7. Concluding remarks

Therefore, a consideration of the parameters obtained α and Ec for a medium density n = 1013 cm�<sup>3</sup> give acceleration times much lower than the time scale of the explosive phase of the flare phenomenon. For instance, for a low efficiency event (α = 0.14) in a high temperature regime, the time necessary to accelerate a proton from 10 MeV to 5000 MeV, is only of the order

It is interesting to comment on the estimated parameter ι on the basis of our results of the parameter α: as pointed out by [102] the time scale of the explosive phase in solar flares, is

τ<sup>d</sup> ¼ 4πσl

where l is the characteristic length of the system and σ the electrical conductivity in flare

It worth comment on the discrepancy between the predicted theoretical energy spectra at the source and the experimental spectra measured in the earth environment: first we note that the physical processes that can occur in a medium as dense as the sun's atmosphere are undoubtedly very diverse, and so, we do not claim to have included in our treatment all loss processes for charged particles, but only those of greatest interest that can affect protons within the energy range we are concerned with and during the short time scale of the acceleration durability. In fact, although Cerenkov losses are included in Eq. (2) we have ignored other losses from collective effects, however, some of them, such as energy 10 s by plasma perturbations see to be negligible for protons o f E > 23 MeV; also we have not considered energy losses caused by viscosity and Joule dissipation as suggested by [120]. On the other hand, we have not included nuclear transformation within the acceleration volume, as for instance proton production by neutron capture, nor loss of particles from the accelerated flux as leakage from the acceleration volume. Therefore, it is expected that the consideration of these neglected processes, together with a lower value of τ as discussed above and a higher proton concentration of the medium would depress our theoretical fluxes in greater congruency with the experimental curves. Again, local modulation of particles at the source level after acceleration are not examined here, either by an energy degradation step in a closed magnetic structure, or

while traversing the dense medium of the solar atmosphere as studied by [121].

In fact, observations of low energy particles indicate the existence of a strong modulation within a small envelope of � 0.2–0.3 A.U. (e.g. [34]). Furthermore, studies of relativistic solar flare particles during the May 4,.1960 and November 18, 1968 events have shown that particles diffuse in the solar envelope (< 30 Rs) [9, 21, 22, 63] which entails a modulation of the solar fluxes. Evidences of partic1e storage in the sun, where particles can be strongly decelerated, have been widely mentioned in the literature (e.g. [1, 65, 106]). Modulation in interplanetary space is a complicated process (e.g. [28, 29]) which provokes both the depression in the number density of particles and their strong deceleration: estimations of [74] indicate that particles lose � 10–64% of their energy through propagation, while [75, 76] sustains a loss of

�1

material is of the order of 2.1 � 1012–2.4 � 1014 <sup>s</sup>

s, and it is believed to be that of the stored magnetic energy dissipation, which is given as

2 =c

–1.8 � l0<sup>5</sup> cm which agrees well with the values estimated in this work and

<sup>2</sup> (35)

. A single calculation with (35) shows us that

of 8 sec.

150 Cosmic Rays

�10<sup>3</sup>

<sup>l</sup> = 1.7 � 104

previously deduced by [79].

In order to provide some answers to the numerous questions associated with the generation of solar particles (e.g. [24, 26, 71, 102, 119]) we have attempted to study the physical processes and physical conditions prevailing in solar cosmic ray sources by separating source level effects from interplanetary and solar atmospheric effects. On this basis, we have drawn some inferences from the intercomparison of the predicted theoretical energy spectra of protons in the acceleration region with the experimental spectra of multi-GeV proton events. Concerning this kind of events a number of modern techniques have been recently developed (e.g. [72]) and the, the PGI group in Apatity, Mursmansk, Russia [124–128]. In some of GLE it has been frequent to discern two particles populations: a prompt component and a delayed one. A new kind of classification has been proposed, GLE's and SubGLE's depending the number of station that register the earth level enhancement, location and latitude of NM stations.

We have chosen to study this particular kind of solar events (GLE) because they allow the study of the behavior of local modulation on protons, through the widest range of solar particle energies. Although one should expect that local modulation by particle energy losses at the source should follow the behavior illustrated in Figure 1, our results on source energy spectra indicate that is not the general case, but local modulation varies from event to event, depending on the particular phenomena that take place at the source according to the particular physical parameters prevailing in each event, such as density, temperature, magnetic field strength as well as the acceleration efficiency and particle remaining time before they escape from the source.

