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Published online by Cambridge University Press: 13 February 2013
Cosmic rays are accelerated in astrophysical plasmas which collide at supersonic speedswhere shock waves are formed, and along with other instabilities, they compete for thedissipation and acceleration mechanisms. The diffusive acceleration mechanism plays aleading role in the explanation of very high energy cosmic rays observed. In thismechanism, particles are repeatedly gaining energy in multiple crossings of anastrophysical shock discontinuity, due to collisions with upstream and downstream magneticscattering centers, resulting in a power-law spectrum extending up to very high energies.Relativistic jets and their shocks in Active Galactic Nuclei (AGN) is a prominent sourcefor particle acceleration. Especially, relativistic single or multiple shocks have beentheorized and observed along the jets of AGN and are claimed to be responsible foraccelerating even the highest-energy cosmic rays observed. In this paper we will reportand discuss the cosmic ray acceleration efficiency and properties of single or multipleshocks in the limit of relativistic plasmas in AGN jet environments.