A Vishniac type contribution to the polarisation of the CMBR?

Radiation which has a quadrupole component of anisotropy, can get polarized by Thomson scattering from charged particles. In the cosmological context, the microwave background photons develop significant quadrupole anisotropy as they free stream away from the the epoch of standard recombination. Reionization in the post recombination era can provide free electrons to Thomson scatter the incident anisotropic $CMBR$ photons. We compute the resulting polarisation anisotropy on small (arc-minute) angular scales. We look for significant non-linear contributions, as in the case of Vishniac effect in temperature anisotropy, due to the coupling of small-scale electron density fluctuations, at the new last scattering surface, and the temperature quadrupole. We show that, while, in cold dark matter type models, this does not lead to very significant signals ($\sim 0.02 - 0.04 \mu K$), a larger small angular scale polarization anisotropy, ($\sim 0.1 - 0.5\mu K$), can result in isocurvature type models.