R14 0 2n32 v5 exp

3.16.3. Summary of main results

Zirakashvili et al. (1999) came to the conclusion that the trapping of thermal particles is essential for the damping of Alfvén waves if the frequency of collisions is small enough. For trapped particles |u| < U*, where ¡u ~ SB/B for Alfvén waves.

Hence the escape time is tesc ~ ¡U ¡v. It should be compared with the period of particle oscillations inside the trap T ~(kvf ¡u )-1. This gives the condition for saturation of nonlinear damping:

The saturated damping rate can be estimated as the unsaturated damping rate multiplied by the ratio T/tesc . It is easy to see that such an estimate is in accordance with Eq. 3.16.17. In the self-consistent model of galactic wind flow (Zirakashvili et al., 1996; Ptuskin et al., 1997) where the unsaturated damping rate was used, sb/b ~ 10 and is determined by the power of CR sources in the Galactic disk. For

this case the critical value for the collision frequency is 10 sec for a

wavenumber k ~ 10 cm that is in resonance with 1 GeV CR protons. This value is close to the value of the collision frequency of a hot rarefied plasma with

number density 10 cm and temperature 106 K . Therefore in the absence of other scattering processes, trapping effects might be relevant for Alfven wave damping in our Galaxy. According to Zirakashvili et al. (1999) another important feature of saturated damping is the possibility of not only damping but also energy transfer to smaller wavenumbers. This property is absent for unsaturated damping of unpolarized (F(k) = I(- k)) waves. Such energy transfer can be important for diffusive shock acceleration because it permits small energy particles to generate Alfven waves that are in resonance with particles of greater energies and, hence determines the rate of acceleration.

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