Fig. 4: The effect of residual charged particles on the ambipolar diffusion.

a Plots of the residual electron density as a function of the time under three different initial peak electron densities, i.e., 1.0 × 10¹³ cm⁻³ (blue solid triangle), 1.0 × 10¹⁴ cm⁻³ (red solid circle), and 1.0 × 10 cm⁻³ (black solid square). \(n_{{\mathrm{ep}}}\) represents the initial peak electron density. The label (white star) shows a typical point, where the residual electron density approximately decays to be the same value 1.8 × 10¹¹ cm⁻³ within a short period of time (54.5 μs, indicated by the magenta vertical line segment) under the three different initial peak electron densities. b Variation of the ambipolar diffusion coefficient (purple solid diamond) with the number density of newly produced electrons in the streamer channel. μ_e, μ_i, D_e, and D_a are the electron mobility, ion mobility, free diffusion coefficient of electrons, and ambipolar diffusion coefficient, respectively. The label (white star) denotes a typical point, where the growth multiple of ambipolar diffusion coefficient increases to 15 with the electron density on the level of 10¹⁰ cm⁻³ near the edge of the streamer channel. The shaded region is introduced in order to focus the attention on the considerable growth of the ambipolar diffuse coefficient near the edge of the streamer channel.