In drawing conclusions about the physical processes at the source, we have assumed a fixed value of the parameter n, taking into account that although spectroscopic measurements show a variation in the value of n from flare to flare, these fluctuations are nonetheless very near the value n = 1013 cm<sup>3</sup> [115], and thus our conclusions about energy loss processes in the acceleration region are not significantly altered by small fluctuation on this parameter. Moreover, an analysis of the electromagnetic emission associated with flares indicate a spread of several decades on the medium temperature in flare regions (104 –108K), hence we have chosen to fix the parameter n in order to concentrate our analysis on the parameter temperature. On the other hand, in drawing conclusions about the physical parameter of the acceleration process we have selected a mechanism with an energy gain rate proportional to particle energy as is the case of stochastic acceleration by MHD turbulence [36]; nevertheless, we believe that our results can in general be considered as valid, in the sense that whatever the acceleration mechanism may be, the physical conditions of the medium (density, temperature, field strength) state undoubtedly state the kind of phenomena occurring at the source. We have shown that even a low efficient mechanism (low values of α) is able to explain the generation process within the observation time scale of the explosive phase of flares, when severe conditions in the density of the medium are assumed.

with a relatively cold plasma, such that below a certain critical temperature, a compression of the sunspot field lines takes place and thus particles are more efficiently accelerated because the characteristic magnetic field length scale is reduced. Moreover, adiabatic heating of protons into the compressed plasma may occur within the short acceleration time of these events raising the net energy exchange rate. Since the energy loss rate is negligible by rapport to the energy gain rate in these events, particles may practically be accelerated regardless of their energies, so that a preferential acceleration of heavy nuclei as suggested by [48, 49], must be expected when acceleration occurs in a region of low temperature regime. Either by assuming that in cold events particles are picked up from a thermal plasma or that in warm and hot events the preliminary heating is of quasithermal nature, a very small fraction (N<sup>0</sup><sup>10</sup><sup>11</sup>-<sup>10</sup>18) of plasma particle of the source volume need to be picked up by the acceleration process in order to explain the experimental spectra.

The most important parameters concerning the source and acceleration process of solar particles deduced under the assumptions made in in this work may be summarized as follows: accelera-

average acceleration time of individual protons t = 12 s, medium temperature <sup>T</sup>104

Finally, we add that whatever the approach may be in developing flare models, an expansion and compression of the source material (e.g. [96]) local modulation of particles after the acceleration processes and a plausible absorption of secondary radiation from nuclear collisions in the

We would like to emphasize that this work is to some extent with the aim to pay homage to the

We are very grateful to the B.S. Alejandro Sánchez Hertz for his valuable help in the prepara-

Energy spectrum of energetic particles accelerated in a plasma by a stochastic type-Fermi acceleration process ( αβW) while losing energy simultaneously by collisional losses according to the general expression of [10], operative throughout all the range from suprathermal to ultrarelativistic energies, given in Eq. (2.1) in Section II. In this case, the

equation to be solved when only collisional losses are competing with acceleration is

field inhomogeneities 500 G, hydromagnetic velocity Va = 3.5 l07

forefathers-founders of solar cosmic ray physics and space physics.

–106 cm, linear dimension of the acceleration volume L = 109 cm, field strength of magnetic

, mean confinement time of particles within the acceleration volume τ 0.1–4 s,

, characteristic magnetic field length in the acceleration volume ι = 3

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

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

cm s<sup>1</sup>

, medium density

–108K.

153

tion efficiency α = 0.1 – 1.5 s<sup>1</sup>

solar environment must be considered.

104

<sup>n</sup>1013 cm<sup>3</sup>

Epilogue

Acknowledgements

tion of the figures.

