Modulations of Generically Related Galactic Cosmic Rays

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A method of analysis of the spectra of generically related cosmic-ray species is formulated. The effects of various spatial modulations between the cosmic-ray sources and the earth are separated from the effect of fragmentation in interstellar space. Predictions are made on how the ratios of the intensities of related cosmic-ray species, for both rigidity and energy/nucleon intervals, would be expected to vary with geomagnetic latitude, solar activity, and energy. These predictions are compared with the experimental results. Variations in the reported abundance ratios of helium isotopes and the light ($3\ensuremath{\le}Z\ensuremath{\le}5$) to medium ($6\ensuremath{\le}Z\ensuremath{\le}9$) elements can be explained in terms of solar and geomagnetic modulation, rather than by invoking the hypothesis of longer interstellar path lengths for low-energy cosmic rays. At a geomagnetic latitude of 55\ifmmode^\circ\else\textdegree\fi{}, on 21 April 1961, the relative transmission of ${\mathrm{He}}^{3}$ to ${\mathrm{He}}^{4}$ through interplanetary and geomagnetic fields in the energy/nucleon interval 250-350 MeV/nucleon is found to be 0.38\ifmmode\pm\else\textpm\fi{}0.2. Statistically limited data favor a rigidity-dependent rather than velocity-dependent solar modulation above a rigidity of 1.2 BV. The local interstellar intensity of cosmic-ray helium (i.e., before solar modulation) at 1.7 BV is 0.6\ifmmode\pm\else\textpm\fi{}0.4 of that at 1.3 BV. Assuming the differential rigidity ($R$) spectrum of local interstellar helium to vary as $\frac{1}{{R}^{q}}$, the exponent $q$ is found to be 1.8\ifmmode\pm\else\textpm\fi{}2 in the rigidity interval 1.2-1.7 BV. The result suggests that considerable solar modulation of the intensity of low-energy cosmic rays may occur even at solar minimum. Based upon the limited available data, the mean interstellar path length for cosmic rays in the region 200-400 MeV/nucleon is found to be 5\ifmmode\pm\else\textpm\fi{}2 g/${\mathrm{cm}}^{2}$. The values of the mean path length of cosmic rays and the exponent of the local interstellar helium spectrum are consistent with the values obtained for higher energy cosmic rays. The effects of modulations occurring in the cosmic-ray source regions are also explored.