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The energy dependence of the path-length distribution of cosmic rays at low energies, below relativistic velocities, is studied, and its implications for models of cosmic-ray confinement and propagation in the Galaxy and Galactic halo, including the effects of a possible Galactic wind, are studied. It is found that the mean free path in Galactic propagation must be fully energy-dependent, with the mean of an exponential path-length distribution increasing with increasing energy below 1 GeV per nucleon and decreasing with increasing energy above 1 GeV per nucleon. This indicates that, at low energies, diffusion is not the controlling process. The path-length distribution is not purely exponential but is depleted in short path lengths at low energies. This depletion is energy-dependent, being largest at low energies and decreasing with increasing energy.

The implications of abundance measurements of cosmic-ray nuclei heavier than Fe are examined in light of standard propagation models and nucleosynthetic theory. Suggestions that the cosmic-ray source abundances differ significantly from solar system abundances are not well supported by the data without assuming ad hoc models of preferential acceleration. The solar system abundances of Pb and Bi are split into r-, standard s-, and cyclic s-process components to assess the contributions of these nucleosynthetic processes to the cosmic-ray source. The apparent deficiency of Pb seen in the HEAO 3 HNE data might indicate an absence of Pb from the recycling s-process.

The cosmic-ray source composition is shown to be related to the observed cosmic-ray abundances by a set of linear equations which are valid for either ad hoc path length distributions or quantitative solutions of galactic propagation models. In the limit of no ionization energy loss, this method is exact for all path length distributions and can replace more detailed numerical integrations; it provides a simple way to calculate directly the source composition implied by a particular set of cross sections, observed abundances, and propagation model. This method is used to determine the source abundances of the galactic cosmic rays in a model-independent manner. Compared to a simple exponential, the path length distribution required by observations is deficient in the contributions from short (not greater than 0.5 g/sq cm) paths at energies of a few GeV per nucleon.

The cosmic ray abundances have traditionally been used to determine the elemental and isotopic nature of galactic ray sources and average measures of propagation conditions. Detailed studies of the physics of propagation are usually paired with relatively straightforward estimates of the secondary-to-primary (S/P) ratios. In the work reported here, calculations of elemental abundances are paired with a more careful treatment of the propagation process. It is shown that the physics of propagation does indeed leave specific traces of Galactic structure in cosmic ray abundances.

The direct inversion method of Margolis is used to explore the dependence of Z less than or equal to 28 source abundance determinations on the choice of the pathlength distribution. The source abundances do not depend strongly on the form of the truncation used, although some truncation at the lower energies (compared to a leaky box) is necessary. The decrease of mean grammage with increasing energy is required by the observations. The effects of errors and he use of other secondary to primary ratios is discussed.

The ratio of cosmic ray source abundance to solar-system abundance was examined for individual elements. Correlations of these ratios with first-ionization potential (FIP) and the expected mass-to-charge ratio (A/Q) of the elements in a million-degree plasma are analyzed. The FIP correlation was examined and it is shown that the correlation is affected by the choice of C2 or C1 chondritic meteorites as the solar-system standard for comparison. An A/Q correlation is suggested as a consequence of the shock acceleration model in the hot interstellar medium. The correlations are presented.

Observations of the abundances of elements of charge 62 or Z or = 73 in the cosmic radiation from the HEAO-3 Heavy Nuclei Experiment (HNE) are discussed. These elements, having solar, and presumably source, abundances much less than the heavier Pt and Pb groups, are expected to be largely products of spallation. Thus they are indicators of the conditions prevailing during the propagation of cosmic rays. The abundances have changed from those reported previously due to a different data selection. This results in better charge resolution and in a higher mean energy for the particles. All the particles included were required to have had a cutoff rigidity R sub c 5 GV. This allowed the charge determination to be based solely on the Cherenkov measurement.

The suggestions that the source abundances of cosmic ray nuclei heavier then Fe differ significantly from Solar System abundances are not well supported by the data without assuming preferential acceleration. The Solar System abundances of Pb and Bi are split into r-, standard s-, and cyclic 8-process components; the apprarent deficiency of Pb seen in the HEAO-3 Heavy Nuclei Experiment data might indicate an absence of Pb from the recycling 8-process.

The energy dependence of the secondary to primary ratios in the Cosmic Rays can be explained by a model accounting for the scattering of the particles by self-generated Alfven waves. This model predicts an energy-dependent truncation of the pathlength distribution.

The cosmic ray source composition is shown to be related to the observed cosmic ray abundances by a set of linear equations which are valid for either ad hoc pathlength distributions or quantitative solutions to Galactic propagation models. These relations can be used to propagate abundances from the source or to the source, and the method described here allows a simple propagation of abundance uncertainties. A simultaneous analysis of B/C and (21-25)Fe indicates a need for truncation of the pathlength distribution.

Results of calculations of ultraheavy cosmic ray propagation are examined in the light of recent observations and theoretical advances with the objective of distinguishing the effects of propagation from nucleosynthesis and preferential acceleration. The results presented here have been calculated by the method described in Margolis (1983), with elements from iron (Z = 26) to uranium (Z = 92) combined in a single calculation. The source abundances of Anders and Ebihara (1982) have been used as a reference composition. It is shown, in particular, that the relative abundances of Sr and Ba are substantially increased by using the modified ionization potential dependence (MIPD) compared with solar abundances and the first ionization potential dependence (FIPD) model. In contrast, Pb shows similar enhancements in both FIPD and MIPD models.

