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Acceleration of ultrahigh-energy cosmic rays in the early afterglows of gamma-ray bursts: Concurrence of jet dynamics and wave-particle interactions
The origin of ultra-high energy cosmic rays $($UHECRs$)$ remains a mystery. It has been suggested that UHECRs can be produced by the stochastic acceleration in relativistic jets of gamma-ray bursts $($GRBs$)$ at the early afterglow phase. Here, we develop a time-dependent model for proton energization by cascading compressible waves in …