Influence of finite injections and of interplanetary propagation on time-intensity and time-anisotropy profiles of solar cosmic rays

Abstract

For an observer in space the intensities and anisotropies of solar cosmic-ray events are governed by the duration and the functional shape of the injection processes near the Sun and by the propagation along the interplanetary magnetic field from the Sun to the observer. We study the influence of four different types of solar injections (Gaussian, exponential, step-function and coronal diffusion), and of a purely diffusive interplanetary propagation, where the diffusion coefficient has a power law dependence on the radial distance from the Sun, K = Mr ~, on both the time-intensity and the time-anisotropy profiles at 1 AU. The main results are as follows: A slow quasi-exponential decay of the intensity can be modelled in some cases; all finite injections produce high anisotropies during the main phase of an event; an 'effective' solar injection length can be determined from simultaneous inspection of the intensities and anisotropies; the intensities and anisotropies do to first order not depend on the analytic shape of the various injection profiles. The model is applied to the November 18, 1968 solar event as observed by Pioneer 9 in the 7.5-21.5MeV and 21.5-60MeV energy channels. We obtain local diffusion coefficients in the range M= (2.5-5)x 1021 cm 2 s -1 and injection periods of the order of 10-20 hr. Closer inspection reveals the change of interplanetary propagation conditions during the event.

Interplanetary Propagation of Solar Energetic Particle Heavy Ions Observed at 1 Au and the Role of Energy Scaling

“…The plot shows that at event onset the particles are all outward moving, but by the time of the intensity maximum the anisotropy has decreased to ∼0.3, with an exponential decay shown throughout most of the event. These results are typical of both simple (e.g., Schulze et al 1977) and more complex models (Ng & Reames 1994;Ruffolo 1995;Li et al 2003), namely smoothly decreasing anisotropies that are initially large during the rise phase.…”

Cross-field gradients: general concept, importance of multi-spacecraft measurements and study at 1 AU of the source intensity gradient for E > 30 keV solar event electrons

“…It has already been shown (Schulze et al, 1977) that the anisotropy and¯ux pro®les respond di erently to the injection pro®le. Therefore, in order to simplify the analysis, only comparisons of pro®les of the same type have been done (i.e.¯ux versus¯ux and anisotropy versus anisotropy).…”

“…Axford, 1965) and the focusing (Roelof, 1969) processes. The third one refers to the injection (acceleration and release) of the particles in the interplanetary medium (Reid, 1964;Axford, 1965;Schulze et al, 1977). All three processes are described together with some of the properties that had been considered and compared to observations so far.…”

“…Therefore, ®nite injection pro®les are required to describe the pro®les seen by the spacecraft. For collisionless plasma, they in¯uence the pro®les at a given spacecraft according to the following relation (Schulze et al, 1977):…”

A New Cosmic Ray Transport Theory in Partially Turbulent Space Plasmas: Extending the Quasilinear Approach

“…Dröge & Kartavykh (2009), Dröge et al (2010), and Sun et al (2011) used Wind satellite data for the angular distributions of solar electrons and protons to compare them with the predictions of the Fokker-Planck equation, solved by the method of stochastic differential equations again for fixed idealized cosmic ray pitch-angle scattering rates. Related work by Schulze et al (1977) and Palmer et al (1978) has used the time profiles of the cosmic ray anisotropy defined by the first harmonic of the gyrotropic particle phase space density F 0 (x, y, z, p, μ, t), providing contributions from both parallel spatial gradients and the Compton-Getting effect from momentum gradients (Schlickeiser et al 2009) for nearly isotropic distribution functions. In these papers, specific simplified forms of the cosmic ray Fokker-Planck coefficient D μμ (μ) as a function of μ have been adopted, which sometimes agree reasonably well with the observed particle distribution functions, although particularly the work of Dröge et al (2010) and Sun et al (2011) shows significant deviations from the adopted simplified forms.…”