Cosmic-ray flow lines and energy changes

In this paper we discuss the particle flow or streaming and energy changes of cosmic rays in the interplanetary region via flow lines in momentum-position space. We consider the steady-state case where particles are released monoenergetically from the Sun or from infinity and study the cosmic-ray traffic pattern in momentum and position arising from monoenergetic sources. The analysis makes extensive use of the result (wherep is the particle momentum,V the solar wind velocity andG the cosmic-ray density gradient) for the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system, developed by us in several recent papers.Deceased.     

Energy changes of cosmic rays in the interplanetary region

A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways:

1. by a rearrangement and reinterpretation of the cosmic-ray continuity equation;
2. by using a scattering analysis based on that of Gleeson and Axford (1967);
3. by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind.

The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉_ad = ?p ?·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.     

Solar wind and spin of small interplanetary particles

The action of the solar corpuscular radiation on the rotational properties of small interplanetary dust particles is investigated. It is shown that the solar wind increases the angular momentum (spin) of the particle. Analytic solutions are presented for dominant terms in which quantities of the orders (v/u) ⁿ ,n 1, are neglected (v is the orbital velocity of dust particle around the Sun andu is the speed of the solar wind particles).     

Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealised solution suggests that the invariant anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.     

Separation of the steady-state cosmic ray equation of transport: A generalization

The one-dimensional, steady-state equation of transport for cosmic rays including convection, diffusion and adiabatic deceleration is separated for a spatial diffusion coefficient with an arbitrary momentum dependence and for an arbitrary spatial dependence of the convection velocityV, and applies for planar, cylindrical and spherical geometries. As an application, the previously obtained spherically symmetric steady-state Green's functions, describing the propagation of cosmic rays in interplanetary space, are generalized to the case where the convection velocity is a function of position.     

Adiabatic Deceleration Effects on the Formation of Heavy Ion Charge Spectra in Interplanetary Space

We investigate the effects of interplanetary propagation on the energy dependence of the mean ionic charge of ~0.1–1 MeV/n iron observed during impulsive solar particle events at 1 AU. A Monte-Carlo approach is applied to solve the transport equation which takes into account spatial diffusion as well as convection and adiabatic deceleration. We find that interplanetary propagation results in a shift of charge spectra observed at 1 AU towards lower energies due to adiabatic deceleration. Taking the above effect into account, we compare predictions of our model of charge-consistent stochastic acceleration with recent ACE observations. A detailed analysis of two particle events shows that our model can give a consistent explanation of the observed iron charge and energy spectra, and allows one to put constraints on the temperature, density, and the acceleration and escape time scales in the acceleration region.     

Interaction of interstellar pick-up ions with the solar wind

The interaction of interstellar pick-up ions with the solar wind is studied by comparing a model for the velocity distribution function of pick-up ions with actual measurements of He⁺ ions in the solar wind. The model includes the effects of pitch-ang'e diffusion due to interplanetary Alfvén waves, adiabatic deceleration in the expanding solar wind and the radial variation of the source function. It is demonstrated that the scattering mean free path is in the range 0.1 AU and that energy diffusion can be neglected as compared with adiabatic deceleration. The effects of adiabatic focusing, of the radial variation of the neutral density and of a variation of the solar wind velocity with distance from the Sun are investigated. With the correct choice of these parameters we can model the measured energy spectra of the pick-up ions reasonably well. It is shown that the measured differential energy density of the pick-up ions does not vary with the solar wind velocity and the direction of the interplanetary magnetic field for a given local neutral gas density and ionization rate. Therefore, the comparison of the model distributions with the measurements leads to a quantitative determination of the local interstellar gas density.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Simulation of solar flare particle interaction with interplanetary shock waves

In order to study the propagation of solar cosmic rays in interplanetary space a computer program has been developed using a Monte-Carlo technique, which traces the histories of particles released impulsively at the Sun. The particle propagation model considers the adiabatic deceleration during the convective and diffusive transport of the particles, and the model of the interplanetary medium incorporates a radially expanding blast wave which exerts a sweeping action on the particles and accelerates them through the first-order Fermi process. It is shown that energetic storm particle events cannot be simulated by assuming a pure sweeping action of the interplanetary blast wave, but that energization of the particles while reflected at the shock can explain many observed features of such events.     

