Abstract
Fast radio burst (FRB) discoveries are occurring rapidly, with thousands expected from upcoming surveys. The dispersion measures (DM) observed for FRB include important information on cosmological distances and the ionization state of the universe from the redshift of emission until today. Rather than considering the DM--redshift relation, we investigate the statistical ensemble of the distribution of dispersion measures. We explore the use of this abundance information, with and without redshift information, to probe helium reionization through simulated data to redshift $z=6$. Carrying out Monte Carlo simulations of FRB survey samples, we examine the effect of different source redshift distributions, host galaxy models, sudden vs gradual reionization, and covariance with cosmological parameters on determination of helium reionization properties. We find that a fluence limited survey with ${10}^{4}$ FRBs can discriminate different helium reionization histories at $\ensuremath{\sim}6\ensuremath{\sigma}$ using the DM-distribution of bursts, without redshift information (and $\ensuremath{\sim}10\ensuremath{\sigma}$ with redshifts).