Relativistic Runaway Electron Research Articles

Marginal stability model for the decay of runaway electron current

A population of relativistic runaway electrons in a tokamak can grow rapidly via avalanche mechanism and replace the bulk electron current. The runaway current will then decay slowly in line with dissipation of the stored magnetic energy. This decay follows a marginal stability scenario: the inductive electric field is close to the avalanche threshold at every location where the runaway current density is finite, and the current density vanishes at any point where the field is subcritical. This nonlinear ‘Ohm’s law' yields a complete picture of the evolving profile of runaway current.

Fundamental processes capable of accounting for the neutron flux enhancements in a thunderstorm atmosphere

Elementary processes capable of producing neutrons in a thunderstorm atmosphere are analyzed. The efficiency of nuclear fusion 2H(2H, n)3He, photonuclear reactions (γ, Xn), electrodisintegration reactions A(e −,n) −1 , and reactions e −(p +, n)ν e opposite to the β-decay is evaluated. It is shown that an unrealistically strong electric field is required for the nuclear fusion to be responsible for the neutron production in the lightning channel. The generation of neutrons in a thunderstorm atmosphere is connected with photonuclear (γ, Xn) and, at a much lower degree, electrodisintegration reactions, the relativistic runaway electron avalanches being primary parent processes.

Relativistic Runaway Ionization Fronts

We investigate the first example of self-consistent impact ionization fronts propagating at relativistic speeds and involving interacting, high-energy electrons. These fronts, which we name relativistic runaway ionization fronts, show remarkable features such as a bulk speed within less than one percent of the speed of light and the stochastic selection of high-energy electrons for further acceleration, which leads to a power-law distribution of particle energies. A simplified model explains this selection in terms of the overrun of Coulomb-scattered electrons. Appearing as the electromagnetic interaction between electrons saturates the exponential growth of a relativistic runaway electron avalanche, relativistic runaway ionization fronts may occur in conjunction with terrestrial gamma-ray flashes and thus explain recent observations of long, power-law tails in the terrestrial gamma-ray flash energy spectrum.

Numerical simulations of compact intracloud discharges as the Relativistic Runaway Electron Avalanche‐Extensive Air Shower process

Compact intracloud discharges (CIDs) are sources of the powerful, often isolated radio pulses emitted by thunderstorms. The VLF‐LF radio pulses are called narrow bipolar pulses (NBPs). It is still not clear how CIDs are produced, but two categories of theoretical models that have previously been considered are the Transmission Line (TL) model and the Relativistic Runaway Electron Avalanche‐Extensive Air Showers (RREA‐EAS) model. In this paper, we perform numerical calculations of RREA‐EASs for various electric field configurations inside thunderstorms. The results of these calculations are compared to results from the other models and to the experimental data. Our analysis shows that different theoretical models predict different fundamental characteristics for CIDs. Therefore, many previously published properties of CIDs are highly model dependent. This is because of the fact that measurements of the radiation field usually provide information about the current moment of the source, and different physical models with different discharge currents could have the same current moment. We have also found that although the RREA‐EAS model could explain the current moments of CIDs, the required electric fields in the thundercloud are rather large and may not be realistic. Furthermore, the production of NBPs from RREA‐EAS requires very energetic primary cosmic ray particles, not observed in nature. If such ultrahigh‐energy particles were responsible for NBPs, then they should be far less frequent than is actually observed.

Numerical analysis of 2010 high‐mountain (Tien‐Shan) experiment on observations of thunderstorm‐related low‐energy neutron emissions

AbstractThe high‐mountain experiment in a thunderstorm atmosphere, in which “extraordinary high flux of low‐energy neutrons” was detected, is analyzed. Due to the lack of data on the radiation source, we do not analyze directly measured absolute count rates. Instead, we address the experimental configuration, namely, simultaneous measurements by shielded and unshielded helium counters, which allow a comparison of relative count rates and, thus, verifying the species of the detected radiation. Results of Monte Carlo simulations of neutron transport executed without aprioristic assumptions, using only data on the experimental configuration, have raised strong doubts as to whether the detected increases of the count rates can be attributed to neutrons. Results of simulations allowing for the neutron transport in atmosphere from distant (100–500 m) photoneutron source with spectrum in the range 0–20.1 MeV produced by relativistic runaway electron avalanche bremsstrahlung demonstrate that ratios R of the count rates of shielded and unshielded counters below 1 keV are manyfold higher than the ratios Rexp ≈ 0.34–1.06 of the measured count rates. In the total range 0–20.1 MeV, the R magnitudes vary from 0.14 to 0.84 depending on the distance to the neutron source. Results of simulations of γ rays transport executed without aprioristic assumptions demonstrate that, most likely, hard γ rays with energies ϵγ > 1 MeV were detected. We note that in thunderstorm environment, a selection is required of neutrons and γ rays, for which the time‐of‐flight technique is the most adequate.

