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JGRA20111A.Pdf (435.8Kb) JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A09301, doi:10.1029/2011JA016494, 2011 Low‐energy electron production by relativistic runaway electron avalanches in air Joseph R. Dwyer1 and Leonid P. Babich2 Received 24 January 2011; revised 31 May 2011; accepted 8 June 2011; published 7 September 2011. [1] This paper investigates the production of low‐energy (few eV) electrons by relativistic runaway electron avalanches. This work is motivated by a growing body of literature that claims that runaway electron avalanches produce an anomalous growth of low‐energy electrons and hence an anomalously large electrical conductivity, a factor of 50 larger than expected from standard calculations. Such large enhancements would have a substantial impact on properties of runaway electron avalanches and their observable effects. Indeed, these purportedly large conductivities have been used to argue that runaway electron avalanches result in a novel form of electrical breakdown called “runaway breakdown.” In this paper, we present simple analytical calculations, detailed Monte Carlo simulations, and a review of the experimental literature to show that no such anomalous growth of low‐energy electron populations exists. Consequently, estimates of the conductivity generated by a runaway electron avalanche have been greatly exaggerated in many previous papers, drawing into question several of the claims about runaway breakdown. Citation: Dwyer, J. R., and L. P. Babich (2011), Low‐energy electron production by relativistic runaway electron avalanches in air, J. Geophys. Res., 116, A09301, doi:10.1029/2011JA016494. 1. Introduction field [Dwyer, 2003]. Because electric fields exceeding the RREA threshold field have been observed inside thunder- [2] In 1925, C. T. R. Wilson discovered the runaway clouds [MacGorman and Rust, 1998; Marshall et al., 2005], electron mechanism for which electrons may obtain large there has been great interest in the RREA mechanism when energies from static electric fields in air [Wilson, 1925]. studying lightning initiation [Gurevich et al., 1999; Gurevich Specifically, when the rate of energy gain from an electric and Zybin, 2001; Dwyer, 2005, 2009, 2010], narrow bipolar field exceeds the rate of energy loss from interactions with events (NBE) [Smith et al., 1999], terrestrial gamma ray air then the energy of an electron will increase and it will flashes (TGFs) [Fishman et al., 1994; Lehtinen et al., 1999; “run away.” The name “runaway electron” was introduced Dwyer and Smith, 2005; Dwyer 2008; Babich et al., 2008], in 1926 by Eddington [1926]. In 1992, Gurevich et al. and thundercloud electrification [Rakov and Uman, 2003]. [1992] showed that when Møller scattering (electron‐ In particular, it has been suggested that RREAs may produce electron elastic scattering) is included, the runaway electrons electrical breakdown inside thunderclouds at electric field described by Wilson will also undergo avalanche multipli- strengths far below the conventional breakdown field. The cation, resulting in a large number or relativistic runaway hypothesized electrical breakdown of air generated by RREAs electrons for each energetic seed electron injected into the has been named “runaway breakdown” [Gurevich and Zybin, high‐field region. Interestingly, on the basis of an analysis 2001]. of research notes by C. T. R. Wilson, Williams [2010] [3] Conventionally, “electrical breakdown” means a argued that Wilson was aware of the runaway electron ava- development of large numbers of electron avalanches or lanche multiplication, referring to it as a “snowball effect.” streamers resulting in the creation of an ionized channel This avalanche mechanism is commonly referred to as the with such large conductivity that the electric field in the relativistic runaway electron avalanche (RREA) mechanism channel will collapse. Generally, in order for a discharge to [Babich et al., 1998, 2001]. The threshold electric field for be considered an electrical breakdown, the discharge must RREA multiplication is E = 284 kV/m × n, where n is the th be a self‐sustained process. Conversely, if the discharge density of air relative to that at sea level, an order of mag- requires the support of externally supplied ionization then it nitude smaller than the conventional breakdown threshold is not considered an electrical breakdown. There are well known discharges supported by external sources of ioniza- 1 tion, for instance, volumetric discharges intended to pump Department of Physics and Space Sciences, Florida Institute of gas lasers. Such discharges are switched off by switching off Technology, Melbourne, Florida, USA. 2Russian Federal Nuclear Center, VNIIEF, Sarov, Russia. the external sources of ionization, for instance, the beam of high‐energy