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For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 90 deg, the actual Fokker-Planck coefficient contains a delta function which has been overlooked in the past. The implications of these corrections on the possibility of relating cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

The possibility is suggested that the enhancement of cosmic-ray oxygen and nitrogen observed at about 10 MeV per nucleon could result from neutral interstellar particles that are swept into the solar cavity by the motion of the sun through the interstellar medium. These particles are subsequently ionized and accelerated. It is pointed out that this mechanism imposes no severe requirements either on the number of particles that have to be accelerated or on the energy that has to be removed from the solar wind to perform this acceleration.

Development of a simple formulation of the cosmic ray modulation problem which involves the use of the omnidirectional part of the distribution function in phase space, and the magnitude of the momentum or the rigidity. It is shown that, by employing the proposed formulation, the Compton-Getting factor is greatly simplified, and the well-known force-field equation is reduced to a one-dimensional Vlasov equation. In addition, another Vlasov equation can be written for the very low energy galactic particles which are convected by the solar wind.

The major features of the propagation of flare particles in the interplanetary medium are discussed in terms of the classic well-behaved flare having unique impulsive injection and a smooth time profile. Topics include flare events, their frequency of occurrence, development of a typical event, energy spectra, proton and electron types, charge and isotopic composition, solar flares and particle accelerations, radio and X-ray observations, the Fermi mechanism, the betatron mechanism, acceleration models, plasma instabilities, two-stage acceleration, propagation mechanisms, the anisotropic stage, the diffusive stage, and the convection and energy loss stage.

The important aspects of solar modulation of galactic cosmic rays are outlined. The conditions in the interplanetary medium that affect the modulation are summarized, and equations are developed to describe the behavior of cosmic rays in the solar system, including the effects of diffusion, convection, and energy loss due to adiabatic deceleration in the expanding solar wind. The particle diffusion coefficient is determined from the power spectra of interplanetary magnetic field irregularities. After some solutions for the modulation equations have been derived, the probable forms of the unmodulated cosmic ray spectra are discussed. Other topics include solar cycle variations, energy loss effects, anisotrophies, and gradients.

It is proposed that the enhancements of cosmic ray oxygen and nitrogen observed at approximately 10 MeV/nucleon could result from neutral interstellar particles which are swept into the solar cavity. This is caused by motion of the sun through the interstellar medium, and the particles are subsequently ionized and accelerated.

One possible explanation for quiet-time electron increases, increases in the intensity of 3-12 MeV interplanetary electrons that have been reported by McDonald, Cline and Simnett, is discussed. It is argued that the electrons in quiet-time increases are galactic in origin, but that the observed increases are not the result of any variation in the modulation of these particles in the inner solar system. It is suggested instead that quiet-time increases may occur when more electrons than normal penetrate a modulating region that lies far beyond the orbit of earth. The number of electrons penetrating this region may increase when field lines that have experienced an unusually large random walk in the photosphere are carried by the solar wind out to the region. As evidence for this increased random walk, it is shown that five solar rotations before most of the quiet-time increases there is an extended period when the amplitude of the diurnal anisotropy, as is measured by the Deep River neutron monitor, is relatively low. Five rotations delay time implies that the proposed modulating region lies at approximately 30 AU from the Sun, assuming that the average solar wind speed is constant over this distance at approximately 400 km/sec.

The problems associated with determining the loss of energy by interstellar cosmic ray particles as they pass through interplanetary space to earth are discussed.

Observations of the scatter-free electron events from solar active region McMath No. 8905 are presented. The measurements were made on Explorer 33 satellite. The data show that more than 80% of the electrons from these events undergo no or little scattering and that these electrons travel only approximately 1.5 a.u. between the sun and the earth. The duration of these events cannot be accounted fully by velocity dispersion alone. It is suggested that these electrons could be continuously injected into interplanetary medium for a time interval of approximately 2 to 3 minutes. Energy spectra of these electrons are discussed.

An explanation for quiet-time electron increases is proposed which predicts as the existence of a modulating region for cosmic ray particles lying at approximately 30 AU from the Sun.

Cosmic ray particle transport in solar corona by drifting along current sheets separating discontinuous magnetic field structures

Astronomical model and theoretical physics of expanding universe with evolving sources effects on low energy cosmic rays

Quiet-time electron increases - measure of conditions in outer solar system

Low energy cosmic ray intensity increase at propagating interplanetary shock wave front, discussing one dimensional model with particles undergoing convection and diffusion

Compound diffusion of cosmic rays along interstellar magnetic field lines

Galactic cosmic ray solar modulation in interplanetary medium, discussing spherically symmetric model

Cosmic ray energy loss in interplanetary medium, discussing solar wind effects on low energy particles

Cosmic ray radial gradients and anisotropies, describing behavior in interplanetary medium

Interstellar cosmic ray spectra from nonthermal radio background, obtainig electrons and protons modulation by diffusion-convection energy loss theory

