Solar Cosmic Rays by Leonty Miroshnichenko

Author:Leonty Miroshnichenko
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

8.2 Change of Average Energy and Spectrum Transformation

In the process of particle transport in interplanetary space the distribution function of the SCR experiences significant changes. They are evident in the observations in the form of space-time variations of the angular distribution and the energy spectrum of the particles. Observations near the Earth’s orbit indicate, in particular, an increase in the hardness (flatness) of the spectrum of solar protons in the energy range E p  ≤ 10 MeV (e.g., Miroshnichenko and Petrov 1985). This tendency is exceptionally important for estimates of the energetics of the SCR and of the flare as a whole (Miroshnichenko 1987). No unambiguous explanation of this effect yet exists.

At present, two possibilities are discussed; (1) formation of the spectrum with a variable slope at the source itself; (2) adiabatic deceleration of the particle in the interplanetary medium. As reviewed by Miroshnichenko (1987), acceleration models based on the concept of a magnetic reconnection indicate the variable form of particle spectrum at the source. Further, typical proton and alpha particle spectra observed near the Earth may be fitted by Bessel function following from a stochastic acceleration model (see Fig. 5.​1). Predicted proton energy spectra from acceleration at turbulent shocks (Fig. 5.​2) also are consistent with a spectral flattening at low energy. As it was demonstrated in Chap. 5, theoretical problems of particle acceleration at the Sun are still far from complete resolving. Therefore, it is of interest now to determine quantitatively what contribution adiabatic deceleration can make to the deformation of the spectrum.

It is customary to assume that the third term on the left-hand side of (8.2) corresponds to the adiabatic cooling, or to the anti-Fermi mechanism of particle deceleration in a spherically diverging solar wind. Estimates and studies of this effect have been made by many authors. In particular, Dorman et al. (1979) noted that the exchange of energy between the SCR and the solar wind plasma does not reduce to a simple adiabatic slowing, but depends on the strength of the redistribution of the particles with different energy in space due to diffusion. These authors were the first to point this out in solving the problem of GCR modulation: it was shown that, in general, the mechanism of energy exchange between the cosmic rays and the interplanetary medium is determined by the specific form of the particle distribution function and is incompatible with the traditional concept of deceleration based on intuitive thermodynamic considerations.

The complete transport equation (8.2) must be solved in order to calculate the change in the average energy and the corresponding deformation of the proton spectrum in interplanetary space. Practical estimates of the quantity dE/dt by this way, as far as we know, have not been made, and most investigators have used a simplified approach. If diffusion and convection are ignored, then the change of the energy due to adiabatic slowing is described by the usual formula (e.g., Parker 1965; Toptygin 1985)

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