A relativistic runaway electron avalanche (RREA) is an avalanche growth of a population of relativistic

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

s driven through a material (typically air) by an electric field. RREA has been hypothesized to be related to

lightning Lightning is a natural phenomenon consisting of electrostatic discharges occurring through the atmosphere between two electrically charged regions. One or both regions are within the atmosphere, with the second region sometimes occurring on ...

initiation,

terrestrial gamma-ray flashes A terrestrial gamma-ray flash (TGF), also known as dark lightning, is a burst of gamma rays produced in Earth's atmosphere. TGFs have been recorded to last 0.2 to 3.5 milliseconds, and have energies of up to 20 million electronvolts. It is spec ...

sprite lightning Sprites or red sprites are large-scale electric discharges that occur in the mesosphere, high above thunderstorm clouds, or cumulonimbus, giving rise to a varied range of visual shapes flickering in the night sky. They are usually triggered b ...

, and spark development. RREA is unique as it can occur at electric fields an order of magnitude lower than the

dielectric strength In physics, the term dielectric strength has the following meanings: *for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becom ...

of the material.

Mechanism

When an electric field is applied to a material, free electrons will drift slowly through the material as described by the

electron mobility In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for Electron hole, holes, called hole mobilit ...

. For low-energy electrons, faster drift velocities result in more interactions with surrounding particles. These interactions create a form of

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

that slow the electrons down. Thus, for low-energy cases, the electron velocities tend to stabilize. At higher energies, above about 100

keV In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. When us ...

, these collisional events become less common as the

mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

of the electron rises. These higher-energy electrons thus see less frictional force as their velocity increases. In the presence of the same electric field, these electrons will continue accelerating, "running away". As runaway electrons gain energy from an electric field, they occasionally collide with atoms in the material, knocking off secondary electrons. If the secondary electrons also have high enough energy to run away, they too accelerate to high energies, produce further secondary electrons, etc. As such, the total number of energetic electrons grows exponentially in an avalanche. The dynamic friction function, shown in the Figure, takes into account only energy losses due to inelastic collisions and has a minimum of ~216 keV/cm at electron energy of ~1.23 MeV. More useful thresholds, however, must include also the effects due to electron momentum loss due to elastic collisions. In that case, an analytical estimate gives the runaway threshold of ~282 keV/cm, which occurs at the electron energy of ~7 MeV. This result approximately agrees with numbers obtained from Monte Carlo simulations, of ~284 keV/cm and 10 MeV, respectively.

Seeding

The RREA mechanism above only describes the growth of the avalanche. An initial energetic electron is needed to start the process. In ambient air, such energetic electrons typically come from

cosmic rays Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar ...

. In very strong electric fields, stronger than the maximum frictional force experienced by electrons, even low-energy ("cold" or "thermal") electrons can accelerate to relativistic energies, a process dubbed "thermal runaway."

Feedback

RREA avalanches generally move opposite the direction of the electric field. As such, after the avalanches leave the electric field region, frictional forces dominate, the electrons lose energy, and the process stops. There is the possibility, however, that photons or positrons produced by the avalanche will wander back to where the avalanche began and can produce new seeds for a second generation of avalanches. If the electric field region is large enough, the number of second-generation avalanches will exceed the number of first-generation avalanches and the number of avalanches itself grows exponentially. This avalanche of avalanches can produce extremely large populations of energetic electrons. This process eventually leads to the decay of the electric field below the level at which feedback is possible and therefore acts as a limit to the large-scale electric field strength.

Effects of RREA

The large population of energetic electrons produced in RREA will produce a correspondingly large population of energetic photons by

bremsstrahlung In particle physics, bremsstrahlung (; ; ) is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic ...

. These photons are proposed as the source of

. Large RREA events in thunderstorms may also contribute rare but large radiation doses to commercial airline flights. The American physicist Joseph Dwyer coined the term " dark lightning" for this phenomenon, which is still the subject of research.

References

{{Reflist, refs= Gurevich, A. V., & Zybin, K. P. (2005). Runaway Breakdown and the Mysteries of Lightning. Physics Today, 58(5), 37. {{doi, 10.1063/1.1995746. Betz, H. D., Schumann, U., & Laroche, P. (Eds.). (2009). Lightning: Principles, Instruments and Applications. Springer Verlag, ch. 15. Dwyer, J. R., & Smith, D. M. (2005)
A comparison between Monte Carlo simulations of runaway breakdown and terrestrial gamma-ray flash observations
Geophysical Research Letters, 32(22), L22804. {{doi, 10.1029/2005GL023848. Lehtinen, N. G., Bell, T. F., & Inan, U. S. (1999). Monte Carlo simulation of runaway MeV electron breakdown with application to red sprites and terrestrial gamma ray flashes. Journal of Geophysical Research, 104(A11), 24699-24712. {{doi, 10.1029/1999JA900335. Carlson, B. E., Lehtinen, N. G., & Inan, U. S. (2008). Runaway relativistic electron avalanche seeding in the Earth's atmosphere. Journal of Geophysical Research, 113(A10), A10307. {{doi, 10.1029/2008JA013210. Colman, J. J., Roussel-Dupré, R. a, & Triplett, L. (2010). Temporally self-similar electron distribution functions in atmospheric breakdown: The thermal runaway regime. Journal of Geophysical Research, 115, 1-17. {{doi, 10.1029/2009JA014509. Dwyer, J. R. (2003). A fundamental limit on electric fields in air. Geophysical Research Letters, 30(20), 2055. {{doi, 10.1029/2003GL017781. Dwyer, J. R., Smith, D. M., Uman, M. A., Saleh, Z., Grefenstette, B. W, Hazelton, B. J, et al. (2010). Estimation of the fluence of high-energy electron bursts produced by thunderclouds and the resulting radiation doses received in aircraft. Journal of Geophysical Research, 115(D9), D09206. {{doi, 10.1029/2009JD012039. Lightning Atmospheric electricity Electrical phenomena Electron