  The electron beam Weibel instability in the electrostatic collisionless shock
is studied via particle in cell simulation. When the non-relativistic incoming
plasmas collide with cold dilute plasmas, an electrostatic shock forms near the
interface. Following that, a filamentary out-of-plane magnetic field is formed
as a result of the Weibel instability. It is demonstrated that the anisotropy
of incoming hot electrons is insufficient to trigger the Weibel instability.
And the Weibel instability is excited by cold electrons in dilute plasmas.
After being accelerated to relativistic velocities by the shock electric field
into the dense plasmas, electrons in the dilute plasma have considerable
anisotropy and can trigger the Weibel instability
