  Magnetic field amplification by relativistic streaming plasma instabilities
is central to a wide variety of high-energy astrophysical environments as well
as to laboratory scenarios associated with intense lasers and electron beams.
We report on a new secondary nonlinear instability which arises for
relativistic dilute electron beams after the saturation of the linear Weibel
instability. This instability grows due to the transverse magnetic pressure
associated with the beam current filaments, which cannot be quickly neutralized
due to the inertia of background ions. We show that it can amplify the magnetic
field strength and spatial scale by orders of magnitude, leading to large-scale
plasma cavities with strong magnetic field and to very efficient conversion of
the beam kinetic energy into magnetic energy. The instability growth rate,
saturation level, and scale length are derived analytically and shown to be in
good agreement with fully-kinetic simulations.
