3.2. Effects of CR pressure

The approximation of CR motion in electro-magnetic fields generally used is not valid in general. In many cases when CR density energy is comparable to the energy density of magnetic fields and kinetic energy of moving plasma, the inverse influence of CR on space plasma dynamics and electro-magnetic field structure are important. As was shown by Ptuskin (1984) on the basis of CR kinetic equation that in the diffusion approximation the ponderomotive force from CR particles on plasma with a stochastic magnetic field is determined by the pressure of these particles (Berezinsky et al., M1990):

where v and p are the velocity and momentum of CR particles and fo (p) is the CR distribution function. The CR pressure Pc is connected with CR total energy density

where E(p) is the kinetic energy of particle with momentum p. As was shown by Ptuskin (1984),


N (E )=(4n Vv )fo (p ) (3.2.4) is the differential energy spectrum and index i shows the sort of CR particles. For

For y = 2.7 this gives Pc = 0.25 Wc and d Pc/d Wc = 0.27. For ultra-relativistic gas (e >> mtc2) it will be Pc = (l/3)Wc and dPc ¬°dWc = 1/3. Let us note that if the gradient of CR pressure is zero then the ponderomotive forces on the elemental volume of space plasma from all directions will be the same and therefore the resultant ponderomotive force acting on the elemental volume will be zero. CR pressure gradient influenced on the dynamic of space plasma according to the set of hydrodynamic equations:

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