Modulation of cosmic ray protons and helium nuclei near solar maximum

Abstract

Balloon observations of proton and helium spectra in 1970, 1971 and 1972, which (1970)(1971)(1972).Computer generated spectra based on simple two parameter modulation models describe the basic features of the observations if one of the variable parameters is used to characterize the rigidity dependence of the diffusion coefficient. On the other hand, models which do not allow such a variation are not consistent with the observations.

A dynamic model for the time evolution of the modulated cosmic ray spectrum

“…years 4 and 7) actually cross as observed (Rygg, et al, 1974). Models which vary f(R) produce this effect near solar maximum by increasing the modulation at low energies at the same time as it is decreasing at high energies.…”

“…For example, in Figure 1 the regressions for the intensity at two different proton energies, -500 MeV and 1~00 MeV with respect to the Deep River neutron intensity show that this hysteresis ratio is energy dependent, varying from %1.9 at 100 MeV to 'nl.6 for n500 MeV protons. The effect was shown to be rigidity dependent by Van Hollebeke, et al (1973) who found values of 2.6 and 2.0 for the hysteresis ratio of 60 MeV/nucleon protons and helium respectively, and by Rygg, et al (1974) who found a somewhat smaller effect for the two species at higher energies.…”

“…In the first interpretation above, the relevant observational parameter to characterize the hysteresis effect is the "hysteresis ratio", the ratio of the relative levels at low energy which are observed on the two branches of the regression curve at the same value of the reference intensity (Van Hollebeke, Wang and McDonald, 1972;Rygg, O'Gallagher and Earl, 1974). For example, in Figure 1 the regressions for the intensity at two different proton energies, -500 MeV and 1~00 MeV with respect to the Deep River neutron intensity show that this hysteresis ratio is energy dependent, varying from %1.9 at 100 MeV to 'nl.6 for n500 MeV protons.…”

“…However, despite the phenomenalogical description of hysteresis in terms of time-lags by some, virtually all of the attempts to explain the phenomena have been based solely on the first interpretation. For example, O'Gallagher (1969), Schmidt (1972), Van Hollebeke, et al (1972), Le.zniak and Webber (1971), Burger and Swanenburg (1973), Bedijn, Burger, and Swaneaiburg (1973), Van Hollebeke, et al (1973), and Rygg, et al (1974), all discuss in one way or another the description of the observations in terms of a change in the rigidity dependence of some "modulating function" in a timeindependent model. On the other hand, the model developed in Paper I and discussed in the Introduction, provides for the first time a framework for the second interpretation by incorporating time-dependent diffusion and convection.…”

“…For example, using a diffusion coefficient consistent with reported magnetic field power spectra (Jokipii and Coleman, 1968), and a solar wind velocity V = 360 km/sec, the delay timescalculated as a function of RO are plotted in It was shown by Rygg, et al (1974) that if such a time variation is not introduced, other variations in R, V,and Ko will not produce a hysteresis in the stationary solutions. That is, the calculated spectra remain essentially unchanged for a wide range of R, V, and K , as long as the effective modulation characterized o by the parameter n = RV/K and the form of f(R) are held constant.…”