Energetic particle transport coefficients in the heliosphere

It is the purpose of this review to summarize and discuss recent research done in the field of particle propagation in the heliosphere. Several lines of approach have been followed to treat this problem. As a starting point the different forms of the transport equation are discussed. Quasi-Linear Theory (QLT) relates the power contained in fluctuations of the Interplanetary Magnetic Field (IMF) to the transport coefficients of energetic particles, an outline of the basic results of this theory is presented followed by a discussion of subsequent corrections made to the original formulation with an emphasis in recent developments where the effects of wave polarization, its propagation respect to the solar wind and the dissipation of power at large frequencies have been taken into account. The numerical approach using test particle trajectory integrations to obtain transport coefficients based on in situ satellite measureents is also discussed. It is well known that the determination of the particles mean free path for solar particle events by alternative methods leads to conflicting results, corrections made to original QLT are attempts to bridge the gap. Determination of the transport parameters from different lines of approach in a comparative basis have been done recently by calculating power spectra of IMF measured at the time solar particles were detected on the same spaceprobe, and performing numerical simulations with equivalent IMF data. Some of the results of such studies point to the solution of the conflicting determinations of the mean free path which has existed for nearly 30 years. An assesment of the present situation in this respect is given. Numerical determinations of transport parameters in the outer heliosphere are also reviewed and its consequences for solar modulation of galactic cosmic rays discussed. Space Science Reviews 62: Printed in Belgium.     

Modulation of Galactic Cosmic Rays at Solar Minimum

Cosmic ray particles respond to the heliospheric magnetic field in the expanding solar wind and its turbulence and therefore provide a unique probe for conditions in the changing heliosphere. During the last four years, concentrated around the solar minimum period of solar cycle 22, the exploration of the solar polar regions by the joint ESA/NASA mission Ulysses revealed the three-dimensional behavior of cosmic rays in the inner and middle heliosphere. Also during the last decades, the Pioneer and Voyager missions have greatly expanded our understanding of the structure and extent of the outer heliosphere. Simultaneously, numerical models describing the propagation of galactic cosmic rays are becoming sophisticated tools for interpreting and understanding these observations. We give an introduction to the subject of the modulation of galactic cosmic rays in the heliosphere during solar minimum. The modulation effects on cosmic rays of corotating interaction regions and their successors in the outer heliosphere are discussed in more detail by Gazis, McDonald et al. (1999) and McKibben, Jokipii et al. (1999) in this volume. Cosmic-ray observations from the Ulysses spacecraft at high heliographic latitudes are also described extensively in this volume by Kunow, Lee et al. (1999). This revised version was published online in August 2006 with corrections to the Cover Date.     

Cosmic Rays at High Heliolatitudes

The Ulysses spacecraft has been the first to orbit the Sun over its poles and to explore the heliosphere at these high heliolatitudes. It has now completed two fast latitude scans, one at solar minimum and one at solar maximum. Since its launch in October 1990, this mission has led to several surprising discoveries concerning energetic particles, cosmic rays, Jovian electrons, the solar wind, the heliospheric magnetic field and the global features of the heliosphere. This review addresses mainly the propagation and modulation of cosmic rays and other charged particles, from both an observational and theoretical point of view, with emphasis on what has been learned from exploring the inner heliosphere to high heliolatitudes. This is done for solar minimum and maximum conditions. The review is concluded with a summary of the main scientific discoveries and insights gained so far from the Ulysses mission.     