electrons. RREAs are exactly such a process, Copyright 2011 by the American Geophysical Union. i.e., not an electrical breakdown, since switching off the 0148‐0227/11/2011JA016494 A09301 1of14 A09301 DWYER AND BABICH: LOW‐ENERGY ELECTRONS A09301 externally supplied seed particles stops the development of where Nair is the number density of the gas atoms (Nair = the discharge. Furthermore, a RREA does not necessarily 5.39 × 1025 m−3 for air at sea level) and Z is the average lead to the collapse of the electric field. One main reason atomic number of the gas atoms (Z = 7.26 for air), re = that RREAs do not lead to an electrical breakdown is the 2.818 × 10−15 m is the classical electron radius, mc2 = concentration of low‐energy electrons is too low. 511 keVpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is the rest energy of an electron, b′ = v′/c, 2 [4] In several papers spanning the last 13 years, propo- g′ =1/ 1 À ′ is the Lorentz factor of the energetic elec- nents of the runaway breakdown hypothesis have stated that tron, I is the effective ionization potential (e.g., I = 85.7 eV the mechanism introduced by Gurevich et al. [1992], in for air), and dden is a correction due to the density effect. addition to producing energetic runaway electrons, also For air, the density effect correction is very small below 30 results in an anomalously large increase in the low‐energy MeV and increases only slowly above that energy. The (few eV) electron population, resulting in an electrical con- density effect also becomes less important at higher alti- ductivity more than an order of magnitude larger than tudes where the density of air is lower. Equation (1) takes expected from calculations using standard ionization rates into account the generation of secondary electrons of all of energetic electrons [Gurevich and Milikh, 1999; Gurevich energies up to half of the primary electron’s energy, the and Zybin, 2001; Gurevich et al., 2004]. This anomalous maximum possible energy. These secondary electrons will increase in the low‐energy electron population, in turn, has also ionize the air, also according to equation (1). The been used to argue that “runaway breakdown” is indeed a energetic secondary electrons are called “delta rays” or true electrical breakdown and to explain various atmospheric “knock‐on electrons” and will sometimes travel consider- phenomena [Milikh and Roussel‐Dupré, 2010]. Recently, able distances before stopping. Note that in this paper we Dwyer has argued that the conductivity generated by the use primed symbols to denote the incident electrons (e.g., runaway electrons produced by the RREA mechanism is too runaway electrons) and the unprimed symbols to denote low to result in electrical breakdown [Dwyer, 2005, 2007, secondary electrons (e.g., delta rays). 2008]. [7] To calculate the total number of free low‐energy (few [5] In this paper, we present results of analytical calcu- eV) electrons produced by ionization, the total energy lations, Monte Carlo simulations and a review of experi- deposited in the air (from equation (1)) is divided by the mental data that all show that there is no anomalous increase W value (W = 34 eV for air) [Jesse and Sadauskis, 1955; in the low‐energy electron populations during RREAs and Knoll, 2000]: that the conductivity that is produced by RREA agrees with standard ionization rates. Because the conductivity that is ¼ FbðÞ"′ =W: ð2Þ predicted by the theoretical work supporting runaway breakdown is more than an order of magnitude too large, we shall argue that the runaway breakdown hypothesis is not Equation (2) is valid for electric fields less than the con- ventional breakdown field. The W value is an experimen- correct and that electrical breakdown directly produced by tally determined quantity that gives the average deposited runaway electron avalanches as first proposed by Gurevich energy by ionizing particles or radiation required to produce et al. [1992] does not occur in our atmosphere. In con- one electron‐ion pair in the gas [Valentine and Curran, trast, the RREA mechanism, along with standard ionization 1958]. It includes the various ionization potentials plus the rates, is the correct mechanism for relativistic runaway amount of energy that goes into excitations rather than electron production and the resulting increase in the con- ionization and the kinetic energy of secondary electrons. ductivity of air. Moreover, the RREA mechanism may still The W value is remarkably constant, applying to different be important for understanding TGFs and other atmospheric types of energetic radiation (X‐rays, gamma rays, energetic phenomena. electrons, etc.) over a very wide range of energies and electric fields [Weiss and Bernstein 1957; International Commission on Radiation Units and Measurements, 1979]. 2.
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