Thunderstorm ground enhancements: Gamma ray differential energy spectra

The shape and evolution of the energy spectra of the thunderstorm ground enhancement (TGE) electrons and gamma rays shed light on the origin of TGEs, on the relationship of modification of the energy spectra (MOS) and relativistic runaway electron avalanche processes, on the nature of the seed particles, and on the strength and elongation of an atmospheric electric field. However, till now the measurements of energy spectra of TGE electrons and gamma rays have been rather scarce. For the first time, we present differential energy spectra of gamma rays in the wide energy range 4--100 MeV for five TGE events detected in 2012--2013 at Aragats. We use the special technique of electron/gamma ray fraction determination to select TGE events with very small contamination of electrons. The network of large NaI spectrometers located 3200 m above sea level measured energy spectra of gamma rays. The power law indices of ``small'' TGEs are rather close to the background cosmic gamma ray spectrum ($\ensuremath{\gamma}\ensuremath{\sim}\ensuremath{-}2$); thus, we may deduce that these small events are due to MOS of cosmic ray electrons in the electric field of a thundercloud. Larger TGEs measured by the NaI network and the two largest TGE events earlier recovered from energy releases in a 60-cm-thick scintillator have much steeper energy spectra typical for the avalanche process in atmosphere. The classification of TGEs according to intensity and gamma ray spectral index pointed toward two main mechanisms of the TGE gamma ray origin: the runaway process and modification of electron energy spectra in the thunderstorm atmospheres.

Properties of the thundercloud discharges responsible for terrestrial gamma‐ray flashes

AbstractThe source of terrestrial gamma‐ray flashes (TGFs) has been an active area of research since their discovery by Compton Gamma‐Ray Observatory/Burst and Transient Source Experiment in 1994. These intense bursts of gamma rays originate within thunderclouds via the rapid production of relativistic runaway electrons, accelerated by thundercloud/lightning electric fields to multi‐MeV energies. Recent studies have shown that electrical discharges within thunderclouds caused by these runaway electrons can generate currents that rival those of lightning and so could serve as an alternative discharge path for thunderclouds. In particular, the discharges responsible for TGFs produce some of the largest amplitude VLF‐LF radio pulses from thunderstorms and, indeed, were previously misidentified as lightning. In this article, we shall provide a brief review of TGFs and present calculations of their electrical properties inside thunderclouds and their gamma‐ray and optical emissions. We shall show that the lightning‐like events responsible for TGFs emit relatively little visible light and, thus, are inherently dark.

Numerical simulation of narrow bipolar electromagnetic pulses generated by thunderstorm discharges

Using the concept of avalanche relativistic runaway electrons (REs), we perform numerical simulations of compact intracloud discharge (CID) as a generator of powerful natural electromagnetic pulses (EMPs) in the HF-VHF range, called narrow bipolar pulses (NBPs). For several values of the field overvoltage and altitude at which the discharge develops, the numbers of seed electrons initiating the avalanche are evaluated, with which the calculated EMP characteristics are consistent with the measured NBP parameters. We note shortcomings in the hypothesis assuming participation of cosmic ray air showers in avalanche initiation. The discharge capable of generating NBPs produces REs in numbers close to those in the source of terrestrial γ-ray flashes (TGFs), which can be an argument in favor of a unified NBP and TGF source.

Observation of a gamma‐ray flash at ground level in association with a cloud‐to‐ground lightning return stroke

Terrestrial gamma‐ray flashes (TGFs) are bright, sub‐millisecond bursts of gamma‐rays, originating within the Earth's atmosphere. Most TGFs have been detected by spacecraft in low‐Earth orbit. Only two TGFs have previously been observed from within our atmosphere: one at ground level and one from an aircraft at 14.1 km. We report on a new TGF‐like gamma‐ray flash observed at ground level, detected by the 19‐station Thunderstorm Energetic Radiation Array (TERA) at the University of Florida/Florida Tech International Center for Lightning Research and Testing (ICLRT). The gamma‐ray flash, which had a duration of 52.7 μs, occurred on June 30, 2009 during a natural negative cloud‐to‐ground lightning return stroke, 191 μs after the start of the stroke. This event is the first definitive association of a gamma‐ray flash with natural CG lightning and is among the most direct links to a specific lightning process so far. For this event, 19 gamma‐rays were recorded, with the highest energy exceeding 20 MeV. The high‐energy radiation exhibited very different behavior from the typical x‐ray emission from lightning. Specifically, the gamma‐ray flash had a much harder energy spectrum, consistent with relativistic runaway electron avalanche (RREA) multiplication; it did not arrive in sub‐microsecond bursts, typical of leader emission from lightning, and it occurred well after the start of the return stroke, which has not been previously observed for the x‐ray emission from lightning. Nevertheless, we present evidence that the source region for the gamma ray flash was the same as that for the preceding leader x‐ray bursts.

