Modulation of low-energy cosmic rays

Abstract

Recent theories have related the diffusion of cosmic rays in the solar wind to the power spectrum of interplanetary magnetic field fluctuations. In this study the power spectrum‐diffusion coefficient relation for low‐energy protons (T < 80 MeV) is tested directly, and the relative contribution to the scattering from directional discontinuities in the magnetic field is examined. Modulation parameters Vw/Krr, the solar wind speed divided by the radial diffusion coefficient, are calculated from Pioneer 6 magnetic field and solar wind data and are compared with simultaneous Imp 3 observations of the 20‐ to 80‐MeV proton flux. Daily variations in the 40‐ to 80‐MeV proton flux are found to respond to changes in Vw/Krr, as is predicted by a perturbation solution of the Fokker‐Planck equation once the contribution from directional discontinuities in the magnetic field is subtracted from the diffusion coefficients. This finding is interpreted to imply that a large percentage of the identified discontinuities are basically tangential. A lack of correlation between the 20‐ to 40‐MeV flux and the parameter changes is interpreted as being due to either the invalidity of the theory at lower energies or the presence of a continuous flux of high‐energy solar protons. A well‐defined time lag between changes in the 60‐ to 80‐MeV proton flux and corresponding changes in Vw/Krr is observed during a period when the interplanetary magnetic field is predominantly radial and the Imp 3‐sun‐Pioneer 6 angle is greater than 10°. This lag is consistent with the interpretation of little or no cross‐field diffusion or a perpendicular diffusion coefficient less than 3 × 1019 cm²/s.

Interplanetary magnetic fields, their fluctuations, and cosmic ray variations

“…In the observer's frame of reference K 11 should be a reasonable Alfvnic with their k vectors oriented along B (Daily, 1973), the measured Kl will be approximately equal to Krr for power spectrum slopes on the order of a = 2 (for details see Sari,,1975).…”

“…The spectra covered the frequency range of 1.4 x 10T7ito 1.7 x 10lO Hz and were computed at an equivalent of 40 degrees of freedom when all data for 24 hours was present (Sari, 1972(Sari, , 1975. Since Pxx and Pyy are not always equal, K 1 I was set equal to the average of Kxx and Kyy as computed from Pxx and P yy A little thought must be given regarding the validity of equation…”

“…In their analysis, the rigidity dependence of solar cycle cosmic-ray modulation was found to agree with theoretical predictions. Sari (1975) (b) The time scale appropriate for the study of Forbush decreases is about a day. During that time, a spacecraft will measure the magnetic field over a perpendicular distance .…”

Heliocentric distance dependence of the interplanetary magnetic field

“…These estimates were based Sari and Ness (1969), Coleman et al (1969), Russell et al (1971), Sari (1972Sari ( , 1975 and Blake and Belcher (1974).…”

Mariner 10 magnetic field observations of the Venus wake

“…On the basis of an automatic computer identification of DD's as changes > 30o in the field direction in 42 sec or less [see Sari (1972 ) for a detailed description of the procedure, there were 22.7 + 6.2 DD's per day ( or slightly less than 1 DD per hour on average) during nine days around the encounter, not including either encounter day itself or the first day post-encounter. The latter was excluded because almost no DD's were observed on that day and was therefore obviously an anomalous day.…”