A. Appendix

Finally, let us discuss the global conception of the generation process of solar particles, according to the results obtained in this work: it is first assumed that in association with the development of solar flare conditions for the acceleration of particles may be such that it can take place either in a hot medium or in a cold one; in the first case, as a result of some powerful heating process, the local plasma must be strongly heated and acceleration of particles up to some few MeV must take place. This preliminary heating must follow to a some specific kind of hydromagnetic instability or a magnetic field annihilation process in a magnetic neutral current sheet, so that by means of electron-ion and electron-neutral collisions, Joule dissipation, viscosity, slow and fast Alfven modes or even acoustic and gravity waves, the local plasma attain very high temperature ≥ 107K. The processes involved in this preliminary process of particle acceleration is not yet completely well understood; several plausible processes capable to accelerate particles up to some MeV have been suggested in the literature (e.g. [112]). Among many possibilities suggested, we believe that the one proposed by [108] presents a very plausible picture: a very select group of fast particles appearing from the preliminary heating can be reaccelerated up to very high energies, probably by a Fermi-type mechanism as proposed by [108]. Because the medium is very hot and dense we propose that collisional and p–p nuclear collisions between the fast protons and particles of the medium take place. Besides, we predict that up to some definite temperature the kinetic pressure of the gas is such that it favors the hydromagnetic expansion of a closed field line configuration, and thus adiabatic deceleration of particles takes place during their acceleration in the expanding plasma. Those particles with very low energy with respect a threshold energy Ec (determined by the competition between the acceleration and the deceleration rates) cannot escape from the sunspot magnetic field configuration because of their low rigidity, and thus, by scattering with the atoms, ions and electrons of the turbulent plasma, their energy is rapidly converted into heat to rise the local plasma temperature while the selected particles go into the main acceleration process. As noted by [110] the increase of electron temperature tends to decrease the efficiency of acceleration, such as that obtained in the case of hot events (Table 1) with regard to the events of Tables 2 and 3. This low efficiency is also related to the relatively large characteristic length- scale of the magnetic field, so that the acceleration time of particles up to high energies is relatively long. A second kind of solar event may be distinguished from the previous one, when the temperature is not so high (warm events in Table 3 and Figure 4) and thus expansion of the source material does not take place, at least during the time of the particle acceleration process. The temperature being lower and the characteristic magnetic field length shorter than in hot events, the acceleration efficiency is higher and consequently the acce1eration time is relatively shorter. In these events or in hot events a low flux of high energy gamma rays generated by nuclear collisions of highly energetic protons is expected, because these fast particles spend very short time in the source before they escape. On the other hand, conditions in solar flares may be such that energy losses of protons are negligible during the acceleration process, because particles are generated by a very efficient process in a shorter acceleration time. This kind of events are assumed to occur when the acceleration region is associated with a relatively cold plasma, such that below a certain critical temperature, a compression of the sunspot field lines takes place and thus particles are more efficiently accelerated because the characteristic magnetic field length scale is reduced. Moreover, adiabatic heating of protons into the compressed plasma may occur within the short acceleration time of these events raising the net energy exchange rate. Since the energy loss rate is negligible by rapport to the energy gain rate in these events, particles may practically be accelerated regardless of their energies, so that a preferential acceleration of heavy nuclei as suggested by [48, 49], must be expected when acceleration occurs in a region of low temperature regime. Either by assuming that in cold events particles are picked up from a thermal plasma or that in warm and hot events the preliminary heating is of quasithermal nature, a very small fraction (N<sup>0</sup><sup>10</sup><sup>11</sup>-<sup>10</sup>18) of plasma particle of the source volume need to be picked up by the acceleration process in order to explain the experimental spectra.

The most important parameters concerning the source and acceleration process of solar particles deduced under the assumptions made in in this work may be summarized as follows: acceleration efficiency α = 0.1 – 1.5 s<sup>1</sup> , characteristic magnetic field length in the acceleration volume ι = 3 104 –106 cm, linear dimension of the acceleration volume L = 109 cm, field strength of magnetic field inhomogeneities 500 G, hydromagnetic velocity Va = 3.5 l07 cm s<sup>1</sup> , medium density <sup>n</sup>1013 cm<sup>3</sup> , mean confinement time of particles within the acceleration volume τ 0.1–4 s, average acceleration time of individual protons t = 12 s, medium temperature <sup>T</sup>104 –108K. Finally, we add that whatever the approach may be in developing flare models, an expansion and compression of the source material (e.g. [96]) local modulation of particles after the acceleration processes and a plausible absorption of secondary radiation from nuclear collisions in the solar environment must be considered.
