Apr. 13 notes

Light from a lightning channel passes through both a prism and a diffraction grating and is imaged on film (or a detector of some kind). An entrance slit is not needed because the lightning channel is essentially a line source. The spectrum that you would obtain in this case would be a series of images of the channel at each of the wavelengths emitted by the discharge. In a 1961 article in Science, Leon Salanave explains that both a prism and a diffraction grating were used and arranged "so that their respective deviations counterbalance, to make a more 'straight-through' optical system." Salanave directed much of the lightning spectroscopic work done at the University of Arizona for several years. He is also the author of "Lightning and Its Spectrum " published by the University of Arizona Press in 1980.

Here's a modern implementation of the principle

These images are from an online PowerPoint presentation "Lightning Spectroscopy" by T. Walker, H. Christian, and D. Sentman. The camera is a Phantom v710 with a CMOS 1280x800 array with 12 bit dynamic range (in a separate conference publication the resolution was reduced to 1040 x 8 pixels so that 673 k images could be acquired per second).

An example spectrum obtained with the system above from a triggered lightning discharge (probably early during the continuing current portion of the discharge) is shown below.

Many of these spectral features appear to be from vaporization of the copper wire used to trigger the discharge.

In the early studies a time resolved spectrum was obtained by isolating a vertical segment of the lightning channel. The spectrum was recorded on moving film.

The film is shown moving downward in this picture (and sorry that the perspective isn't quite right). Spectra from two separate return strokes, perhaps, have been recorded on the film.

Here are actual implementations that provide moderate and very fast time resolution (from E.P. Krider, "Lightning Spectrosocpy," Nuclear Instruments and Methods, 110, 411-419, 1973).

The rotating drum in the lower figure provides the fastest time resolution. Rapidly rotating drums in streaking cameras are also used in photographic measurements of return stroke velocity.

The next figure shows an actual example of a very fast time resolved spectrum from a return stroke.

Several emission features are identified on this spectrum early in the return stroke discharge (NII denotes a singly ionized nitrogen atom). Now what is usually done next is to scan across the film image using a densitometer at say perhaps the level of the green line (i.e. at a time about 10 microseconds after the beginning of the return stroke).

Here is an example of a "digitized" spectrum. Film's response to light is nonlinear, so the film must be calibrated. Film also reacts different to short bright impulses of light than it does to longer duration low amplitude light signals. So that effect must also be considered.

Six emission lines in the NII(5) multiplet spectrum above have been identified. I am not familiar enough with spectroscopy and quantum mechanics to be able to say for sure what precise states and transitions cause these features

but I'm guessing it looks something like shown here. Transitions from 2 slightly different energy levels from an excited state to 1 of 3 levels at a lower energy state could produce emissions of 6 slightly different wavelengths.

In any event it is the relative amplitudes of lines in a multiplet group that can be used to estimate lightning channel temperature. The procedure is described below. Our goal is not understand all the steps but rather to get a flavor for the procedure or method.

The first assumption made is that the number of atoms in a particular energy level can be described using a Maxwell-Boltzmann distribution

N_n is the number of atoms in energy level n, N is the total number of atoms.

The intensity of the emission produced by transitions from energy level n to r is shown above.

Now we will look at the ratio of measured intensities from two different transitions: n to r and m to p

It is these transition intensities that can be measured on the fast time resolved lightning spectra. Note that many of the parameters cancel. This is fortunate because some of them (such as the geometric factor) might be difficult to determine. Solving for temperature yields

Often what is done is that several determinations of temperature are made using different combinations of lines in the multiplet group and an average is computed. In the case of the NII(5) multiplet 5 ratios could be computed: 4630/4601, 4630/4607, 4630/4613, 4630/4621, and 4630/4643.

The next several figures shown some of the results of these spectroscopic measurements and analyses.

Concentrations of NIII (doubly ionized atomic nitrogen), NII (singly ionized atomic nitrogen), and NI (neutral atomic nitrogen) early in a return stroke discharge. NII is initially the most abundant species and is used in spectroscopic determinations of peak temperature in the return stroke channel.

Estimate of peak return stroke channel temperature. The value approaches 30,000 K which is approximately 5 times hotter than the surface of the sun (6000 K).

Here are estimates of channel pressure. This requires a measurement of temperature and probably density (including electron density from the ionized air molecules).

references:
T.D. Walker and H.J. Christian, "Novel Observations in Lightning Spectroscopy," XV International Conference on Atmospheric Electricity, Norman OK, 2014.