Solar modulation of galactic cosmic rays: 3. Implications of the Compton-Getting Coefficient

Abstract

It is useful to express spectra of modulated galactic cosmic rays in terms of the Compton‐Getting coefficient C. This parameter can reveal the energy range over which the force field approximation is valid and the range where convection effects dominate over those of diffusion. A value of C near zero over an extended low‐energy range (according to recent observations this is the situation for protons) implies that the radial gradient at low energies cannot be large. This small gradient may imply, in turn, that the diffusion coefficient increases beyond 1 AU less rapidly than if it were proportional to heliocentric radial distance and/or that there is essentially no scattering for a sizeable distance from the sun to earth. The behavior of C with rigidity (or energy) is discussed in terms of the omnidirectional distribution function ƒ0. Contours of constant ƒ0 in the heliocentric distance versus rigidity plane are useful for illustrating the mean rigidity loss experienced by cosmic rays in the interplanetary medium.

Acceleration of Low‐Energy Ions at the Termination Shock of the Solar Wind

“…Equations (1) and (2) were derived initially by Parker (1965), modified by Gleeson & Axford (1967), and cast in terms of the distribution function by Fisk et al (1973). We neglect transport by spatial diffusion, and we assume that these low-rigidity particles do not experience significant transport by gradient and curvature drifts.…”

Modulation of the Galactic Low-Energy Proton Spectrum in the Inner Heliosphere

“…At relatively low energies (∼10-100 MeV), where adiabatic cooling plays a dominant role, using the force-field approximation for analytical one dimensional spherical approximation (Gleeson & Axford 1968;Fisk et al 1973), one obtains ν = 1, that is, the spectrum tends to J ∼ E. Instead, as shown here, in the majority of spectra investigated, ν turns out to be significantly larger than unity. This finding, at first sight, seems to contradict the conventional physical pattern of particle propagation and has an important consequence.…”

“…At about 10-100 MeV, where adiabatic cooling plays the primary role, its effect can be best visualized in the framework of the force-field approximation (Gleeson & Axford 1968;Fisk et al 1973). Particles entering the inner heliosphere lose a fixed amount of their energy, corresponding to a so-called force-field potential Φ, irrespective of their initial energy provided the radial diffusion coefficient has the rigidity-dependence κ rr ∝ vP (where v and P denote particle speed and rigidity, respectively).…”

Variability of Low Energy Cosmic Rays Near Earth

“…Using the experimental data from various space missions, an overview of the current understanding of the modulation over the past decade is given by (Potgieter, 2011). At low energies, 10-100 MeV, where the adiabatic cooling plays the primary role, its effect can be best seen in the framework of the force-field approximation (Gleeson & Axford 1968;Fisk et al 1973). In addition, the curvature and gradB drifts in IMF play role in the modulation.…”