The Astrophysical Journal · 1968 · 1.2K citations · 0 references
Natural SciencesAstronomyPhysicsAstrophysicsGalactic AstronomyRadiation TransportRadiation Transport In MatterSolar RadiationSolar WindConvection-diffusionConvection-diffusion ModelingCosmic-ray DiffusionCosmic-ray Energy LossesCosmic-ray ModulationCosmic-ray Transport CoefficientsEnergy Loss ProcessesGalactic Cosmic Rays
Galactic cosmic rays streaming in the solar‑wind cavity can be neglected above a few hundred MeV per nucleon, as shown by convection‑diffusion equations that include energy losses. The authors derive an integral that links the cosmic‑ray intensity inside the solar‑wind cavity to that at infinity using a separable diffusion coefficient and an energy‑loss parameter defined from observable quantities, equivalent to Liouville’s theorem. Experimental data from 1963–1966 confirm the model, showing that modulation of protons, helium, and electrons follows the predicted energy dependence, the diffusion coefficient scales with charge magnitude, and the e‑folding distance for diffusion lies between 0.8 and 1.6 AU, constraining the radial scattering process.
view Abstract Citations (915) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solar Modulation of Galactic Cosmic Rays Gleeson, L. J. ; Axford, W. I. Abstract Beginning with the equations of the convection-diffusion model including energy losses, it is shown that the streaming of galactic cosmic rays in the solar-wind cavity can be neglected above a few hundred MeV per nucleon. For the case in which the diffusion coefficient is separable into radially and rigidity dependent parts, an integral is derived which relates the intensity at points within the cavity to that at infinity through an energy-loss parameter. This parameter is a function of energy; it is defined in terms of observable quantities and is identified, tentatively, as the mean energy lost by the cosmic-ray particles in moving into the interplanetary region. The integral is formally equivalent to that obtained by using Liouvilie's theorem. Experimental data for the modulation of protons and helium ions in 1963-1965 and electrons and protons in 1965-1966 are shown to behave as predicted, down to kinetic energies of a few hundred MeV per nucleon. The diffusion coefficient was proportional to the magnitude of the charge of the cosmic-ray species during these periods, and the analytical results are formally equivalent to those obtained for a heliocentric force field proportional to the magnitude of the charge of the cosmic-ray species. Making use of the observed lower limits of validity, it is shown that the e-folding distance for the diffusion coefficient lies between 0.8 and 1.6 a.u., thus setting limits on the radial dependence of the scattering process. Estimates are given of the changes in energy loss in the periods 1963-1965 and 1965- 1966 and of the energy loss at solar minimum Publication: The Astrophysical Journal Pub Date: December 1968 DOI: 10.1086/149822 Bibcode: 1968ApJ...154.1011G full text sources ADS |