Plasma Wakefield Acceleration for Ultrahigh Energy Cosmic Rays
  A cosmic acceleration mechanism is introduced which is based on the wakefields excited by the Alfven shocks in a relativistically flowing plasma, where the energy gain per distance of a test particle is Lorentz invariant. We show that there exists a threshold condition for transparency below which the accelerating particle is collision-free and suffers little energy loss in the plasma medium. The stochastic encounters of the random accelerating-decelerating phases results in a power-law energy spectrum: f(e) 1/e^2. The environment suitable for such plasma wakefield acceleration can be cosmically abundant. As an example, we discuss the possible production of super-GZK ultra high energy cosmic rays (UHECR) through this mechanism in the atmosphere of gamma ray bursts. We show that the acceleration gradient can be as high as G ~ 10^16 eV/cm. The estimated event rate in our model agrees with that from UHECR observations. 
Pisin Chen, Toshiki Tajima, and Yoshiyuki Takahashi