The cosmic-ray-source abundances inferred from HEAO-3 observation by the Heavy Nuclei Experiment for Z = 30-60 generally follow the correlation with first-ionization potential which has previously been observed for Z less than 30. However the low Ge abundance suggests that the elemental 'volatility' may be an organizing factor.

The HEAO-3 Heavy Nuclei Experiment has measured elemental abundances of ultraheavy cosmic rays near earth. The elements with atomic number (Z) in the intervals Z = 44-48 and Z = 62-74 arriving at earth are expected to have significant secondary components. However, their source abundances are unlikely to be low enough to warrant treating them as pure secondaries. The present results are consistent with solar system abundances modified for first ionization potential with possibly some enhancement of the r to s ratio.

The interstellar propagation of cosmic rays is investigated using current 'best estimates' for the partial and total cross sections and their energy dependence and the current model of solar modulation. The experimental boron to carbon ratio is reproduced if the mean of the path length distribution decreases with decreasing energy below approximately 1 GeV/nucleon. This energy dependence is compared to shock acceleration models and dynamical halo models using different galactic wind velocities.

The geometry of sunspots has been used to suggest a problem in heat flow. The equation of heat transport is solved for the case of a cylinder with a given thermal conductivity imbedded in an otherwise uniform medium with different conductivity. The surface of this region radiates heat with flux proportional to temperature. At a lower surface, either in heat flux or temperature is held constant. The cylinder can have an anisotropic thermal conductivity. The variations in temperature along the radiating surface have been determined. A simple approximation is noted which has been found to give a general solution with acceptable accuracy. This method may be of some use in other situations requiring the solution of Laplace's equation with a free surface. The analysis is used to set limits on the ratio of diameter to depth for cases which preserve the sharp surface temperature transition across the cylinder.

The secondary to primary ratios B/C, N/O and (Sc-Mn)/Fe in the galactic cosmic rays have been measured in the overall energy interval 30-180 MeV/n with the University of Chicago cosmic ray telescope on board the satellite IMP-8 during the period 1974-1978. These results, together with the values of the same ratios measured at higher energies, have been compared to the results of cosmic ray propagation calculations using different pathlength distributions (PLD) and different levels of solar modulation, in order to select a single set of parameters consistent with all the measured ratios.

Measurements of ultraheavy cosmic rays will provide radioactive chronometers, including the actinides, which are expected to be present in the source. These primary chronometers differ from the Be-10 secondary chronometer in total inelastic cross-section and decay half-life. A propagation code, which includes nuclear fragmentation, radioactive decay, and ionization energy-loss of cosmic rays is being used to investigate the variations in the fluxes and mean ages which would be expected for various models of cosmic ray propagation. Some preliminary results in the actinide region are presented here which indicate that measurements of the relative abundances of the actinides in the cosmic rays will be very useful for understanding source abundances but less useful for studying propagation effects.

The dynamics of grain motion through gas are examined in terms of the injection of isotopically anomalous (compared to solar abundances) material into the early solar nebula. Calculations indicate that the injected grains cannot penetrate to the center of any of a range of reasonable configurations, suggesting the formation of an edge region enriched in injected material. Furthermore, the dynamical behavior of grains in turbulent flows indicates that pockets of grains can have some resistance to turbulent diffusion. The constraints developed here are used to delineate a set of consistent, injected-grain models for the origin of the isotopic anomalies in meteorite inclusions.

The effectiveness of injecting material from outside the solar system into the early solar nebula was studied. Hydrodynamic calculations showed that the conditions of external injection of isotopically anomalous matter resemble a supernova remnant shell impacting an interstellar H I cloud. Since the injection process for grains or gas is determined before the impinging material penetrates a skin layer, the results for an H I edge should be valid for any configuration which joins the interstellar medium with an H I boundary zone. The effects of initial injection velocity, gas cooling, and magnetic fields are considered, and it is shown that grain penetration is limited to a layer with column density on the order of the grain mass/area ratio and that Rayleigh-Taylor instabilities are not expected to be effective at mixing the anomalous matter into the nebula during a cloud/shell interaction.

Isotopic analyses of meteorites suggest the possibility that some interaction between supernova ejecta and grains occurred in the solar nebula. In particular, the dynamics of grain motions in the solar nebula can explain the observed mixing of nucleosynthetic components. The effect of a shock wave on the motions of grains is examined. On the basis of calculations, it is estimated that if grains carried the isotopic anomalies investigated by Lee, Papanastassoiu, and Wasserburg (1978), then those grains could be no bigger than 0.0002 cm in size. A scenario is suggested in which the sluggishness of grains provides a natural way to concentrate and mix the nucleosynthetic components carried by grains in the ejecta and in the solar nebula.

High-energy cosmic-ray interactions can produce neutrinos. The neutrino fluxes are calculated over a range of energies. The sources considered (and their ranges of importance) are cosmic-ray interactions in earth's atmosphere (neutrino energies less than 10,000 GeV), cosmic-ray interactions with ambient hydrogen in galaxies (neutrino energies between 10,000 and 1 million GeV), regions of cosmic-ray acceleration - e.g., pulsars - and cosmic-ray interactions with the microwave background radiation (neutrino energies greater than 100 million GeV). In addition, estimates of the flux from compact sources, such as active galaxies, are made. These flux levels, calculated conservatively, may be high enough for practical detection with a 1-cu km seawater detector; i.e., count rates greater than 1 per day. Such observations would provide information mainly about high-energy physics, but also (over long times) about cosmic-ray spectra, composition, and acceleration, as well as supernova and galactic-nucleus explosions.