Astroparticle Physics

74 5 Acceleration MechanismsFig. 5.8Acceleration model for relativisticjets powered by a black hole or anactive galactic nucleus (thereactions are only sketched)shock-acceleration modelassume that the majority of galactic cosmic rays is producedby shock acceleration where the particles emitted from thesource are possibly further accelerated by the Fermi mechanismof 2nd order. In contrast, it is likely that the extremelyenergetic cosmic rays are predominantly accelerated in pulsars,binaries, or in jets emitted from black holes or activegalactic nuclei. For shock acceleration in supernova explosionsthe shape of the energy spectrum of cosmic-ray particlescan be derived from the acceleration mechanism.Let E 0 be the initial energy of a particle and εE 0 theenergy gain per acceleration cycle. After the first cycle onegetsE 1 = E 0 + εE 0 = E 0 (1 + ε) (5.30)while after the nth cycle (e.g., due to multiple reflection atshock fronts) one has