Ultrarelativistic plasma shell collisions in γ-ray burst sources: Dimensional effects on the final steady state magnetic field

Ultrarelativistic electron-positron plasma shell collisions as an integral part of generic γ-ray burst (GRB) fireball models are studied in the framework of self-consistent three-dimensional particle-in-cell simulations. We compare scenarios at moderately relativistic (γ ≃10) and ultrarelativistic (γ ≃ 100) energies that directly correspond to the regimes of internal and external shell collisions, respectively, in GRB synchrotron emission models. Simulated systems comprise 5 × 10 particles, applying a relativistic, fully electromagnetic, massively parallelized code. It is found that Weibel-generated, steady state magnetic equipartition ratios in external collisions reach up to ε ∼12%, exceeding the respective internal ratios by nearly a power of 10. Enhanced ε yields can be explained theoretically by the effective reduction of dimensionality in the ultrarelativistic limit, i.e., the energy-dependent confinement of the three-dimensional Weibel instability within quasi-two-dimensional plasma shell slices.