Why sprites are red and jets are blue

Energy levels

On small scales nature behaves differently from what our everyday experience tells. The particles that make up an atom, a molecule or an ion cannot have just any energy. On the contrary, they have specific energy levels. This is because of a seemingly strange fact: For states of particles which are bound to each other, the probability of finding a particle in a certain state must satisfy a wave equation, much in the same way as the motion of air in an organ pipe creates standing waves and only a certain tone and its overtones are ever heard. ("State" here may be thought of as a certain energy of the whole atom or molecule.)

This wave-like behaviour of probabilities is the basis of quantum mechanics, which was developed in the early 20th century by Max Planck, Erwin Schrodinger, Niels Bohr and many others. It is probably the most successful scientific theory ever invented. Among many other things, it explains why atoms are stable, i.e. why the negative electrons do not simply fall into the positive atomic nuclei.

Quantisation of energy levels does apply to large objects, such as people in a room, as well, but for the very large objects of the everyday world the steps of energy quantisation are so tiny compared with the total energy that the quantisation is simply not observable.

Excited states

From the above principles of quantum mechanics we can understand that each atom or molecule has a certain limited number of energy states. What will then happen if energy is "added" to an atom or molecule, for example by thermal collisions or electromagnetic radiation? If the additional energy is less than the difference between the current energy level and the closest higher level, nothing happens! The atom or molecule simply cannot absorb such energies.

But if the energy is equal to the difference of the energy levels, the whole atom or molecule will be transferred to the higher energy state. This is called excitation. The excited atom or molecule will then, of course, "try" to get rid of the excess energy because it "wants" to reach its ground state, the state of lowest possible energy. There are more than one way for this to happen:

1. The atom or molecule could react with other particles, to form new chemical substances, and in that process give the excess energy away to the products, which may in turn be excited particles, and so on... 2. The atom or molecule could collide with other particles and give away the excess energy as kinetic energy 3. An atom or molecule can transfer to a lower energy state by emitting a photon, i.e. a quantum of light, carrying exactly the energy corresponding to the difference between the energies of the original and the final energy states. Now, the wavelength of the light (and therefore the perceived colour) is inversely related to the energy of the photon, i.e. a higher energy means a shorter wavelength.

Allowed and forbidden transitions

All transitions must satisfy the physical laws of conservation of energy, momentum and angular momentum. (Don't get confused by these terms). Since each photon can have only one certain energy and a specific angular momentum (corresponding to its polarisation, if you have studied some physics), arbitrary transitions between energy states are not allowed. There is a set of mathematical selection rules which tell if a certain transition is allowed or forbidden.

The optical properties of TLEs

In the TLEs, accelerated electrons hit the atoms and molecules of the atmosphere, much as in the aurorae (Northern and Southern lights). This can cause:

• Ionisation of the atoms or molecules, i.e. one or more electrons are removed completely. The remaining ion is often in an excited state.
• Electronic excitation of the atoms or molecules (Their outer electrons are transferred to a state of higher energy)
• Vibrational and rotational excitation of molecules, i.e. the atoms of a molecule start to oscillate with respect to each other, or rotate around their center of mass.

From the above we now understand that TLEs excite atmospheric atoms and molecules and that these excited particles can emit light of specific wavelengths only.

This is what gives us the colours of all optical emissions from excited gasses, including those of TLEs. The red colour of sprites comes from the fact that the difference in energies between the first and second excited states of a nitrogen atom happens to correspond to a wavelength our eye perceives as "red". Blue jets are blue due to the transitions of nitrogen atoms between the third and second excited states of nitrogen molecules and emission from molecular nitrogen ions. Note: In reality, these emissions are not single-wavelength emissions but emission bands. This is because both the upper and lower electronic state may be in a different vibrational state with slightly different energies.

Long-lived states and quenching

A complication is that in the atmosphere, even forbidden transitions do happen, since there are always particles available to "sneak in" and take up or provide any excess energy or momentum. But the intensities of these transitions will be lower than those of the allowed transitions. States from which all possible transitions are forbidden are called long-lived or metastable. Long-lived states are very likely to deexcite through collisions instead of radiation. Spectroscopists call this "quenching".

Thus, even if the same excited states would be present, TLEs in the lower part of the mesosphere would look different from those in the upper mesosphere, because in the denser lower mesosphere the long-lived states would be quenched more efficiently than in the rarefied upper mesosphere.

Instruments for optical observations

Three different types of optical instruments are important in studies of sprites: photometers, imagers (cameras), and spectrographs.

Photometers

The photometer is the simplest optical instrument. It collects light from the whole field of view onto one single detector. The output is an electrical current or voltage which can be converted into numbers and stored on a computer. Not shown in the figure below is the filter that is often used to select a wavelength range of interest.

Cameras

The camera can be thought of as many photometers with a single optical system. Instead of the single detector covering the full field of view, the camera has many "sub-detectors", called pixels (short for "picture elements"). The most common detector type is called CCD, or charge-coupled device.

Each pixel sees a part of the frame and has its own output. An image is simply a matrix of many values of light intensity.

Ordinary "digital" cameras have colour filters on the detector. Cameras for scientific purposes often have monochromatic filters in the optical system in front of the detector.

Image intensifiers

For studying sprites it is often necessary to have an image intensifier in the camera. The most commonly used image intensifiers use electron multipliers. The principle is shown in the following figure:

Image intensifier using an electron multiplier of the "channeltron-plate" type: An incident photon releases an electron from the photocathode and enters one of many narrow channels, one per pixel. A high-voltage field accelerates the electron until it hits the wall and releases more electrons, and so on, until a burst of many electrons is obtained at the end of the channel. These electrons can be detected directly or directed onto a phosphor screen, which in turn emits new, detectable light.

The disadvantage of these image intensifiers is that they have high sensitivity but low efficiency. That may sound like a contradiction but it is not. Simply put, it just means that most incident photons do not produce any electrons at all, but those that do give a very large output. Therefore the images become noisy. You have probably seen movies or news reports where soldiers use low-light telescopes, so you will know what that noise looks like.

Modern image intensifiers use so-called electron multiplication CCDs instead. In these detectors the light hits a bare CCD detector, where (very nearly at least) each incident photon generates exactly one electron. These electrons are then transferred to a second detector layer where electron multiplication takes place. These instruments are promising candidates for detailed studies of TLEs with both high time resolution and high sensitivity.

Spectrographs

A spectrograph is an instrument that separates light into its different wavelengths and records the intensities at all wavelengths at once. Old spectrographs used glass prisms while modern spectrographs use gratings.

A grating consists of several narrow slits of a width comparable to the wavelength of light. The waves from the different slits interfere with each other. At the centre there is no difference between different wavelengths (the difference is, of course, always 0 wavelengths) but at higher-order maxima, the differences of 1,2, ...etc, wavelengths occur at larger angles for larger wavelengths. Thus the wavelength components of the incident light can be separated and recorded on a detector.

Carl-Fredrik