Energy losses of solar cosmic rays in interplanetary space

A simple model of solar cosmic ray propagation which includes diffusion, convection, and energy loss by adiabatic deceleration is studied. A Monte Carlo technique is employed to investigate the variation of mean particle energy in the interplanetary medium after the impulsive release of mono-energetic particles at the Sun. At 1 AU typical energy losses are 43% at 20 h and 64% at 60 h after particle release for a diffusion coefficient (r)= ₀r with =+1/2 and ₀=1.33 × 10²¹ cm² s^–1. When ₀ in this model is reduced by a factor of 4, the energy loss is greater by a factor of 2 at 60 h after particle release. When is increased, the energy losses are greater. Using the model parameters above, an increase in solar wind speed from 300 to 600 km s^–-1 gives rise to energy losses that are greater again by factor of 2 at a time of 60 h. Results are compared with an observation by Murray et al. (1971) of a knee in the energy spectrum of solar protons. It is not considered likely that the change in the energy of the knee with time requires, in addition to adiabatic deceleration, another energy change process which acts to increase the energy of particles.Part of this work was performed while the author was at CSIRO, Division of Radiophysics, Epping, NSW, Australia; also supported in part by the U.S. Atomic Energy Commission.     

Three solar filament disappearances associated with interplanetary low-energy particle events

Three low-energy particle events (35–1600 keV) associated with interplanetary shocks, detected at 1 AU by ISEE-3, have been identified as originating in solar disappearing filaments instead of large flares. This increases to fourteen the number of events of this kind presently known. The observational characteristics of these non-flare generated events are similar to the ones of the other eleven events already known (i.e., absence of type II or IV bursts, weak X-ray emission, H brightening in the surroundings of the filament disappearance, frequent presence of a double-ribbon event, slow propagation of the generated interplanetary shock, lack of shock deceleration).     

Aberration of light and the Poynting-Robertson effect

Correct and complete (to terms of orderv/c) derivation of the Poynting-Robertson effect is presented. It is based on the idea that aberration of light is an important part in the effect of radiation on the motion of (interplanetary) dust particle. Derivations are presented for spherical particles, however, not only for perfectly absorbing ones. It follows from the presented derivations that the Poynting-Robertson effect is purely relativistic phenomenon and cannnot be treated in nonrelativistic manner, although results in orderv/c are sufficient for calculation in the Solar System studies.     

Adiabatic Deceleration of Solar Energetic Particles as Deduced from Monte Carlo Simulations of Interplanetary Transport

Monte Carlo simulations of interplanetary transport are employed to study adiabatic energy losses of solar protons during propagation in the interplanetary medium. We consider four models. The first model is based on the diffusion-convection equation. Three other models employ the focused transport approach. In the focused transport models, we simulate elastic scattering in the local solar wind frame and magnetic focusing. We adopt three methods to treat scattering. In two models, we simulate a pitch-angle diffusion as successive isotropic or anisotropic small-angle scatterings. The third model treats large-angle scatterings as numerous small-chance isotropizations. The deduced intensity–time profiles are compared with each other, with Monte Carlo solutions to the diffusion-convection equation, and with results of the finite-difference scheme by Ruffolo (1995). A numerical agreement of our Monte Carlo simulations with results of the finite-difference scheme is good. For the period shortly after the maximum intensity time, including deceleration can increase the decay rate of the near-Earth intensity essentially more than would be expected based on advection from higher momenta. We, however, find that the excess in the exponential-decay rate is time dependent. Being averaged over a reasonably long period, the decay rate of the near-Earth intensity turns out to be close to that expected based on diffusion, convection, and advection from higher momenta. We highlight a variance of the near-Earth energy which is not small in comparison with the energy lost. It leads to blurring of any fine details in the accelerated particle spectra. We study the impact of realistic spatial dependencies of the mean free path on adiabatic deceleration and on the near-Earth intensity magnitude. We find that this impact is essential whenever adiabatic deceleration itself is important. It is also found that the initial angular distribution of particles near the Sun can markedly affect MeV-proton energy losses and intensities observed at 1 AU. Computations invoked during the study are described in detail.     

