We derive the acceleration, velocity and distance of a cosmic ray (CR) due to an astrophysical electric field in the framework of special relativity. The relation between distance and time has been inverted, which allows expressing the velocity as a function of the distance. A simulation is performed for the observed spectrum of CRs adopting two distributions for them: the Maxwell Jüttner distribution and the gamma-Pareto II distribution.
KeywordsCosmic RaysParticle Acceleration
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