Fast Radio Burst Dispersion Measure Distribution as a Probe of Helium
  Reionization
  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. 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 $\sim6\sigma$ using the DM-distribution of bursts,
without redshift information (and $\sim10\sigma$ with redshifts).
