Abstract
Hydrodynamic equations were simplified to a layman understanding together with the diffusion-convection transport equation for the cosmic-ray distribution function f(t,r,p), which depends on time t , radial distance from the point of supernova explosion r and the particle momentum p. From the results, gas density p is inversely proportional to the gas velocity u ; flux tubes have a tendency to rise at an appreciable speed; pressure of the atmospheric gas Pg depends on the cosmic-ray pressure Pc and the internal energy of the electron U is directly proportional to the gas density p . Based on what Vladimir, et al. [1] said: “More work is needed to understand how robust our results are”, this has helped in making their bulky equations clearer and showing how robust their work are. In the cause of breaking down or simplifying the high energy equations, it was found that cosmic rays move with Alfven speed.
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