the intensity Iv extended alone the sight line L will be
where f (y) is some function of y (at y = 3, f (y)~ l70); Iv is measured in erg.cm-2.ster-1sec-1Hz-1. In determining experimentally the radio emission spectrum we find the dependence on v, hence the power exponent (y-1)/2 and then Y in the electron spectrum (for example for the total radio emission from the Galaxy (y-1)/2 = 0.7 whence Y = 2.4). As shown in (Dorman and Miroshnichenko, M1968) the above-mentioned processes of radio emission are also of great importance to the fast particle generation on the Sun. As a result of bremsstrahlung generation of relativistic electrons of CR, non-thermal radiation from various objects in Metagalaxy (radio galaxies, Seifert galaxies, quasars etc.) and the disc and halo of the Galaxy, of remnants of Supernovae and of the other objects in our Galaxy is formed.
1.7.2. Acceleration and deceleration of particles in their interactions with moving magnetic fields
The charged particle motion in plasma with magnetic fields is accompanied, apart from the various energy losses, by particle acceleration and deceleration by various mechanisms based on one or another mode of the transfer of the magnetic field energy and the energy of plasma kinetic motion to a comparatively small number of particles. In this case the particle acceleration up to comparatively low energies is owed to the first-order mechanisms, namely, the betatron acceleration in enhanced magnetic field, the acceleration in magnetic traps or, in general, in some region between two mutually approaching magnetic plasma formation, the particle acceleration owing to magnetic field dissipation during collapse of oppositely directed fields, etc. These mechanisms are probably realized under the conditions of chromospheric flares and, in general, in the active regions of the solar corona. They may also be the injectors during supernova explosions and explosions in quasars, with subsequent particle acceleration up to higher energies by the second-order mechanisms including the Fermi statistical acceleration mechanism (CR particle collisions with chaotically moving magnetic clouds). In the latter mechanism the particles gain energy in head on collisions and lose energy in overtaking collisions; since, however, the head on collisions are somewhat more probable, the particle energy, on the average, gradually increases. The statistical mechanisms also include the mechanisms of acceleration by various types of waves, namely, plasma waves, radio waves, Alfven waves, magneto-sonic and shock waves. The energy gain is accompanied by energy loss owed to the various effects considered above. The energy loss depends on particle energy, and in many cases, starting with some energy called the injection energy the loss becomes smaller than the gain due to some acceleration mechanism. Therefore, only a small portion of the plasma particles satisfying definite conditions, and not all of them, are accelerated. As a result the composition of the accelerated particles may be significantly different from the composition in the source. There may probably also exist injection-less mechanisms when practically all plasma particles are accelerated in a small region of the space within a comparatively short period (it is natural that in this case the chemical composition of the accelerated particles will resemble the composition in the source). An example of an injection-less mechanism may be the acceleration daring dissipation of oppositely directed magnetic fields collapsing at a sufficiently high velocity. The energy spectrum constraint at the low energy side is most probably owed to the increase of the loss with decreasing of the particle energy. At the high energy side the spectrum is constrained by the finite time of acceleration owed to either a limited period of the acceleration mechanism action or to the ejection of fast particles from the acceleration zones. Since the probability of ejection increases with particle energy, the generated particle flux decreases pronouncedly with increase of the particle energy. We shall limit ourselves to the above brief pattern, the more that the problem of particle acceleration mechanisms and formation of nuclear composition and energy spectrum of CR in their sources is one of the fundamental problems in the astrophysical aspect of CR studies and will be quantitatively studied and analyzed in details in Chapter 4.
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