Thursday Mar. 7, 2013
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The Midterm Exam has been graded and was returned in class today.  In the past I would spend today's class going over the exam, but scores were high enough to make that unnecessary.  I will put together a set of solutions at some point during Spring Break.

You probably didn't enroll in this class thinking that you'd be spending so much time reviewing principles of electricity & magnetism, learning about small ions, conductivity, Maxwell currents and that sort of thing.   No you probably thought (hoped?) the class would be mostly about lightning.  And much of the class will be, beginning with this lecture.  We'll start with a fairly qualitative look at lightning phenomenology.  We'll concentrate primarily on cloud-to-ground lightning. 

Broadly speaking there are two types of lightning

Intracloud (IC) lightning remains in the cloud and is the most common type of discharge.  Approximately 1/3 of lightning discharges travel between charge in the cloud and the ground.  We'll use the term cloud-to-ground even though some relatively rare lightning discharges start at the ground and travel upward toward the cloud.

Most CG discharges, "negative cloud-to-ground", carry negative charge to ground.



Most CG discharges begin with an in-cloud, preliminary breakdown, process.  Also one of the lower positive charge centers LPCC) is probably involved in the initiation of most negative CG discharges.  One of the interesting and as yet unsolved problems is how localized fields in the cloud become high enough to breakdown air (30,000 volts/cm is needed at sea level altitude, 3 x 106 V/m).  Once breakdown is initiated fields in a larger volume must be high enough for a discharge to continue to propagate.

Pay attention to the branching in this and the figures that follow.  The branching tells you the direction of the initial leader process in the discharge (we'll learn more about the leader processes shortly).  The photograph above is from a Wikipedia article on lightning.

We've mentioned before that some CG discharges begin higher in the cloud and carry positive charge to the ground.  They too are initiated by a positively charged downward moving leader process.



Positive CG discharges are more common
(i)  in severe thunderstorms where vertical wind shear is present (faster winds at upper levels than lower altitudes).  Normally the positive charge center is above the main negative charge and discharge between the two remain in the cloud.  Wind shear can cause the cloud to tilt and move some of the positive charge away from a position directly above the main negative charge center.  Discharges can then travel from the cloud to the ground.

(ii)  in storms at high latitudes where the positive charge center is closer to the ground.

(iii)  in winter storms.  The positive charge center is closer to the ground.  Vertical wind shear may also be present

(iv)  at the ends of summer air mass thunderstorms like we have in Arizona.  The cloud may tilt or the anvil and positive charge can be blown away from the main body of the cloud. 

(v)  in storms with an inverted charge distribution as discussed in Lecture 12.

Positive CG discharges usually just have a single return stroke though the return stroke peak current is often very large 100,000 A or more (negative CG discharge peak return stroke currents are usually 30,000 A or less).  The positively charged leader than initiates a positive CG discharge shows little or no stepping (we'll discuss the negatively charged "stepped leader" that initiates negative CG discharges shortly). 

Tall buildings and towers are struck relatively often by lightning.  Often these are discharges initiated or triggered by the structure itself.






Note the direction of the channel branching.  These discharges begin at the ground with the development of an upward moving, positively charged, leader (very rarely the discharge can begin with an upward negatively charged leader).  The upward leader is followed by downward negatively charged leaders and upward return strokes, which is, as we shall see, the normal sequence of events in negative CG lightning.  The photo above shows upward lightning initiated by the Suchá Hora transmitter tower as seen from Banksa Bystrica, Slovakia, and is from a Wikipedia article on lightning.

We saw in an earlier lecture that because they enhance the local electric field, launch vehicles sometimes trigger and are struck by lightning.  Researchers are now able to trigger lightning discharges using small rockets.  A spool of wire attached to the base of the rocket unwinds as the rockets travels upward.  If conditions are right, an upward leader is initiated when the rocket reaches an altitude of 100 m or so.  Direct measurements of lightning return stroke currents and close (10 meters or less) E and B field measurements can be made.

Now we'll look in more detail at the sequence of processes that occur during negative cloud-to-ground discharges.



The discharge begins with some kind of in-cloud preliminary discharge involving the main negative charge center and one of the lower positive charge centers.  Then a downward moving, negatively-charged discharge begins moving toward the ground.  This is called the stepped leader discharge because the channnel advances in steps of about 50 m length every 50 microseconds or so.  The 50 m long channel extensions occur rapidly (less than 1 microsecond duration) and produce a bright flash of light.  Think of dropping a strobe light from aircraft altitude and watching it flash on and off as it falls to the ground.

