Wednesday April 22, 2015

Two more Final Exam questions
Here's the first of today's questions (from the Spring 2009 Final Exam)
On April 26, 1986, an accident at the Chernobyl nuclear reactor sent a plume of radioactive cesium (137Cs), iodine (131I), and ruthenium (103Ru) into the lower atmosphere that was subsequently carried to many locations in Europe in a few days.  The plume arrived over Greece on May 3.  The figure below compares the long term average daily variation of positive conductivity λ+ observed in May (dotted line) with enhanced conductivity observed in May 1986 (solid line).  (figure adapted from D. REtalis and A. Pitta, "Effects on Electrical Parameters at Athens Greece by Radioactive Fallout from a Nuclear Power Plant Accident," J. Geophys. Res., 94, 13093-13097, 1989)

The exam question has 3 parts:
(i)   Would you have expected the higher conductivity in May 1986 to have increased or decreased the strength of the fair weather electric field at the ground? 

(ii)   Use the positive conductivity values in the figure above to determine the positive small ion concentrations, n+, before and after the arrival of the radioactive plume.

(iii)  Assuming steady state conditions and neglecting small ion to particle attachment, determine the small ion production rate, q, before and after the arrival of the plume.
  You may assume the numbers of positive and negative small ions are equal.

The charge on an electron is 1.6 x 10-19 C, you may used the values given for 0 km altitude on the "Summary of Electric Parameters vs Altitude" handout for any other constants that you might need.

Here's today's second question (from the Spring 2011 Final Exam)

Assume that there are N strikes per kilometer per year to a long power line.  What is the probability that the nearest strike is between x and x + dx.  Basically you are being asked to derive a one-dimensional version of the nearest neighbor probability density function.  You can assume that the point of reference is on the left end of the line (0 in the sketch below) and that the line extends to the right without limit.

Sprites, blue jets, and elves
The preferred term for these types of events is Transient Luminous Event (TLE). 

In a 1924 paper, C.T. Wilson suggested that "The electric field of the [thunderstorm] cloud may cause ionization at great heights..."  "At a height of 60 km, the density of the air is about 1.6 x 10-4 of that near the ground, while the composition of the air is not very different, so that the critical value of the field may be taken as about 30,000 x 1.6 x 10-4 = 4.8 volts per centimetre."

Despite many reports of optical phenomena high above thunderstorms (often from pilots flying at night), credit for the first photographic evidence of these kinds of phenomena is given to John Winckler, a researcher at the University of Minnesota.  On the night of July 6, 1989 he was testing a low light level video camera and later found two images of sprites on the video he had recorded (ref).

Here's a pretty good figure summarizing the various types of luminous event (source:; CNES is the French Centre National d'Etudes Spatiales)

The following figure is adapted from a review article by C.J. Rodger (1999) and shows some of the forms sprites may take:

And some general characteristics of red sprites (from the Rodger, 1999, paper cited above).  Sprites seem to follow positive cloud to ground discharges.

Minimum altitude
50 km (tendrils < 40 km)
Maximum altitude
90 km
Width (km)
25 - 50 km (columns >2 km)
5 - 300 ms
Association with lightning
positive cloud-to-ground (ELF slow tail)
Occurrence rate
1 in 40 to 1 in 2.3

Sprites are dim and hard to see with the naked eye (adapted from

To see a sprite you need an unobstructed view of the region above an active thunderstorm.  The best viewing distance is about 100 - 200 miles from a storm.
The dark adapted eye most readily sees sprites in parfoveal vision (looking out the corner of your eye (rods) rather than looking directly at the sprite (cones which respond better to colors).

It must be very dark, no city light, no twilight.  Cloud illumination from lightning activity may be too bright or may be distracting.

Sprites are very brief (3-10 ms usually).  They are produced by only about 1% of lightning strokes.

Sprite videos:
sprite movie (Univ. AK, Geophys. Inst.)
sprite in slow motion (H.H.C. Stenbaek-Nielsen, U. Alaska Fairbanks, DARPA, NSF)
sprite movie high speed video (NM Tech)
sprite movie high speed video (NM Tech)
here are some spectacular pictures and videos (not sure how to cite this page)

Some of my favorite pictures are still images (especially ones that include the foreground and surroundings)
Mike Hollingshead (Astronomy Picture of the Day)
Sprite with Aurora (Walter Lyons and an Astronomy Picture of the Day)
A hard to spot sprite viewed from the International Space Station (ISS Expedition 31 crew, NASA)
sprite (National Geographic) (click here if the link is slow to respond)
sprite (Geospace Physics Laboratory, Florida Inst. of Tech.)
sprite (
sprite (Weatherscapes)

Blue jets
These begin and extend upward from the tops of thunderstorms.  Characteristics of blue jets and blue starters are shown below (from Rodger 1999).

