  After quasars ionize intergalactic HeII at z~3, a large radiation field
builds up above the HeII ionization edge. Unlike the background responsible for
HI ionizations, this field should be highly variable, thanks to the scarcity of
bright quasars and the relatively short attenuation lengths (~50 Mpc) of these
high-energy photons. Recent observations of the HeII and HI Lyman-alpha forests
show that this background does indeed vary strongly, with substantial
fluctuations on scales as small as ~2 Mpc. Here we show that such spatial
fluctuation scales are naturally expected in any model in which the sources are
as rare as bright quasars, so long as the attenuation length is relatively
small. The correlation length itself is comparable to the attenuation length
(~10 Mpc) for the most plausible physical scenarios, but we find
order-of-magnitude fluctuations on all scales smaller than ~6 Mpc. Moreover,
aliasing along the one-dimensional skewers probed by the HeII and HI
Lyman-alpha forests exaggerates these variations, so that order-of-magnitude
fluctuations should be observed on all scales smaller than ~20 Mpc. Complex
radiative transfer is therefore not required to explain the observed
fluctuations, at least at the level of current data.