Numerical simulations of local thundercloud field enhancements caused by runaway avalanches seeded by cosmic rays and their role in lightning initiation

We investigate the possibility of the production of an ionized domain by the ionization of the atmosphere by cosmic rays amplified by relativistic runaway electron avalanches (RREAs), the polarization of which could lead to the localized boosting of thundercloud fields, triggering the sequence of processes leading to lightning development. For this goal, a 2D numerical model was developed of atmospheric discharges in a self‐consistent electric field allowing for the kinetics of high‐energy REs, low‐energy electrons, and positive and negative ions. The effects are tested for cosmic ray air showers and for the continuous background of low‐energy cosmic radiation. It is shown that lightning cannot be triggered by the joint action of the cosmic ray shower and RREAs. On the contrary, with realistic rates of the cloud charging, the RREAs seeded by low‐energy cosmic rays, produce a plasma domain, at the edges of which the electric field of the cloud is enhanced above the magnitude required for the selfsustained growth of the free electron population, potentially resulting in lightning initiation.

Terrestrial gamma ray flashes with energies up to 100 MeV produced by nonequilibrium acceleration of electrons in lightning

Using Monte Carlo models simulating energetic electrons in inhomogeneous electric field and the transport of energetic photons in the Earth's atmosphere, we show that the spectrum of bremsstrahlung photons generated by nonequilibrium energetic electrons produced during stepping of lightning leaders can deviate from the typical spectrum of relativistic runaway electron avalanches (RREA) developing in weak homogeneous electric fields. This deviation is especially pronounced in the high‐energy tail of the electron energy distribution for lightning leaders possessing high voltages (several hundreds of megavolts) and extremely high fields around their tips. The photon spectrum obtained accurately reproduces the recently discovered high‐energy tail (up to 100 MeV) of terrestrial gamma‐ray flashes (TGFs). This analysis provides the first direct evidence that TGFs are produced by lightning and not over large distances in weak thunderstorm electric fields.

Neutron bursts associated with thunderstorms

The basis of our analysis is the observation of the simultaneous enhancements of the gamma ray and neutron fluxes detected in 2009--2010 during thunderstorm ground enhancements at the mountain altitude of 3200 m. We investigate the correlated time series of the gamma rays and neutrons measured by the surface particle detectors of Aragats Space Environmental Center. The photonuclear reactions of the gamma rays born in the runaway breakdown (RB, now referred to as relativistic runaway electron avalanche, RREA) process with air were considered as the main process responsible for the copious neutron production. We consider also the mesoatom nuclei decay as a possible source of the additional neutrons registered by the neutron monitor due to enhanced population of the negative muons accelerated in the thunderclouds.

Reply to comment by A. V. Gurevich et al. on “Low‐energy electron production by relativistic runaway electron avalanches in air”

Reply to comment by A. V. Gurevich et al. on “Low‐energy electron production by relativistic runaway electron avalanches in air”

Source altitudes of terrestrial gamma‐ray flashes produced by lightning leaders

Terrestrial gamma‐ray flashes (TGFs) are energetic photon bursts observed from satellites and associated with lightning activity. Comparison between calculations based on the model of relativistic runaway electron avalanches (RREA) in large‐scale weak electric field in thunderstorms and satellite measurements usually shows that the photon spectrum is consistent with source altitudes around 15 km. However, recent observations have located intra‐cloud lightning (IC) discharges responsible for TGFs much deeper in the atmosphere (at altitudes ∼10 km). In the present work, we show that the TGF spectrum as produced by acceleration of electrons in the strong electric field of stepping IC leaders is consistent with the lower altitudes recently discovered. This study reconciles observations and measurements by setting new altitudes for the TGF sources based on mechanism of direct acceleration of electrons in the lightning leader field. Moreover, the photon source beaming geometry is consistently determined from the geometry of electric field lines produced by the lightning leader.

On the Production of Relativistic Runaway Electrons in Damavand Tokamak

Experimental observations in Damavand tokamak show that hard X-ray is produced by either disruption with Ip 20 kA. Hard X-ray also persists from the initiation of plasma discharge to the end. Occurrence of multiple spikes in hard X-ray during the discharge is evident. The propagation of hard X-ray is attributed to runaway electrons. We observe runaway electrons in two regimes with different characteristics. Regime (RADI) is similar to the observations of other Tokamak during disruption on that the plasma current is reduced abruptly and interpreted by Dreicer theory. In the regime of RADII, hard X-ray and subsequently runaway electrons are observed from starting of plasma discharge which provides the condition that the most of runaway electrons contain the toroidal plasma current. Runaway electron beam excites whistler waves and scattered electrons in velocity space and prevent growing the runaway electrons beam.

