  We investigate the feasibility of detecting and probing various components of
the ionized intergalactic medium (IGM) and their turbulent properties at radio
frequencies through observations of scatter broadening of compact sources.
There is a strong case for conducting targeted observations to resolve scatter
broadening (where the angular size scales as $\sim \nu^{-2}$) of compact
background sources intersected by foreground galaxy haloes and rich clusters of
galaxies to probe the turbulence of the ionized gas in these objects,
particularly using Space VLBI with baselines of 350,000 km at frequencies below
800 MHz. The sensitivity of the Square Kilometre Array (SKA) allows
multifrequency surveys of interstellar scintillation (ISS) of $\sim 100
\,\mu$Jy sources to detect or place very strong constraints on IGM scatter
broadening down to $\sim 1\, \mu$as scales at 5 GHz. Scatter broadening in the
warm-hot component of the IGM with typical overdensities of $\sim 30$ cannot be
detected, even with Space VLBI or ISS, and even if the outer scales of
turbulence have an unlikely low value of $\sim 1$ kpc. Nonetheless,
intergalatic scatter broadening can be of order $\sim 100\, \mu$as at 1 GHz and
$\sim 3\, \mu$as at 5 GHz for outer scales $\sim 1$ kpc, assuming a
sufficiently high source redshift that most sight-lines intersect within a
virial radius of at least one galaxy halo ($z \gtrsim 0.5$ and $z \gtrsim 1.4$
for $10^{10} {\rm M}_\odot$ and $10^{11} {\rm M}_\odot$ systems, following
McQuinn (2014)). Both Space VLBI and multiwavelength ISS observations with the
SKA can easily test such a scenario, or place strong constraints on the outer
scale of the turbulence in such regions.
