Left, a): induced electric field from Langmuir waves produced from an electron beam propagating through a constant mean background density for different levels of density fluctuations after t = 277 s of propagation. The top panel has Δn/n = 0. The remaining panels increase Δn/n from Δn/n = 10^-5 to Δn/n = 10^-1.5 in the bottom panel, as indicated on the right-hand side. Right, b): probability distribution functions of the electric field on the left. The bin size is 0.125 mV/m in log space. The top panel has Δn/n = 0 and the red dashed line represents the PDF of a Gaussian distribution. The remaining panels increase Δn/n from Δn/n = 10^-5 to Δn/n = 10^-1.5. Note the change in y-axis limits at Δn/n ≥ 10^-3. The black vertical line indicates the thermal level of the electric field from Langmuir waves in plasma with n_e = 5 cm^-3.