We investigate the growth of ion density perturbations in large-amplitude linear laser wakefields
via two-dimensional particle-in-cell simulations. Growth rates and wave numbers are found to
be consistent with a longitudinal strong-field modulational instability (SFMI). We examine the
transverse dependence of the instability for a Gaussian wakefield envelope and show that growth
rates and wavenumbers can be maximised off-axis. On-axis growth rates are found to decrease with
increasing ion mass or electron temperature. These results are in close agreement with the dispersion
relation of a Langmuir wave with energy density that is large compared to the plasma thermal energy
density. The implications for wakefield accelerators, in particular multi-pulse schemes, are discussed
