The Alfvén speed is given by
and B is constant in the one dimensional problem.
Ko (1992) gave a simple model of the coupling between plasma, CR and waves. The diffusion coefficient k, the stochastic acceleration rate 1/t and e± (which are related to streaming instability) are given by k =
where c is the speed of light, and «indicates the strength of coupling.
3.4.3. Steady state profiles of the CR-plasma system
According to Ko (1999), in steady state there are six integration constants: 1) magnetic flux
2) mass flux
3) entropy constant
4) total energy flux
5) total momentum and 6) wave-action
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