  Plasma streaming instabilities play an important role in magnetic field
amplification and particle acceleration in relativistic shocks and their
environments. However, in the far shock precursor region where accelerated
particles constitute a highly relativistic and dilute beam, streaming
instabilities typically become inefficient and operate at very small scales
when compared to the gyroradii of the beam particles. We report on a plasma
cavitation instability that is driven by dilute relativistic beams and can
increase both the magnetic field strength and coherence scale by orders of
magnitude to reach near-equipartition values with the beam energy density. This
instability grows after the development of the Weibel instability and is
associated with the asymmetric response of background leptons and ions to the
beam current. The resulting net inductive electric field drives a strong energy
asymmetry between positively and negatively charged beam species. Large-scale
particle-in-cell simulations are used to verify analytical predictions for the
growth and saturation level of the instability and indicate that it is robust
over a wide range of conditions, including those associated with pair-loaded
plasmas. These results can have important implications for the magnetization
and structure of shocks in gamma-ray bursts, and more generally for magnetic
field amplification and asymmetric scattering of relativistic charged particles
in plasma astrophysical environments.
