Propagation of cosmic rays in the solar wind

Abstract

This paper presents a coherent exposition of the modern statistical theory of the transport of fast charged particles (cosmic rays) in the solar wind. Observations are discussed only as they illustrate the phenomena under discussion. A brief introductory section surveys the historical development of the theory. The dominant effect on the motion of cosmic rays in the solar wind is the interplanetary magnetic field, which is irregular and which is therefore best treated statistically, using random functions. The magnetic irregularities scatter the cosmic rays in pitch angle, so that to a good approximation the cosmic rays diffuse through the irregular magnetic field. Using a statistical analysis of the equations of motion, one may relate the diffusion tensor to the power spectrum of the magnetic field, which is in principle measurable. The resulting general transport theory relates the motion of cosmic rays, statistically, to the solar‐wind velocity and magnetic field. Application of the theory both to the modulation of galactic cosmic rays by the solar wind and to the propagation of solar cosmic rays is discussed in detail. It is concluded that the present theory explains the principal phenomena quite well. Future theoretical work will probably be devoted to obtaining better solutions of the equations, to obtaining better values of the parameters, and to studying higher‐order or more subtle effects.

Cosmic ray detector response to transient solar modulation: Forbush decreases

“…This implies that the radial diffusion coefficient is directly proportional to particle rigidity (R) for transient modulation for positive as well as negative cycles over a large range of rigidities. This rules out the existence of a ''transition rigidity'' suggested by Jokipii [1971] even for a short-term modulation. At this point, one should also note that Lockwood and Webber [1967] compute R m values in an ad hoc manner.…”

“…[19] Sometime ago, Jokipii [1971] proposed a diffusion theory of cosmic ray modulation and used it to deduce the rigidity (R) dependence of the diffusion coefficient (k) in IMF, at the Earth's orbit. He used the measured magnetic field power spectra in space and concluded that the dependence changes from k / R 0.5 to k / R 2 , at R $ 2 GV (termed transition rigidity).…”

Heliocentric distance dependence of the interplanetary magnetic field

“…It is believed that they play the role of scattering centers for the particles, producing a spatial gradient in' cosmic ray intensities as well as a modulation with solar.activity (see reviews by Jokipii, 1971;vblk, 1975b;Moraa, 1976). The radial variation of magnetic field fluctuations causes a corresponding variation of the particle diffusion, with an obvious beafng ofxithh&_avie-ifht of models of particle propagation.…”

“…Most models of this propagation up to the quasilinear approximation assume that to zeroth order such particles follow a helical orbit along the mean spiral field while undergoing some spatial diffusion due to the effects of field fluctuations (Jokipii, 1971;Vlk, 1975a,b)° Recent nonlinear approaches (V61k, 1975b;Goldstein, 1976;Jones et al, 1977) and the local approximation quasilinear approach of Klimas et al (1976a,b; seek to remedy the inability of previous theories to accurately describe the more complex motions of cosmic ray particles with large (near 900) pitch angles and/or moderate to strong magnetic turbulence. There have been several attempts to determine the radial distance dependence of the cosmic ray diffusion tensor (Jokipii, 1973;V6Ik et al, 1974), but these have relied heavily on theoretical models for the spatial dependence of the magnetic spectrum which.may not correspond to the real situation (V5lk, 1975b).…”

The Acceleration of High-energy Protons at Coronal Shocks: The Effect of Large-scale Streamer-like Magnetic Field Structures

“…We assume a well-developed magnetic turbulence with a Kolmogorov power spectrum P∝k −5/3 in the coronal region. κ P can be calculated from the quasilinear theory (Jokipii 1971). The resulting diffusion coefficient has a momentum dependence, κ P ∝p 4/3 , when the particle gyroradius is much smaller than the correlation length of turbulence.…”