Cosmic ray propagation in the Universe in presence of a random magnetic field

Abstract

The origin of the ultrahigh energy cosmic ray remains being a mystery. However, aconsiderable progress has been made in the past few years due to the good quality data recordedby current cosmic ray observatories. One of the recent achievements is obtaining firm observationalevidence about the extragalactic origin of the most energetic cosmic rays by the Pierre Augerobservatory. On the other hand, it is believed that there is a non-null turbulent magnetic fieldthat fills the intergalactic medium. Therefore, the presence of the intergalactic magnetic fieldcan play an important role on the propagation of the ultrahigh energy cosmic rays through theUniverse, which in principle can be relevant to interpret the experimental data. In this work wepresent a system of partial differential equations that describes the propagation of the ultrahighenergy cosmic rays through the Universe, in the presence of a turbulent intergalactic magnetic field,that includes the diffusive and the ballistic regime of propagation and also the transition betweenthem. Also, as an example of application, the system of equations is solved numerically in asimplified physical situation.