Relativistic Runaway Electron Research Articles

Time-of-flight technique for estimation of the energy of runaway electron bunches formed in magnetized gas diodes

Time-of-flight estimates of the kinetic energy of magnetically insulated bunches of moderately relativistic runaway electrons (RAEs) were obtained with the use of an air diode equipped with a drift section. The measurements have demonstrated that the bunch energy can be controlled by changing the conditions for RAE emission in an air diode with a sharply inhomogeneous electric field, which can be done by varying the cathode geometry and material and the length of the cathode-anode gap. It has been demonstrated that if the measured electron current peaks are resolved to within 10 ps, and the bunch duration and spread in RAE emission moments are close to this resolution, the characteristic energies of the bunches can be estimated with an accuracy of ≈10%. Examples of energy measurements are given for paraxial and tubular bunches accelerated at cathode potentials of up to −250 kV. The estimated characteristic energies of the bunches, even not corrected for drift losses in the fill gas, turned out to be greater than the energies that could be achieved for bunches accelerated in a vacuum diode with due account for the variations in diode voltage.

On the Self‐Quenching of Relativistic Runaway Electron Avalanches Producing Terrestrial Gamma Ray Flashes

AbstractTerrestrial gamma ray flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by relativistic runaway electron avalanches (RREAs). It is usually admitted that the number of high‐energy electrons produced in the brightest TGFs remains mostly confined within a range from 1017 to 1019. To understand the constraints in the development of RREAs, we perform self‐consistent simulations using a newly developed model with a finite acceleration region and various injection rates. We find that RREAs should naturally self‐quench for a fixed total number of runaway electrons, and hence a fixed number of bremsstrahlung photons. From the idea that TGF sources quench themselves, we derive a simple equation controlling the total number of runaway electrons. In this framework, the existence of a saturation in the electron density discovered in a previous work places a lower limit on TGF durations.

An enormous increase in atmospheric positron flux during a summer thunderstorm on Mount Aragats

On July 11, 2023, we observed a remarkable 500% increase in positron flux, coinciding with a significant Thunderstorm Ground Enhancement (TGE). The enhanced flux of electrons and gamma rays was attributed to relativistic runaway electron avalanches (RREAs) generated within the dipole formed between the main negatively charged layer in the middle of the thundercloud and the Lower Positively Charged Region (LPCR) at the bottom of the thundercloud. Concurrently, a substantial enhancement in the 511 keV gamma-ray flux resulting from electron-positron annihilation was recorded. This surge is intricately linked to the LPCR within the thundercloud. The emergence of the LPCR induces a polarity change in the atmospheric electric field (AEF) below the LPCR (fourth dipole), leading to the deceleration of electrons and the acceleration of positrons.Particle flux measurements were conducted using scintillation and NaI(TL) spectrometers. To mitigate the contamination of natural gamma radiation and refine the 511 keV flux measurements, the ORTEC spectrometer was shielded with a 4 cm thick lead filter. CORSIKA simulations corroborate the observed positron flux enhancement.Highlighting the synergy between high-energy physics in the atmosphere and astroparticle physics, we introduce a new scenario to elucidate the enigmatic large flux of galactic positrons measured by the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station (ISS).

Self Consistent Modeling of Relativistic Runaway Electron Beams Giving Rise to Terrestrial Gamma‐Rays Flashes

AbstractTerrestrial Gamma Ray Flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by Relativistic Runaway Electron Avalanches (RREAs). In this paper, we present a new numerical model based on the Particle‐In‐Cell (PIC) method to simulate the interactions between the electromagnetic fields and the electron avalanche self‐consistently. The code uses a cylindrical Yee lattice to numerically solve the electromagnetic fields, a Monte Carlo approach to simulate collisions with air molecules, and a plasma fluid model to calculate the effects of low‐energy electrons and ions. The model is first tested through the reproduction of dispersion relations in a hot plasma. RREAs propagating under a homogeneous background electric field are then simulated. Owing to the self‐consistent nature of this description, we report here new physical properties such as saturation processes in the electron density and in the number of high‐energy electrons, detailed dynamical screening of the electric field in the ion trail of the avalanche, and the associated electric currents. We find that the saturation of RREAs is obtained when the numbers of high‐energy electrons and photons is consistent with those believed to be representative of TGF sources.

