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 gamma-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 (gamma(0) similar or equal to 10) and ultrarelativistic (gamma(0) similar or equal to 100) energies that directly correspond to the regimes of internal and external shell collisions, respectively, in GRB synchrotron emission models. Simulated systems comprise 5x10(8) 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 epsilon(B) similar to 12%, exceeding the respective internal ratios by nearly a power of 10. Enhanced epsilon(B) 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.