The relativistic feedback discharge model of terrestrial gamma ray flashes

As thunderclouds charge, the large‐scale fields may approach the relativistic feedback threshold, above which the production of relativistic runaway electron avalanches becomes self‐sustaining through the generation of backward propagating runaway positrons and backscattered X‐rays. Positive intracloud (IC) lightning may force the large‐scale electric fields inside thunderclouds above the relativistic feedback threshold, causing the number of runaway electrons, and the resulting X‐ray and gamma ray emission, to grow exponentially, producing very large fluxes of energetic radiation. As the flux of runaway electrons increases, ionization eventually causes the electric field to discharge, bringing the field below the relativistic feedback threshold again and reducing the flux of runaway electrons. These processes are investigated with a new model that includes the production, propagation, diffusion, and avalanche multiplication of runaway electrons; the production and propagation of X‐rays and gamma rays; and the production, propagation, and annihilation of runaway positrons. In this model, referred to as the relativistic feedback discharge model, the large‐scale electric fields are calculated self‐consistently from the charge motion of the drifting low‐energy electrons and ions, produced from the ionization of air by the runaway electrons, including two‐ and three‐body attachment and recombination. Simulation results show that when relativistic feedback is considered, bright gamma ray flashes are a natural consequence of upward +IC lightning propagating in large‐scale thundercloud fields. Furthermore, these flashes have the same time structures, including both single and multiple pulses, intensities, angular distributions, current moments, and energy spectra as terrestrial gamma ray flashes, and produce large current moments that should be observable in radio waves.

Effect of applied toroidal electric field on the growth/decay of plateau-phase runaway electron currents in DIII-D

Large relativistic runaway electron currents (0.1–0.5 MA) persisting for ∼100 ms are created in the DIII-D tokamak during rapid discharge shut down caused by argon pellet injection. Slow upward and downward ramps in runaway currents were found in response to externally applied loop voltages. Comparison between the observed current growth/decay rate and the rate expected from the knock-on avalanche mechanism suggests that classical collisional dissipation of runaways alone cannot account for the measured growth/damping rates. It appears that a fairly constant anomalous dissipation rate of order 10 s−1 exists, possibly stemming from radial transport or direct orbit losses to the vessel walls, although the possibility of an apparent loss due to current profile shrinking cannot be ruled out at present.

Low-energy electron production by relativistic runaway electron avalanches in air

[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.

Runaway electron losses caused by resonant magnetic perturbations in ITER

Disruptions in large tokamaks can lead to the generation of a relativistic runaway electron beam that may cause serious damage to the first wall. To suppress the runaway beam the application of resonant magnetic perturbations (RMPs) has been suggested. In this work we investigate the effect of RMPs on the confinement of runaway electrons by simulating their drift orbits in magnetostatic perturbed fields and calculating the transport and orbit losses for various initial energies and different magnetic perturbation configurations. In the simulations we model the ITER RMP configuration and solve the relativistic, gyro-averaged drift equations for the runaway electrons including a time-dependent electric field, radiation losses and collisions. The results indicate that runaway electrons are rapidly lost from regions where the normalized perturbation amplitude δB/B is larger than 0.1% in a properly chosen perturbation geometry. This applies to the region outside the radius corresponding to the normalized toroidal flux ψ = 0.5.

Long-durationγray emissions from 2007 and 2008 winter thunderstorms

The Gamma-Ray Observation of Winter THunderclouds (GROWTH) experiment, consisting of two radiation-detection subsystems, has been operating since 2006 on the premises of Kashiwazaki-Kariwa nuclear power plant located at the coastal area of Japan Sea. By 2010 February, GROWTH detected 7 long-duration $\gamma$-rays emissions associated with winter thunderstorms. Of them, two events, obtained on 2007 December 13 and 2008 December 25, are reported.On both occasions, all inorganic scintillators (NaI, CsI, and BGO) of the two subsystems detected significant gamma-ray signals lasting for >1 minute. Neither of these two events were associated with any lightning. In both cases, the gamma-ray energy spectra extend to 10 MeV, suggesting that the detected gamma-rays are produced by relativistic electrons via bremsstrahlung. Assuming that the initial photon spectrum at the source is expressed by a power-law function,the observed photons can be interpreted as being radiated from a source located at a distance of 290-560 m for the 2007 event and 110-690 m for the 2008 one, both at 90% confidence level.Employing these photon spectra, the number of relativistic electrons is estimated as 10^9 - 10^{11}. The estimation generally agrees with those calculated based on the relativistic runaway electron avalanche model. A GROWTH photon spectrum, summed over 3 individual events including the present two events and another reported previously, has similar features including a cut-off energy, to an averaged spectrum of terrestrial gamma-ray flashes.