Next we will take a very quick look at another lightning return stroke current model - a specification of return stroke current as a function of altitude (z) and time (t).



Here again is a schematic view of the transmission line model.  The return stroke current begins at the ground and travels up a vertical channel at constant speed, v, without changing shape.  The current waveform measured at the ground at the beginning of the return stroke passes a point z above the ground at t = z / v.

The new, traveling current source model, is illustrated below.



In this model (originally proposed by Heidler (1985)) current begins not at the ground but above the ground at the return stroke front as charge as charge is drained from the leader channel (charge surrounding the leader channel at about cloud potential drains into the return stroke channel which is at ground potential).  The current then travels down the channel to the ground at the speed of light.  The return stroke is assumed to propagate upward at constant speed v.  The figures and discussion of the traveling current source (TCS) model found in this section are taken from Diendorfer and Uman (1990).

The current that develops at altitude z consists of two components: a "breakdown" current due to relatively rapid draining of charge in the leader head and leader core and a "corona" current due to slower movement of charge surrounding the leader channel.

 
An illustration of the two current components in the TCS model (BD is breakdown and C is corona).  The breakdown component is largely responsible for determine peak E and peak dE/dt field amplitudes.  The Current-1 and Current-2 waveforms are thought to be good approximations of subsequent and first return stroke current waveforms that would be observed at the ground.



This figure shows the distribution of charge along the leader channel as a function of altitude (the lowest 250 m in (a) and the bottom 2500 m in (b)).  Note the buildup of charge at the bottom tip of the leader.  This is the charge distribution needed to produce the Channel-1 (subsequent stroke) waveform.



This figure shows the current waveforms that would be observed at different altitudes above the ground (at ground level the Channel-1 waveform peaks at about 14 kA).  Changes in signal shape like this are seen in measurements of the optical signals coming from short segments of the return stroke channel at different altitudes above the ground (a topic we might cover later in the semester).