energy changes in the transport process, and the effects the energetic particles have on the solar-wind plasma. The evolution of the distribution function of the energetic particles can be measured with ERNE to a better accuracy than ever before. This gives us the opportunity to contribute significantly to the modeling of interplanetary transport and acceleration. Once the acceleration/transport bias has been removed, the acceleration-site abundance of elements and their isotopes can be studied in detail and compared with spectroscopic observations.