Sprites in varying air density: charge conservation, glowing negative trails and changing velocity.

We study the initial downward propagation of long sprite streamers in naturally varying air density with numerical simulations on adaptively refined grids. We find that the ionization rate and the light emission from the streamer head increase approximately linearly with air density (therefore exponentially with time) while the radius hardly changes, in contradiction with a naive application of scaling laws. Charge conservation creates a negative charge and a consecutively enhanced electric field in the upper section of the streamer channel, while the head carries a growing positive charge. The high electric field in the upper part of the channel generates a secondary ionization wave and a luminous trail. The negative charging explains the emergence of upward, negative streamers from a channel and the attraction of positive heads to a previously formed channel. Finally we show that the vertical gradient in the air density initially accelerates the streamer head and subsequently slows it down, in agreement with recent observations