  A new magnetic field generation mechanism in electrostatic shocks is found,
which can produce fields with magnetic energy density as high as 0.01 of the
kinetic energy density of the flows on time scales $ \tilde \, 10^4 \,
{\omega}_{pe}^{-1}$. Electron trapping during the shock formation process
creates a strong temperature anisotropy in the distribution function, giving
rise to the pure Weibel instability. The generated magnetic field is
well-confined to the downstream region of the electrostatic shock. The shock
formation process is not modified and the features of the shock front
responsible for ion acceleration, which are currently probed in laser-plasma
laboratory experiments, are maintained. However, such a strong magnetic field
determines the particle trajectories downstream and has the potential to modify
the signatures of the collisionless shock.