On the relative magnitude of streaming velocities of alpha particles and protons at 1 AU

The occurrence at a heliocentric distance of 1 AU of alpha particle streaming velocities larger than proton streaming velocities,v /v _p >1 (Ogilvie, 1975) is investigated on the basis of the theory suggesting the existence in the solar wind of an accelerating force acting preferentially on the alpha particles.Accurate solution of the three-fluid model equations for the quiet solar wind indicates that anecessary andsufficient condition for (v /v _p )_{1 AU}>1 is the presence of a relativelyweak accelerating forceacting in a limited region in the vicinity of 1 AU. If the force is effectiveonly at small heliocentric distances, the alpha particle streaming velocity excess vanishes at distances less than 1 AU, because of the (equalization) action of the dynamical friction force.     

Solar flare injection and propagation of low-energy protons and electrons in the event of 7–9 July, 1966

Simultaneous observations of the 7–9 July 1966 solar particle event by energetic particle detectors on three satellites, IMP-III, OGO-III and Explorer 33 are utilized to show that large spatial gradients are present in the fluxes of 0.5–20 meV protons and 45 keV electrons. The event is divided into three parts: the ordinary diffusive component, the halo, and the core. The core corotates with the interplanetary field, and therefore it and the surrounding halo are interpreted as spatial features which are connected by the interplanetary magnetic field lines to the vicinity of the flare region. Upper limits to the interplanetary transverse diffusion coefficient for 4–20 meV protons at 1 AU are derived from the width of the halo. These are at least two orders of magnitude less than the parallel diffusion coefficient for the same energy particles.It is argued that the observed flux variations cannot be explained by an impulsive point source injection for any physically reasonable diffusion model. Instead, since the interplanetary transverse-diffusion coefficient is small for these low-energy particles, the observed spatial features are interpreted as the projection to 1 AU by the interplanetary field lines of an extensive injection profile at the sun. The geometry of the injection mechanism is discussed and it is suggested that some temporary storage of the flare particles occurs near the sun.Now at NASA, Goddard Space Flight Center, Greenbelt, Md., U.S.A.     

Analysis of the complex solar particle event on April 29–30, 1973

Based on the data of the high-apogee satellite Prognoz-3, the April 29–30, 1973 solar particle event is analysed. The event's complex energetic particle, interplanetary magnetic field and solar wind plasma properties are discussed. The unusual behaviour of solar particles up to energies 100 MeV can well be explained in terms of the interaction with an interplanetary shock wave system passing the Earth. Assuming that the structure of the interplanetary shock wave system is similar to that considered first by Parker (1961) and Gold (1959) and reviewed later by Hundhausen (1972) and Dryer (1974, 1975), the main characteristics of the energetic particle fluxes, solar wind and interplanetary magnetic field can be understood.     

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.     

