Top: characteristic scale of the plasma inhomogeneity when Δn/n = 10^-3 for a constant mean background electron density, over an area of space 56 Mm in length. Bottom: Langmuir wave energy density, normalised by the initial value, at four different times t = 150,200,250 and 300 s. The earliest time corresponds to spontaneous emission from the front of the beam. The other three times correspond to wave growth from the bump-in-tail instability. Wave propagation smooths out the fine structure present in the plasma inhomogeneity.