Cosmic-Ray Modulations in the Solar System and in Interstellar Space

The intensity of cosmic-ray protons between 1959 and 1963 (i.e., near solar maximum and near solar minimum) was modulated twice as much as the intensity of helium at the same velocity, for energies from 0.2 to 0.7 BeV/nucleon. Similar results were obtained by other authors for the modulation between 1963 and 1964 when the intensities of protons and helium nuclei were measured by many investigators. It has been shown by other authors that the ratio of helium nuclei to protons of the same velocity decreases with increasing cosmic-ray energy from about 0.3 to about 0.05 in the energy interval 0.2-10 BeV/nucleon. These observations are shown to be in agreement with Dorman's modification of Parker's solar-modulation theory for intermediate values of rigidity, i.e., with a modulation function of the form $\exp [-\frac{K\left(t\right)\mathrm{}}{R\beta }]$, where $R$ and $\beta$ are the rigidity and velocity of the cosmic-ray particle, respectively, $t$ is time, and $K\left(t\right)\mathrm{}$ depends on various solar-wind parameters. Additional investigations show that while Dorman's expression fits the data well between rigidities of 1.5 and 15 BV, it no longer does so at lower rigidities at certain times of the solar cycle. A transition to Parker's modulation function $\exp [-\frac{K\left(t\right)\mathrm{}}{\beta }]$ seems to occur. Also a purely rigidity-dependent modulation function of the form $\exp (-\frac{K\left(t\right)\mathrm{}}{R}]$ fits nearly all of the experimental data. The local interstellar spectra of cosmic-ray protons and helium are investigated, assuming that these spectra are similar in shape between energy values of 1 and 10 BeV/nucleon. Using these results, such parameters of the interplanetary medium as the number of scattering centers along the cosmic-ray path and the radial extent of the cosmic-ray convection and diffusion region are evaluated, and are found to agree with those proposed by Parker. The scale factors of the scattering centers are found to be distributed between 6×${10}^{10}$ cm and ${10}^{12}$ cm, or more, provided that the magnetic field strengths of the scattering centers do not vary beyond the earth's orbit with the radial distance from the sun.