It takes a few 10s of milliseconds for the step leader to travel a few kilometers from the cloud to near the ground.  This corresponds to an average speed of 1 to 2 x 105 m/sec (traveling from 6 km altitude in the cloud to the ground in 30 msec would result in a speed of 2 x 105 m/sec.  Negative charge is carried from the main negative charge center and distritbuted along the length of the leader channel.   Currents flowing in the leader channel range from 100s to about 1000 Amps.

The individual step, or extension of the leader channel, occurs in less than 1 microsecond.  The velocity of the step is 5 x 107 m/s or faster (50 m in 1 μs is 5 x 107 m/s) and the step current is 1 kA or more.

Images of stepped leader have been captured using streaking cameras (cameras with moving film) and, more recently, on video cameras with high frame rates.  The next figure tries to illustrate how a descending leader might appear on film.

Because the film is moving (to the left), each of the images is displaced slightly (to the right) on the film.  Extensions of the channel produce the most light (highlighted in yellow above) but the remainder of the channel is usually weakly illuminated.  The descending channel breaks up into brances and then the ends of the separate branches begin to independently step and move toward the ground.

Here's a short description of the Boys Camera that was used originally to photograph the sequences of processes in cloud-to-ground lightning with fast time resolution.  This is from Martin A. Uman's book Lightning (reissued by Dover Publications, New York, 1984) which has an excellent survey of early photographic studies of lightning. 




Here are a couple images of actual streak camera photographs of a stepped leader (left) and a dart leader (right).  They were given to me by Dr. Vince Idone a professor at the State University of New York at Albany. 

You can clearly distinquish the separate steps in the upper half of the left image.  We haven't really discussed dart leaders yet but they travel continuously from the cloud to ground (without stepping) and at a higher speed than stepped leaders.

You can see some additional examples of streak photographs of lightning leaders in "Lightning Leader Characteristics in the Thunderstorm Research International Program (TRIP)", by R.E. Orville and V.P. Idone, in an article titled "Novel Observations of Lightning Discharges: Results of Research on Mount San Salvatore" by Karl Berger (check the Articles folder for a complete citation) and in "Progressive Lightning" by B.F.J. Schonland and H. Collens (published in the Proceedings of the Royal Society of London and the first of a  series of reports on early lightning research conducted in South Africa).   Here's a short description of the Boys Camera that was used originally to photograph the sequences of processes in cloud-to-ground lightning with fast time resolution.  This is from Martin A. Uman's book Lightning (reissued by Dover Publications, New York, 1984) which has an excellent survey of early photographic studies of lightning.  You'll find some additional discussion of streaking photography in
"Lightning Return Stroke Velocities in the Thunderstorm Research International Program (TRIP)"  by V.P. Idone and R.E. Orville.

We won't cover the attempts that have been made to understand or simulate stepped leader channel development.  It would be very difficult to produce a stepped leader discharge in a laboratory because each step is 50 m long.  Here's my conception of what leads up to an extension of the stepped leader channel.


Basically the leader consists of a low resistance arc core that is surrounded by a space charge envelope.  High fields at the bottom end of the propagating channel create discharge tendrils that grow out into the air ahead of the leader.  Initially this is a high resistance glow discharge.  As the discharge filaments increase in number and lengthen, more and more current flows from the bottom end of the arc core.  At some point, a portion of the glow discharge channel will change to a conducting arc.  It is this sudden change from glow to arc discharge that produces a brief pulse of current and light.  This is the step that effectively lengthens the leader channel. 

This seemed like a good point to have a look at a slow motion video of an actual stepped leader.  This first video is a negative cloud to ground discharge with just a single return stroke.  A video camera that captures 7200 images per second was used (the video is then slowed down considerably during play back).  And here is a site with high-speed videos of a negative stepped leader, a downward positive leader, and an upward positive leader.

When the stepped leader approaches to within a few hundred meters of the ground, the electric field at the ground intensifies to the point that several positively charged, upward propagating discharges are initiated.  One of these will intercept the stepped leader and determine where the lightning will strike the ground.




The striking distance referred to in the figure is typically 10 to 20 m above flat ground and 20 to 100 m above taller objects.  This is a reasonably important parameter in the design of lightning protection design, a topic we will cover later in this class.

