Constraints on Primordial Magnetic Fields from their impact on the ionization history with Planck 2018

We update and extend our previous CMB anisotropy constraints on primordial magnetic fields through their dissipation by ambipolar diffusion and MHD decaying turbulence effects on the post-recombination ionization history. We derive the constraints using the latest Planck 2018 data release which improves on the E-mode polarization leading to overall tighter constraints with respect to Planck 2015. We also use the low-multipole E-mode polarization likelihood obtained by the SROLL2 map making algorithm and we note how it is compatible with larger magnetic field amplitudes than the Planck 2018 baseline, especially for positive spectral indices. The 95% CL constraints on the amplitude of the magnetic fields from the combination of the effects is $\sqrt{\langle B^2 \rangle} <0.69 (<0.72)$ nG for Planck 2018 (SROLL2) by marginalizing on the magnetic spectral index. We also investigate the impact of a damping scale allowed to vary and the interplay between the magnetic field effects and the lensing amplitude parameter.