where p is the plasma density, and u represents the characteristic velocities of macroscopic movements. Then the movements of magnetic fields frozen in space plasma lead to the generation of electric fields, and by them the generation of non-thermal particles, which give electromagnetic radiation, thermal heating of plasma and runaway accelerated particles (internal CR). Let us note that in fact the situation is much more complicated, because usually there are also external CR which together with internal CR influence space plasma through the non-linear processes: CR pressure and (in the case of existing of CR anisotropy) kinetic stream instability effects. The channels of energy transformation in space plasma, according to Syrovatsky (1968), taking into account non-linear CR processes (Section 1.7, and in more details Chapter 3) are shown in Fig. 1.1.1.
1.1.7. Particle acceleration in space plasma and the second fundamental law of thermodynamics
The phenomenon of particle acceleration in space plasma is, at first sight, in sharp contradiction with the second fundamental law of thermodynamics. Namely, by particle acceleration processes plasma transforms, one would think, into an evidently non-equilibrium state: thermal plasma + very small number of accelerated particles with energy density of the same order or much higher than energy density of the thermal plasma. However, as was emphasized by Syrovatsky (1968), there is no contradiction. The matter is that the particle acceleration proceeds during a time that is much smaller than the time of thermal relaxation of space plasma. In fact, the system of space plasma is very far from the state of thermodynamically equilibrium. As it was shown in Dorman (M2004, Section 1.1.2), for space plasma it is statistically advantageous to have particle distribution with a raising 'tile' in the high energy range. So the acceleration processes transform the space plasma into a more advantageous state (i.e., in full agreement with the second fundamental law of thermodynamics), into a state of bigger entropy.
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