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.