There are probably less than a dozen good photographs of upward connecting discharges.  One of the best was taken by Johnny Autery in Alabama.  The photograph is copyrighted but I've sketched it below and have pointed out some of the main features.

You can see the actual photograph on the photographers homepage and in this Wikipedia article on lightning.  There were at least 3 upward discharges initiated by the approach of the stepped leader (1, 2, and 3 in the sketch).  Streamer 1 connected to the bottom of the stepped leader.  It isn't clear where the exact junction point was, perhaps at the point where the channel takes a bend to the right.  The downward branching at Point 4 indicates that was part of the descending stepped leader.  A very faint upward discharge can be seen at Point 3.

Since class I have learned more about another image that I showed in class.  It was taken by Carey Walton and can be viewed here (the first two images in a sequence of images). 

Many of the remaining examples can be seen on pps 141 & 142 in Rakov and Uman's book "Lightning Physics and Effects."  As chance would have it this portion of the book can be viewed online here (you may have to scroll up or down to find pps 141 & 142).  There are also some good examples in this gallery of images.

Junction between the upward connecting discharge and the stepped leader electrically connects charge in the cloud to ground and a large amplititude pulse of current travels rapidly back up the channel.  This is the first return stroke discharge.



The tip of the return stroke propagates up the channel at a speed of about 1 x 108 m/s (1/3 the speed of light) taking about 100 microseconds to travel from the ground to the cloud.  The 1st return stroke has a peak current of typically 30 kA.  Current rises to peak value in a few microseconds and the peak dI/dt is about 100 kA/us.  The return stroke heats the air to a peak temperature of about 30,000 K (5 times hotter than the surface of the sun).  The overpressure creates a shock wave that quickly decays into a sound wave that we hear as thunder. 

I often use the following analogy to help understand the return stroke process.

Now imagine what you would see if the hand at the bottom of the tube is removed.




And now back to the stepped leader channel and all the negative space charge surrounding it.

The intense action is really at the tip of the upward propagating return stroke.  The large potential difference (cloud potential in close proximity to ground potential) ionizes the air, creates large currents, heats the air, and produces a bright flash of light.  The potential difference wave can propagate rapidly up the channel (and out into the branches).  Once the potential wave passes a point on the channel the space charge envelope collapses and electrons flow more slowly down the conducting channel to ground.



Some cloud-to-ground discharges end at that point (you'll find some statistics in our next class).  I.e. they consist of (i) a downward, negatively charged, stepped leader, (ii) a relatively short upward connecting discharge, and (iii) an upward return stroke that travels from the ground to the cloud at about 1/3 the speed of light. 

Most cloud-to-ground discharges however contain multiple strokes.  A schematic illustration of a 4 stroke cloud-to-ground is shown below.


The discharge begins at left in the figure with a branched stepped leader that is followed by a 1st return stroke.  The stepped leader takes a few 10s of milliseconds to travel from the main negative charge center in the cloud to the ground. The ensuing 1st return stroke travels back up the channel to the cloud is about 100 microseconds.

Then, with a few slight differences, the process repeats itself.  Additional discharges occur typically at intervals of 50 to 100 ms and are usually preceded by a dart leader that travels, without stepping or branching, down the existing main channel.  A short upward connecting discharge is initiated when the dart leader gets close to the ground and then a subsequent return stroke travels back up the channel to the cloud.  We'll look at the dart leader and subsequent return stroke processes in a little more detail shortly.

The 3rd return stroke in the illustration above is following by a continuing current.  This is a low amplitude (100s of Amperes) current that continues to flow for 10s of milliseconds or more typically, which keeps the return stroke channel luminous.  Short rebrightenings of the channel sometimes occur during the continuing current, these are called M-components.

The bright flashes of light produced by multiple return strokes produces the flickering that you sometimes sees when observing cloud to ground lightning.  If you deliberately move a camera back and forth while photographing lightning the separate strokes will be displaced on the image.  The technique is described in an article "Panning for Lightning," by John Hendry Jr. that was published in Weatherwise Magazine (vol. 45, No. 6, pps 18-19, Dec. 1992/Jan 1993 issue).   Here is an example (source: http://www.odec.ca/projects/2005/schu5s0/public_html/lightning.html ).



This appears to have been a 4 stroke flash.  The rightmost channel in the photograph is branched so that is the first return stroke.  Separation of the return strokes channels like this can sometimes be caused by wind.  That is referred to as "ribbon lightning."  As long as we're on the subject of lightning photograph, here is a good lightning photograph guide.