Analyses of sidereal and solar anisotropies in cosmic rays

The Sun's interplanetary magnetic field and the solar wind modulate the distribution of galactic cosmic-ray particles in the heliosphere. The particles diffuse inward, convert outward and have drifts in the motion of their gyro-centres. Irregularities in the IMF also scatter particles from their gyro-orbits. These processes are the components of solar modulation and produce streaming (and higher-order anisotropies) of particles in the heliosphere. The anisotropies can be investigated at the Earth by examining the count rates of cosmic-ray detectors. The anisotropic streams appear as diurnal variations in solar and sidereal time in the count rates. Higher-order anisotropies produce generally much smaller semi-diurnal and higher-order variations. Theoretical models of solar modulation predict effects that depend on the polarity of the Sun's magnetic dipole. The solar diurnal and north-south anisotropies can be used to test these predictions. This paper is a short review of analyses of 60 years of cosmic-ray data collected at the Earth for the solar and sidereal diurnal variations present. Past analyses have yielded interesting and controversial results regarding the rigidity spectra and components of these anisotropies. Some of the controversy remains today. Analyses of these anisotropies have also yielded quantitative information about parameters important to solar modulation, such as latitudinal and radial density gradients. The relatively new techniques used for these determinations are explained here. Calculations of these modulation parameters from Earth-based cosmic-ray detectors are reviewed and compared to spaceprobe measurements and theoretical predictions of their values. Recently, investigations of the sidereal and solar diurnal anisotropies have been combined to calculate mean-free-paths of cosmic rays in the heliosphere. The latest conclusions from these analyses are that the parallel mean-free-paths of cosmic rays may depend on the polarity of the Sun's magnetic field. The results of these investigations are included in this paper to indicate the present state of knowledge concerning this facet of cosmic-ray research.Now at Department of Physics, Shinshu University, 3-1-1 Asahi, Matsumoto 390, Japan.     

Three-dimensional cosmic-ray simulations: Heliographic latitude and current-sheet tilt

We present the results from a study of the variations of the cosmic-ray intensity with time, heliographic latitude, and longitude, and for varying interplanetary conditions, using our three-dimensional, time-dependent computer code for cosmic-ray transport in the heliosphere. Our code also produces a solar-wind and interplanetary magnetic field (IMF) configuration which is compared with observations. Because of the fully threedimensional nature of the model calculations, we are able to model time variations which would be expected to be observed along Ulysses's trajectory as it moves to high latitudes. In particular we can model the approximately 13-and 26-day solar-rotation induced variations in cosmic rays, solar wind and IMF, as a function of increasing heliographic latitude, as one moves poleward of the interplanetary current sheet. Our preliminary model results seem to be in general form quite similar to published data, but depend on the physical parameters used such as cosmic-ray diffusion coefficients, boundary conditions, and the nature of the solar wind and IMF and current sheet.     

Energetic particles at high latitudes

We review work on diffusion coefficients of energetic particles with an attempt to extract implications on their behaviour at high latitudes. In the ecliptic plane results from solar energetic particle propagation between the Sun and about 5 AU can be described by an effective radial mean free path _r which is approximately constant as a function of distancer. When particle propagation in three dimensions in the heliosphere is considered it is not sufficient to consider _r only. Jovian electrons can be used as probes to determine the parameters of three-dimensional diffusion. In the polar regions diffusion is dominated by its parallel component. Some predictions how should vary with latitude are discussed. For different choices of this variation we present expectations for intensity-time profiles of solar particle events during the Ulysses polar passages.     

Cosmic Rays Through the Solar Hale Cycle

The Ulysses spacecraft had been the first to orbit the Sun over its poles and to explore the heliosphere at these high heliolatitudes. It has now completed three fast latitude scans, two at solar minimum and one at solar maximum. Since its launch in October 1990, this mission has led to several surprising discoveries concerning energetic particles, cosmic rays, Jovian electrons, the solar wind, the heliospheric magnetic field and the global features of the heliosphere. This review addresses the propagation and modulation of cosmic rays and other charged particles from an observational point of view with emphasis on what has been learned from exploring the inner heliosphere to high heliolatitudes.     

Challenges for the Advanced Composition Explorer

This report is a brief introduction to some of the vital contributions that the Advanced Composition Explorer Mission will make towards our understanding of the origins of matter and acceleration of particles on a wide range of solar and astrophysical scales. Examples of these contributions are drawn from two broad areas of the space sciences. They are: (1) Dynamical phenomena at the Sun and in the inner heliosphere; and (2) The elemental and isotopic composition of matter in the solar wind, solar accelerated ejecta, galactic cosmic radiation and the anomalous nuclear component in the heliosphere. Some current problems with theories intended to account for these phenomena are discussed, including interpretations of the stable and radioactive isotopes in the galactic cosmic rays. This revised version was published online in June 2006 with corrections to the Cover Date.     

