Temperature as a function of distance from the centre of the lightning discharge channel for a current I = 105 A, gas density ρg = 3 × 10-7 kg m-3, dust density ρ1 = 10-3 kg m-3, pebble density ρ2 = 10-2 kg m-3 and optical depth τ⋆ = 300. The discharge channel has a width of 100 m, indicated by the vertical dotted line. The discharge is assumed to last 2 × 103 s, followed by a cooling phase that is evolved up to a time of 104 s. Heating is rapid and uniform within the discharge channel, while the outer regions only heat after radiation diffuses out from the discharge region. The equilibrium temperature follows the analytical solution outside of the discharge channel.
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