  The shape of the anisotropic velocity distribution function, beyond the realm
of strict Maxwellians can play a significant role in determining the evolution
of the Weibel instability dictating the dynamics of self-generated magnetic
fields. For non-Maxwellian distribution functions, we show that the direction
of the maximum growth rate wavevector changes with shape. We investigate
different laser-plasma interaction model distributions which show that their
Weibel generated magnetic fields may require closer scrutiny beyond the second
moment (temperature) anisotropy ratio characterization.