Clusters of Compact Intracloud Discharges (CIDs) in Overshooting Convective Surges

AbstractWe observed five clusters of upper‐level compact intracloud discharges (CIDs) moving positive charge up over land and over water in Florida. The clusters each contained 3 to 6 CIDs, and the overall cluster duration ranged from 27 to 58 s. On average, the CIDs in a given cluster occurred 11 s apart and were separated by a 3D distance of about 1.5 km. All the clustered CIDs were located above the tropopause and were likely associated with convective surges that penetrated the stratosphere. The average periodicity of CID occurrence within a cluster (every 11 s) was comparable to the periodicity at which the average cluster area is expected to be bombarded by ≥1016 eV cosmic‐ray particles (every 5 s). Each of such energetic particles gives rise to a cosmic ray shower (CRS) and, in the presence of sufficiently strong electric field over a sufficiently large distance, to a relativistic runaway electron avalanche (RREA). We infer that each of our upper‐level CIDs is likely to be caused by a CRS‐RREA traversing, at nearly the speed of light, the electrified overshooting convective surge and triggering, within a few microseconds, a multitude of streamer flashes along its path, over a distance of the order of hundreds of meters (as per the mechanism recently proposed for lightning initiation by Kostinskiy et al., 2020, https://doi.org/10.1029/2020JD033191). The upper‐level CID clustering was likely made possible by the recurring action of energetic cosmic rays and the rapid recovery of the negative screening charge layer at stratospheric altitudes.

Effects of thunderstorms electric field on secondary photons of cosmic ray at large high altitude air shower observatory

Large high altitude air shower observatory (LHAASO) is a complex of extensive air shower (EAS) detector arrays, located on the Mt. Haizi (29°21' N, 100°08' E) at an altitude of 4410 m a. s. l., Daocheng, Sichuan Province, China. The information about primary cosmic rays can be obtained by using data from secondary particles measured at LHAASO, with photons make up the majority among these secondary particles. During thunderstorms, the atmospheric electric field can affect secondary charged particles (mainly positrons and electrons), thus changing the information of photons on the ground. In this work, Monte Carlo simulations are performed to investigate the effects of near-ground thunderstorm electric fields on cosmic ray secondary photons at LHAASO. A simple model with a vertical and uniform atmospheric electric field in a layer of atmosphere is used in our simulations. During thunderstorms, the number and energy of photons are found to significantly change and strongly depend on the electric field strength. In a field of -1000 V/cm (below the threshold of the relativistic runaway electron avalanche (RREA) process), the number of photons is increased by 23%. Also, the spectrum of photons softens, and the increased number of photons with energy less than 2 MeV exceeds 29%. In an electric field of –1700 V/cm (above the threshold of the RREA process), the number of photons experiences exponential growth, with an increase of 279%. The spectrum of photons becomes softer than that at –1000 V/cm, and the increased number with energy less than 2 MeV is more than 361%. It is consistent with the theory of RREA. For these phenomena of photons at LHAASO, the main factor is that the number of positrons and electrons are increased due to the acceleration of negative electric field on electrons, with increase of 65% in –1000 V/cm and 992% in –1700 V/cm, and the spectrum of positrons and electrons soften. Newborn free positrons/electrons may undergo bremsstrahlung and deposit part of their energy into photons, causing the change of number and energy of photons to follow roughly the same pattern as positrons and electrons. The simulation results can provide the information for understanding the variations of the data detected by LHAASO during thunderstorms and the acceleration mechanisms of secondary charged particles caused by an atmospheric electric field.

