A perturbation approach to cosmic ray transients in interplanetary space

Abstract

A general linear response analysis is presented for investigating cosmic ray transients in interplanetary space. The diffusion equation for energetic particle transport in the solar wind is first linearized about a stationary configuration. The perturbation in the particle omnidirectional distribution function resulting from perturbations to the solar wind velocity, drift velocity, or spatial diffusion tensor corresponding to transient solar wind conditions may then be found by solving an inhomogeneous boundary value problem. As illustrative examples of the general analysis, transient perturbations in the cosmic ray number density due to variations in the spatial diffusion coefficient are computed in a one‐dimensional solar wind based on the convection‐diffusion equation, which disregards cosmic ray energy changes in the solar wind. Two variations are considered, corresponding to (1) a Forbush decrease arising from the passage of an interplanetary traveling disturbance (shock) and (2) the solar cycle variation arising from an 11‐year sinusoidal variation of the spatial diffusion coefficient at the sun which then propagates out through the heliosphere. The predicted solar cycle variation exhibits a hysteresis effect in which high‐energy particles lead low‐energy particles and a time delay which increases with heliocentric distance within the inner heliosphere. The predicted Forbush decrease profiles exhibit precursors, precipitous decreases, and gradual approximately energy‐independent recoveries arising from a decay of the propagating disturbance. The general features of both variations are in accord with observations.

Forbush decreases and turbulence levels at coronal mass ejection fronts

“…This means that the corresponding interplanetary CMEs (ICMEs) would have been intercepted at the Earth as ejecta/magnetic clouds, and the observed cosmic ray depressions corresponding to these events would have had contributions from the shock ahead of the ICME, as well as from the ejecta/magnetic cloud itself (Cane et al 1994(Cane et al , 1995. Theoretical treatments of Forbush decreases model the effect as arising due to a general propagating region of enhanced turbulence/scattering and decreased diffusion (e.g., Nishida 1983;le Roux & Potgieter 1991) and do not distinguish between the shock and the ejecta, or implicitly assume that the decrease is only due to the shock (e.g., Chih & Lee 1986). It is fairly well known that magnetic clouds are well-correlated with Forbush decreases (e.g., Zhang & Burlaga 1988;Badruddin et al 1986;Badruddin et al 1991;Venkatesan & Badruddin 1990;Sanderson et al 1990; see, however, Lockwood et al 1991, for the opposite viewpoint).…”

Simple analytical solutions for propagating diffusive barriers and application to the 1974 minicycle

“…We discuss the temporal variation of the cosmic ray density U caused by a propagating disturbance in the forcefield approximation valid at high energies, in combination with a continuous recovery process [see Chih and Lee, 1986;Wibberenz, 1998] …”

Corotating Solar Wind Structures and Recurrent Trains of Enhanced Diurnal Variation in Galactic Cosmic Rays

“…Thus corotational variations in solar wind speed are associated with well-known "synodic" or "27 day variations" in the GCR flux (Fonger 1953;Simpson 1998;da Silva et al 2007), which have sometimes been called "recurrent Forbush decreases." An HSS causes a temporary cosmic ray decrease, either due to shielding by the CIR (Heber et al 1999;Richardson 2004) or due to a change in particle diffusion properties in local interplanetary space in low and middle heliolatitudes (Chih & Lee 1986;Kóta & Jokipii 1991). The temporary reduction of the GCR flux is followed by a recovery phase in the trailing portion of the HSS.…”