1. Introduction

Most of the information on solar flares has been generally supplied by the analysis of their electromagnetic spectrum; however, the confrontation of timing synchronization between

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

electromagnetic flare emissions with those of energetic particles and coronal mass ejections (CME) is the method utilized to explore the physical conditions and processes taking place in the sources of particle generation. For example, results obtained from the SEPS server project and future HESPERIA HORIZON 2020 project. However, the study of the corpuscular radiation emitted in some flares can also provide us with very valuable information about the physical conditions and processes occurring in association with this solar phenomenon. It is known, for instance, that the processes involved in the generation of solar particles are probably of a non-thermal nature, because the intensity of particles usually decays more softly than an exponential of a the thermal type does, and so other properties may be deduced in order to investigate how and where multi-GeV solar protons originate, that means the source parameters and the parameters involved in the generation process of particle [69, 70]. In this chapter, we attempt to draw some inferences concerning solar sources by the analysis of 12 ground level enhancements (GLE) of solar cycles 19 and 20.

It has been shown [40] that the best representation of the energy spectrum of solar protons through the whole energy domain explored experimentally at present is given by an inverse power law with an upper cutoff in its high energy portion. In fact, a good fit of the experimental data can be obtained with an exponential law in a limited energy band; however, a strong deflection is obtained with them as soon as a wider energy domain is involved. Besides, it has been established [11] that the measured differential intensity in solar proton events, as well as the source spectrum (inferred as an inverse power law in energy) are both velocity-dependent. Therefore, we infer that the acceleration rate of particles in the sun must provide the spectral shape and velocity dependence such as suggested by those results. This is the case with an energy gain rate of the form

$$
\left(\frac{d\mathcal{W}}{dt}\right)\_{\text{acc}} = \alpha\beta\mathcal{W} = \alpha \left(\mathcal{W}^2 - \left(Mc^2\right)^2\right)^{1/2} \tag{1}
$$

particle sources. In Section 3, we present the observational energy spectrum of the concerned GLE as reported by several authors. In Section 4, we deduce theoretical source spectra, without and with energy losses during acceleration, disregarding energy changes of after acceleration while traversing the dense medium of the solar atmosphere to attain the interplanetary medium. In Section 5, we describe the criterion employed to construct integral energy spectra of solar proton (GLE) as well as the methods used in calculations; the results are presented graphically. In Section 6, the interpretation and significance of our results are discussed. In

Exploration of Solar Cosmic Ray Sources by Means of Particle Energy Spectra

http://dx.doi.org/10.5772/intechopen.77052

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Some researchers who study radiation and secondary particle fluxes consider an acceleration stage followed by a slowing down phase in the solar material once the action of the acceleration mechanism on particles has ceased (e.g. [86–89]); and they generally neglect the simulta-

However, particle acceleration is not performed in the vacuum but in the high density medium of flare regions; therefore, we shall study the local modulation of the acceleration spectrum as the protons are broken during the short-time scale of solar particle generation. The most important processes occurring in astrophysical plasmas capable of affecting the net energy change rate of particles in the range of kinetic energies of energetic solar protons

These depend strongly on the density and temperature of the plasma; thus we assume that the main energy dissipation of particles must occur in the generation region, in the body of the flare itself. The rate of collisional losses in a medium of density n has been given in a simplified

¼ � <sup>7</sup>:<sup>62</sup> � <sup>10</sup>�<sup>9</sup>

where β= v/c is the particle velocity in terms of the light velocity, L is a unidimensional factor and logarithmically depending marginally on the particle energy. We shall assume a value of L � 27 for solar flare conditions, when the medium concentration is <sup>n</sup>�1012 – 1013 cm<sup>3</sup>

Figure 1, the behavior of Eq. (2) with energy is shown. The complete description of collisional losses through the entire energy range including losses in the low energy portion (the so called nuclear stopping and electronic stopping) has been given by [10] for fully ionized hydrogen as:

nL

<sup>β</sup> ð Þ eV=sec (2)

. In

Section 7, the concluding remarks are summarized.

neous occurrence of energy loss and acceleration.

dW dt

ion

(E�10<sup>6</sup>

expression [37]

–10<sup>10</sup> eV) are:

2.1. Collisional energy losses

2. Energy losses of protons during acceleration in solar flares

where β is the velocity of the particles in units of light velocity and W the total energy of particles. The parameter α denotes the efficiency of the acceleration mechanism, which in the case of solar sources may be considered as roughly constant when the acceleration process reaches the steady-state in a given event [79, 80]. It has been generally thought that the energy loss processes of solar particles acceleration stage are not important in practice, and have only been taken into account after the acceleration stage in order to explain some features of electromagnetic emissions in solar flares and heating of the chromosphere [87].

In this chapter we shall consider, together with acceleration, energy loss processes occurring in the high density plasma of the solar source. It will be shown that energy losses in some proton flares can modulate the acceleration spectrum, thus implying that if such a small effect compared to the acceleration rate is able to modify the spectrum during the short lapse of the acceleration process, then the source spectrum is actually the result of a strong modulation due to local energy losses during acceleration and not only through interplanetary propagation; thus in Section 2, we discuss the basic equations of the more plausible energy loss processes in particle sources. In Section 3, we present the observational energy spectrum of the concerned GLE as reported by several authors. In Section 4, we deduce theoretical source spectra, without and with energy losses during acceleration, disregarding energy changes of after acceleration while traversing the dense medium of the solar atmosphere to attain the interplanetary medium. In Section 5, we describe the criterion employed to construct integral energy spectra of solar proton (GLE) as well as the methods used in calculations; the results are presented graphically. In Section 6, the interpretation and significance of our results are discussed. In Section 7, the concluding remarks are summarized.