Solar modulation of galactic cosmic rays

Increases in low energy cosmic ray intensity at front of propagating interplanetary shock waves

Force field model for galactic cosmic rays modulation by solar cycles, noting agreement with Fokker-Planck equation analytic and numerical solutions

Radial gradients and anisotropies of cosmic rays in interplanetary medium

Equations governing cosmic ray modulation and approximate equations valid at high and low energies

Solar cosmic ray anisotropies in terms of model with particles propagating along interplanetary magnetic field undergoing pitch-angle scattering

Solar wind convection and energy changes effects on solar cosmic rays, solving time dependent spherically symmetric Fokker-Planck equation

It is argued that it is necessary to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyroradii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies of above several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities. Particles with gyroradii much less than this mean separation appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. With this system of two correlation lengths the cosmic ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (about 50 MeV/nucleon).

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Cyclotron damping by suprathermal fluxes of protons and electrons in the interplanetary medium will greatly attenuate high frequency Alfven waves and whistler waves within distances 1 AU of the sun. Electrons with energies between 50 eV to 2 KeV are heated as a result of damping interplanetary whistler waves with frequencies 2 omega meson/2 pion 30 Hz in the frame of the solar wind. This heating may account, in part, for the observed suprathermal tail of solar wind electrons. Protons with energies approximately 50 KeV damp Alfven waves with frequencies .001 omega meson/2 pion .01 Hz. This damping mechanism may explain several features of a scatter free solar electron events and high intensity, anisotropic solar proton streams.

Consideration is given to whether the modulation of low energy solar cosmic ray nuclei between the sun and earth can be so extreme that the fluxes observed at 1 AU imply (1) that the cosmic ray energy density in the solar atmosphere is comparable to the thermal energy density, and/or (2) that the cosmic ray intensity is sufficient in the solar atmosphere to produce detectable fluxes of secondary particles such as low energy positrons. It was found that such large modulation is compatible with observations, provided that the modulation occurrence is confined within a solar envelope lying within approximately 0.2 to 0.3 AU of the sun. There is, however, no compelling observational evidence to require that the modulation is this large.

It is argued that it is appropriate to consider two correlation lengths for interplanetary magnetic field fluctuations. For particles with gyro-radii large enough to encounter and be scattered by large-scale tangential discontinuities in the field (particles with energies greater than or approximately equal to several GeV/nucleon) the appropriate correlation length is simply the mean spatial separation between the discontinuities, L approximately 2 x 10 to the 11th power. Particles with gyro-radii much less than this mean separation (energies less than or approximately equal to 100 MeV/nucleon) appear to be unaffected by the discontinuities and respond only to smaller-scale field fluctuations. For these particles the correlation length is shown to be L approximately 10 to the 10th power cm. With this system of two correlation lengths the cosmic-ray diffusion tensor may be altered from what was predicted by, for example, Jokipii and Coleman, and the objections raised recently by Klimas and Sandri to the diffusion analysis of Jokipii may apply only at relatively low energies (approximately 50 MeV/nucleon).

The suggestion by Lin et al. (1972) that a distinct spectral feature exists at about 200 keV, which could be due to a neutron-decay electron component of either solar or galactic origin, is examined. Alternative sources models, including production by nearby galactic objects or acceleration at the outer boundary of the solar system, are also considered.

The IMP spacecraft monitoring of the behavior of cosmic rays in the interplanetary medium is considered, especially the behavior of 0.5 to 1.9 pj (3 to 12 MeV) interplanetary electrons. A cosmic ray phenomenon was detected in the behavior of these electrons, and a possible explanation for this phenomenon is presented, which, if correct, gives clues about interplanetary conditions far beyond the orbit of the earth.

A quiet time component of interplanetary electrons having energies above solar wind energies and below those characterized as cosmic radiation was observed. Its energy spectrum falls with energy from 18 keV to 1.8 MeV, but it shows a feature in the 100 to 300 keV range. The observed temporal variations of the intensity suggest that the 18 to 100 keV portion is solar and the 0.3 to 1.8 MeV portion is galactic in origin. Solar and terrestrial neutron decay electrons appear inadequate to explain the 100 to 300 keV feature.

Spectra of modulated galactic cosmic rays are expressed in terms of the Compton-Getting coefficient C. This parameter can reveal the energy range over which the force field approximation is valid, and the range where convection effects dominate those of diffusion. A value of C near zero over an extended low energy range implies that the radial gradient at low energies can not be large. This small gradient may imply that the diffusion coefficient increases beyond 1 AU less rapidly than proportionally to heliocentric radial distance, and/or there is essentially no scattering for a sizeable distance from the Sun to earth. The behavior of C with rigidity (or energy) is discussed in terms of the omnidirectional distribution function f sub zero. Contours of constant f sub zero in the heliocentric distance vs rigidity plane are useful for illustrating the mean rigidity loss experienced by cosmic rays in the interplanetary medium.