The multifuid solar wind termination shock and its influence on the threedimensional plasma structure upstream and downstream

The solar wind termination shock is described as a multi-fluid phenomenon taking into account the magnetohydrodynamic self-interaction of a multispecies plasma consisting of solar wind ions, pick-up ions and shock-generated anomalous cosmic ray particles. The spatial diffusion of these high energy particles relative to the resulting, pressure-modified solar wind flow structure is described by a coupled system of differential equations describing mass-, momentum-, and energy-flow continuities for all plasma components. The energy loss due to escape of energetic particles (MeV) from the precursor into the inner heliosphere is taken into account. We determine the integrated properties of the anomalous cosmic ray gas and the low-energy solar wind. Also the variation of the compression ratio of the shock structure is quantitatively determined and is related to the pick-up ion energization efficiency and to the mean energy of the downstream anomalous cosmic ray particles. The variation of the resulting shock structure and of the solar wind sheath plasma extent beyond the shock is discussed with respect to its consequences for the LISM neutral gas filtration and the threedimensional shape of the heliosphere.     

Integration of Neutron Monitor Data with Spacecraft Observations: a Historical Perspective

Beginning in the early 1950s, data from neutron monitors placed the taxonomy of cosmic ray temporal variations on a firm footing, extended the observations of the Sun as a transient source of high energy particles and laid the foundation of our early concepts of a heliosphere. The first major impact of the arrival of the Space Age in 1957 on our understanding of cosmic rays came from spacecraft operating beyond the confines of our magnetosphere. These new observations showed that Forbush decreases were caused by interplanetary disturbances and not by changes in the geomagnetic field; the existence of both the predicted solar wind and interplanetary magnetic field was confirmed; the Sun was revealed as a frequent source of energetic ions and electrons in the 10–100 MeV range; and a number of new, low-energy particle populations was discovered. Neutron monitor data were of great value in interpreting many of these new results. With the launch of IMP 6 in 1971, followed by a number of other spacecraft, long-term monitoring of low and medium energy galactic and anomalous cosmic rays and solar and interplanetary energetic particles, and the interplanetary medium were available on a continuous basis. Many synoptic studies have been carried out using both neutron monitor and space observations. The data from the Pioneer 10/11 and Voyagers 1/2 deep space missions and the journey of Ulysses over the region of the solar poles have significantly extended our knowledge of the heliosphere and have provided enhanced understanding of many effects that were first identified in the neutron monitor data. Solar observations are a special area of space studies that has had great impact on interpreting results from neutron monitors, in particular the identification of coronal holes as the source of high-speed solar wind streams and the recognition of the importance of coronal mass ejections in producing interplanetary disturbances and accelerating solar energetic particles. In the future, with the new emphasis on carefully intercalibrated networks of neutron monitors and the improved instrumentation for space studies, these symbionic relations should prove to be even more productive in extending our understanding of the acceleration and transport of energetic particles in our heliosphere. This revised version was published online in August 2006 with corrections to the Cover Date.     

The modulation of cosmic rays in the high latitude heliosphere: A computer simulation

Modulation models based on the numerical solution of Parker's transport equation for galactic cosmic rays in the heliosphere make clear predictions about modulation in the high latitude heliosphere. However, for these predictions certain assumptions have to be made, for example, what the heliospheric magnetic field (HMF) looks like above the solar poles and what the spatial dependence of the diffusion coefficients are. For this presentation the general predictions of a standard drift model for the modulation of cosmic rays in the high latitude heliosphere, in particular predictions for the Ulysses trajectory, are discussed and critically reviewed. Preliminary results from Ulysses show a significant increase in the solar wind speed towards higher latitudes. The effects of this strong latitudinal dependence together with different modifications of the HMF at these high latitudes on the apparently too large diffusion and drifts predicted by current models are also shown.     