It is still not clear what produces blue jets, they do not necessarily follow directly after a lightning discharge.  The propagate upward at about 1 x 105 m/s.  The deep blue color, which is more readily scattered by air, makes them difficult to see and photograph.  Some characteristics of blue jets are shown below (from Rodger, 1999)

deep blue
Minimum altitude
about 20 km
Maximum altitude
40 to 50 km
Width (km)
about 3 km (cone about 15 degrees)
about 250 ms
Occurrence rate
2.8 per minute (in 22 min.)

blue jet videos

blue jet movie (Univ. AK, Geophys. Inst.)

still photographs
blue jet (PBS Nova)
Stanford University photograph (this might be an example of a giant blue jet)
blue jet photographed above a thunderstorm in the Northern Territory, Australia (Thijs Bors published in The Telegraph)
blue jet on St. Barth (credit: Elka Liot, Muskapix Gregory Moulard.  "St. Barth" refers to Saint Barthelemy a French Overseas Collectivite Territoriale in the Carribean.  Together with Saint Martin, Guadeloupe, and Martinique it is part of the French West Indies)

The name is an acronym for Emission of Light and Very Low Frequency Perturbations Due to Electromagnetic Pulse Sources.

 . . .
Minimum altitude
75 km
Maximum altitude
105 km
Width (km)
100 - 300 km
< 1 ms
Association with lightning
intense positive cloud-to-ground
(average 148 kA)
Occurrence rate
 . . .

Videos of Elves
Blue jets, Sprites, and Elves (New Scientist video)

Production of X-rays and γ-rays by lightning
This section needs some updating

Moore et al. (2001) have reported observing bursts of high energy radiation associated produced in a 1 to 2 ms interval just before the start of the return stroke and as the stepped leader was nearing the ground.  Dwyer et al. (2003) observed bursts of energetic radiation in the last 160 μs of the dart leader and possibly right at the start of the return stroke in 31 out of 37 triggered events studied.  The shorter interval may be because dart leaders have a higher propagation speed.  My understanding is that the sensors used in both these two experiments were unable to distinguish between energetic electrons, X-rays, and gamma rays.

A NaI (sodium iodide) scintillation detector was used in both experiments.  Light is emitted when the high-energy radiation strikes the NaI.  The weak light signal is then detected and converted into an electrical current using a photomultiplier tube (source of the figure below)

A sketch of the signal produced by the scintillation detector used by Dwyer et al.,  when exposed to a Cesium-137 γ-ray source, is shown below (the control sensor was identical except it did not include the NaI scintillator). 

The exponential decay following the peak is the response of the preamplifier circuit. 

The figure below is a sketch of high energy radiation produced by a triggered lightning discharge from the Dwyer et al. (2003) paper.

The output of the scintillation detector is shown at top.  This signal began 160
μs before the start of the return stroke (the return stroke began at time 0 in the figure).  The complex signal shape during the rise to peak indicates that several energetic particles were detected.  A very small pulse is just visible on the control signal trace and may have been caused by energetic particles directly striking the photocathode of the photomuliplier tube.  The return stroke current was measured at the strike point and rose to a peak value of about 22.5 kA.  The electric field was measured at a point 260 m away from the strike point and has the characteristic asymmetric V-shape described by Rubenstein et al. (1995) for the leader-return stroke transition observed at close range.

An improved sensor was used during the summer 2003 campaign and Dwyer et al. (2004) report X-rays were measured 0 to 80 μs prior to and at the beginning of 73% of triggered return strokes studied.  Each X-ray burst usually lasted less than 1 μs.  The most intense bursts come from parts of the channel that is within 50 m of the ground.  A sketch of one of the recorded signals is shown below.  The return stroke began at time t=0.

Energies for most of the x-rays that were detected are shown in the publication, some of the values are included in the sketch above (in keV).
  Note how the amplitudes of the x-rays in this and the next figure increase as the leader (a dart leader in this case) nears the ground.

Dwyer et al. (2005) has measured X-ray emissions coming from the stepped leader process in natural cloud to ground discharges.  The last 11 steps of the stepped leader are shown in the sketch below (the start of the return stroke is at time = 0).

The lightning struck about 50 m from the electric field derivative antenna (the E field signal above is an integration of the measured dE/dt signal) and about 260 m from the x-ray detector. 

It seems clear that the x-rays are produced during the stepping process.   Because of the similarity between x-rays produced by dart leaders in triggered lightning and stepped leaders in natural lightning Dwyer et al. (2005) suggests that the production mechanisms are similar and that dart leaders also step, but with a frequency that isn't resolved on optical or field records.

Emissions from dart leaders in triggered lightning and stepped leaders in natural lightning are similar.  This suggests some similarities in the discharge process (dart leaders may actually step)

Observations may provide some clues about leader propagation processes.

The standard "relativistic runaway electron avalanche model" might have some trouble trying to explain the lightning generated X-ray emissions.

Schumann resonance
Lightning signals excite the earth - ionosphere cavity.  Resonant frequencies are amplified. 

source of the image above
source of the plot above