Cross correlations of the CMB Doppler mode and the 21 cm brightness temperature in the presence of a primordial magnetic field

The cross correlation between the CMB Doppler mode and the 21 cm line brightness temperature is calculated in the presence of a stochastic primordial magnetic field. Potential detectability is estimated for Planck 2018 bestfit parameters in combination with configuration and survey design parameters of 21 cm line radio telescopes such as LOFAR and the future SKAO. Homogeneous as well as inhomogeneous reionization has been considered. In particular the latter in combination with SKA1-mid shows promising signal-over-noise ratios.