Theoretical studies of interplanetary propagation and acceleration

Studies evaluating the transport coefficients for energetic particles in interplanetary space are described in relation to particle data.In position space, the main mode of propagation is along field lines but perpendicular diffusion and drift motion is also possible. Diffusion coefficients based on interplanetary magnetic field data are either derived from quasi-linear, adiabatic theory or this theory corrected for finite scattering near 90° pitch angle or by numerical techniques. Relevant particle data includes solar proton event time profile and anisotropy measurements. In general, when Fokker-Planck transport equation solutions are fitted to particle data, the parallel diffusion coefficients obtained still appear rather larger than those given by theoretical estimates. Perpendicular diffusion is shown to be due to field line wandering and random drift motion effects. The importance of drift motion in cosmic ray modulation theory is mentioned.Although much emphasis is currently placed upon shock acceleration in CIR's, statistical acceleration in interplanetary space must be considered. Energetic particles may gain energy from longitudinal waves and cyclotron resonance interactions. Analytical and numerical estimates of the energy space diffusion coefficients are considered. Some reveal a surprising importance to this statistical acceleration and can explain a variety of data.Presented at the Fifth International Symposium on Solar-Terrestrial Physics, held at Ottawa, Canada, May 1982.     

Martian Radiation EnvIronment Experiment (MARIE)

Measurements of radiation levels at Mars including the contributions of protons, neutrons, and heavy ions, are pre-requisites for human exploration. The MARIE experiment on the Mars-01 Odyssey spacecraft consists of a spectrometer to make such measurements in Mars orbit. MARIE is measuring the galactic cosmic ray energy spectra during the maximum of the 24^th solar cycle, and studying the dynamics of solar particle events and their radial dependence in orbit of Mars. The MARIE spectrometer is designed to measure the energy spectrum from 15 to 500 MeV/n, and when combined other space based instruments, such as the Advanced Composition Explorer (ACE), would provide accurate GCR spectra. Similarly, observations of solar energetic particles can be combined with observations at different points in the inner heliosphere from, for example, the Solar Heliospheric Observatory (SOHO), to gain information on the propagation and radial dependence in the Earth-Mars space. Measurements can be compared with the best available radiation environment and transport models in order to improve these models for subsequent use, and to provide key inputs for the engineering of spacecraft to better protect the human crews exploring Mars.     

The Inner Heliosphere - Outer Heliosphere Comparison for Cosmic Ray Modulation

This paper summarizes cosmic ray data on both galactic and anomalous particles in the inner and outer heliosphere near the sunspot minimum in 1995 and 1996 at the end of solar cycle 22. These data come from the IMP spacecraft in the inner heliosphere and the Voyager and Pioneer spacecraft in the outer heliosphere. In the inner heliosphere, the cosmic ray intensities at all energies in 1996 have recovered to almost the same maximum values they had at the last sunspot minimum in 1987 and the intensities are an even closer match to those observed two 11-year cycles earlier in 1976. In the outer heliosphere beyond 40 AU the intensity recovery is very slow and the intensities at all energies and for all species are almost constant in 1995-96 indicating that little further recovery can be expected in this cycle. The intensity of galactic cosmic rays in 1996 is only 0.3-0.5 of that observed at the same radius of 42 AU in 1987 and for anomalous cosmic rays this ratio is only 0.1-0.2. This suggests a dramatically different entry of particles into the heliosphere in the two cycles for both types of particles as well as significantly different particle flow characteristics in the outer heliosphere. The net result of these different characteristics is that near the Earth only a relatively small intensity difference is observed between successive 11-year solar cycles whereas in the outer heliosphere the differences between cycles become very large and may even dominate the overall modulation.     