The 1990 May 24 solar cosmic-ray event

This paper presents an integrated analysis of GOES 6, 7 and neutron monitor observations of solar cosmic-ray event following the 1990 May 24 solar flare. We have used a model which includes particle injection at the Sun and at the interplanetary shock front and particle propagation through the interplanetary medium. The model does not attempt to simulate the physical processes of coronal transport and shock acceleration, therefore the injections at the Sun and at the shock are represented by source functions in the particle transport equation. By fitting anisotropy and angle-average intensity profiles of high-energy (>30 MeV) protons as derived from the model to the ones observed by neutron monitors and at GOES 6 and 7, we have determined the parameters of particle transport, the injection rate and spectrum at the source. We have made a direct fit of uncorrected GOES data with both primary and secondary proton channels taken into account.The 1990 May 24–26 energetic proton event had a double-peaked temporal structure at energies 100 MeV. The Moreton (shock) wave nearby the flare core was seen clearly before the first injection of accelerated particles into the interplanetary medium. Some (correlated with this shock) acceleration mechanism which operates in the solar corona at a height up to one solar radius is regarded as a source of the first (prompt) increase in GOES and neutron monitor counting rates. The proton injection spectrum during this increase is found to be hard (spectral index 1.6) at lower energies ( 30 MeV) with a rapid steepening above 300 MeV. Large values of the mean free path ( 1.8 AU for 1 GV protons in the vicinity of the Earth) led to a high anisotropy of arriving protons. The second (delayed) proton increase was presumably produced by acceleration/injection of particles by an interplanetary shock wave at height of 10 solar radii. Our analysis of the 1990 May 24–26 event is in favour of the general idea that a number of components of energetic particles may be produced while the flare process develops towards larger spatial/temporal scales.Visiting Associate from St. Petersburg State Technical University, St. Petersburg 195251, Russia.     

The propagation of solar cosmic-ray bursts

A model is presented in which we show analytically the three phases of anisotropy which occur during solar cosmic-ray events observed in the 7.5 MeV to 21 MeV kinetic-energy interval and reported by McCracken et al. (1971): (i) a highly anisotropic, near field-aligned, initial phase, (ii) a convective phase, and (iii) a late-time phase in which the anisotropy is approximately perpendicular to the mean interplanetary magnetic field. The model is based on the cosmic-ray particles being convectively transported out from the Sun, undergoing anisotropic diffusion along the interplanetary magnetic-field lines, and losing energy by adiabatic deceleration or by collision processes. The event is seen simply as a pulse moving outward from the Sun after a cosmic-ray burst with a negative density-gradient in front of it and a positive gradient behind. The convective phase (ii) occurs as the spatial peak moves past the observer and has a propagation speed V _d associated with it; the anisotropy vector late in the decay phase (iii) is the result of a residual balance between the radial outward convection and the inward radial component of the anisotropic diffusion. The mathematical solutions are based upon a diffusion coefficient proportional to heliocentric radius and independent of energy and are thus rather special. However they yield formulae for the propagation speed of the convective phase and the direction in space of the long-time anisotropy which are useful as a guide to the dependence of these quantities on the solar wind speed V, the diffusion coefficient and the spectral index . In this model V _d increases with V, , and ; and , the angle between the anisotropy vector at infinite time and the outward radial direction increases with /V and decreases as is increased. These predictions of the dependence of and V _d upon V, , and are open to observational verification.     

Study of travelling interplanetary phenomena report

Scientific progress on the topic of energy, mass, and momentum transport from the Sun into the heliosphere is contingent upon interdisciplinary and international cooperative efforts on the part of many workers. Summarized here is a report of some highlights of research carried out during the SMY/SMA by the STIP (Study of Travelling Interplanetary Phenomena) Project that included solar and interplanetary scientists around the world. These highlights are concerned with coronal mass ejections from solar flares or erupting prominences (sometimes together); their large-scale consequences in interplanetary space (such as shocks and magnetic bubbles); and energetic particles and their relationship to these large-scale structures. It is concluded that future progress is contingent upon similar international programs assisted by real-time (or near-real-time) warnings of solar activity by cooperating agencies along the lines experienced during the SMY/SMA.     

SCR Steady State Distribution Function and Scattering Properties of the Interplanetary Medium

The propagation of energetic particles in the interplanetary space is considered on the basis of kinetic equation describing the scattering of charged particles by magnetic irregularities and the particle focusing by regular magnetic field. Our analysis confirms that angular distribution of solar cosmic rays contains a valuable information about properties of the particle scattering in the interplanetary magnetic field. Steady state solutions of the kinetic equation are applied to the analysis of solar proton events.