Mechanisms for Latitudinal Transport of Energetic Particles in the Heliosphere

Energetic particles in the heliosphere, from relatively low-energy particles which are accelerated in Corotating Interaction Regions (CIRs) to galactic cosmic rays, are observed to propagate relatively easily in heliographic latitude. Two mechanisms for this transport appear possible: cross-field diffusion, or, in a recent model for the heliospheric magnetic field, by direct magnetic connection. The commonalties and differences of these two mechanisms are considered, and the need for future observations and modeling efforts are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stochastic Acceleration of Energetic Particles in the Heliosphere

In this paper we assess possible roles of stochastic acceleration by random electric field and plasma motion in the production and transport of energetic particles in the heliosphere. Stochastic acceleration can occur in the presence of multiple small-scale magnetohydrodynamic waves propagating in different directions. Usually, this type of stochastic acceleration is closely related to particle pitch angle scattering or parallel diffusion. Given the values of the parallel diffusion coefficient inferred from the observations of cosmic ray modulation or other energetic particle phenomena in the heliosphere, stochastic acceleration by small-scale waves is much slower than acceleration by shock waves and it is also much slower than adiabatic cooling by the expansion of the solar wind; thus it is considered as inefficient for producing heliospheric energetic particles or for the modulation of cosmic rays. Another type of stochastic acceleration occurs when particles go through random compressions or expansions due to large-scale plasma motion. This acceleration mechanism could be very fast when the correlation time of the fluctuations in plasma compression is short compared to the diffusion time. Particle acceleration by an ensemble of small shock waves or intermittent long wavelength compressible turbulence belongs to this category. It tends to establish an asymptotic p ^?3 universal distribution function quickly if there is no or little large-scale adiabatic cooling. Such a particle distribution will contain an infinite amount of pressure. Back reaction from the pressure is expected to modify the amplitude of plasma waves to an equilibrium state. At that point, the pressure of accelerated particles must remain finite and the accelerated particles could approach a p ^?5 distribution function.     

Theoretical modeling for the stereo mission

We summarize the theory and modeling efforts for the STEREO mission, which will be used to interpret the data of both the remote-sensing (SECCHI, SWAVES) and in-situ instruments (IMPACT, PLASTIC). The modeling includes the coronal plasma, in both open and closed magnetic structures, and the solar wind and its expansion outwards from the Sun, which defines the heliosphere. Particular emphasis is given to modeling of dynamic phenomena associated with the initiation and propagation of coronal mass ejections (CMEs). The modeling of the CME initiation includes magnetic shearing, kink instability, filament eruption, and magnetic reconnection in the flaring lower corona. The modeling of CME propagation entails interplanetary shocks, interplanetary particle beams, solar energetic particles (SEPs), geoeffective connections, and space weather. This review describes mostly existing models of groups that have committed their work to the STEREO mission, but is by no means exhaustive or comprehensive regarding alternative theoretical approaches.     

Corotating Particle Events

The corotating particle events give us a unique opportunity to probe the three-dimensional structures of the heliosphere. This is especially true if we have observations over a period of extreme stability of the CIRs, such as existed over the recent solar minimum. We discuss how the observations fit into the context of current heliospheric magnetic field models. The energetic particle signatures of CIRs throughout the regions of the heliosphere covered by the deep-space missions are reviewed. The CIRs accelerate these particles and at the same time modulate both the high energy galactic cosmic rays and the anomalous cosmic rays.     

Simultaneous Observations of Solar Energetic Particle Events by imp 8 and the Ulysses Cospin High Energy Telescope at High Solar Latitudes

With Ulysses approaching the south solar polar latitudes during a period of high solar activity, it is for the first time possible to study the distribution of solar energetic particles (SEPs) in solar latitude as well as in radius and longitude. From July 1997 to August 2000, Ulysses moved from near the solar equator at ∼5 AU to ∼67° S latitude at ∼3 AU. Using observations of >∼30 MeV protons from Ulysses and IMP-8 at Earth we find good correlation between large SEP increases observed at IMP and Ulysses, almost regardless of the relative locations of the spacecraft. The observations show that within a few days after injection of SEPs, the flux in the inner heliosphere is often almost uniform, depending only weakly on the position of the observer. No clear effect of the increasing solar latitude of Ulysses is evident. Since the typical latitudinal extent of CMEs, which most likely accelerate the SEPs, is only ∼30°, this suggests that the enhanced cross-field propagation for cosmic rays and CIR-accelerated particles deduced from Ulysses’ high latitude studies near solar minimum is also true for SEPs near solar maximum. This revised version was published online in August 2006 with corrections to the Cover Date.