Reconstruction of high energy thunderstorm radiation effects on soil matrix using Monte Carlo simulations

Due to their electromagnetic properties, thunderclouds can act as natural particle accelerators. Electrons accelerated in the thunderclouds can reach energies up to tens of MeV. Large populations of high energetic electrons formed by avalanche growth driven by electric fields in the Earth atmosphere called Relativistic Runaway Electron Avalanches (RREA) propagate through matter. They are decelerated and deflected in the course of collisions with particles in the atmosphere and emit gamma rays known as bremsstrahlung. The produced gamma rays can further trigger photonuclear reactions in the air and soil. This article reports on the work of project CRREAT (Research Centre of Cosmic Rays and Radiation Events in the Atmosphere), studying various lightning-related phenomena in various ways, both in situ and in the laboratory. This paper focuses on the simulation of the laboratory experiments at the Microtron accelerator in Prague and the neutron generator in Ostrava, where we irradiated various soil samples with 20 MeV electron beams. Experiments showed which radionuclides can be formed during the reactions of high-energy electrons with various soils and can be as targeted products in the thunderstorm radiation effect analysis. Radionuclides produced in exposed samples were measured using a highpurity germanium (HPGe) detector. A computer simulation was done with a simple source and sample geometry using the general-purpose 3D Monte Carlo code PHITS.

How can we simulate ionizing radiation at aviation altitudes from TGFs?

So-called thunderclouds, which are large dark clouds that are able to generate thunder and lightning, can act as natural particle accelerators, producing complex high-energy phenomena such as terrestrial gamma-ray flashes (TGFs) and gamma-ray glows. These events are often described through the mechanism of relativistic runaway electron avalanches (RREAs), cascades of high-energy electrons accelerated by atmospheric electric fields. Since the energies of the RREAs are up to several tens of MeV, they can also trigger nuclear reactions with atoms of the air and in the soil while entering the ground. Although these phenomena are intriguing, their lack of precise measurement and still not completely understood origins pose a significant challenge for assessing their impact on aviation safety. This paper introduces the project Research Centre of Cosmic Rays and Radiation Events in Atmosphere (CRREAT), aimed at providing measurements of TGFs, thunderstorm ground enhancements (TGEs), and other ionizing radiation phenomena during thunderstorms, as well as at aviation altitudes, stratosphere, and low Earth orbits (LEO). The paper argues that without accurate data on the origins and physical characteristics of TGEs and TGFs, it is impossible to reliably simulate their impact on aircraft crews and passengers. The paper also mentions how the general-purpose 3D Monte Carlo (MC) code PHITS can be used for future simulations and comparisons with measurements related to ionizing radiation phenomena in the atmosphere.

The mechanism of the global vertical force reduction in disruptions mitigated by massive material injection

Disruptions lead to a rapid loss of thermal and magnetic energy and can cause large heat loads, mechanical forces, and the excitation of a beam of relativistic runaway electrons. The operation of tokamaks at high energy and plasma current requires the use of a mitigation system to limit such detrimental effects. Mitigation techniques rely mainly on the injection of a large amount of impurities to radiate the majority of the thermal and magnetic energies. Heat loads and electro-magnetic (EM) forces as well as their toroidal asymmetries can be greatly reduced by such measures. In this paper, a theory is lined out to explain the reduction of the global vertical force based on large toroidal halo currents that keep the current centroid stationary in the midplane. As a consequence, the vertical current moment, which is linked to the EM-force, is reduced. The theory is backed up by experimental observations in shattered pellet injection mitigated vertical displacement event experiments in ASDEX Upgrade (AUG) and JET as well as by 2D simulations with the extended MHD code JOREK. Scans in the boundary heat flux are carried out to estimate the correct scrape-off layer temperature and the influence of the fraction of conducted energy. Finally, predictive simulations for ITER confirm the reduction of the vertical force by the injection of impurities.

Tokamak plasma equilibrium with relativistic runaway electrons

We consider axisymmetric equilibrium of a tokamak plasma that includes current carried by relativistic runaway electrons (REs). Using a guiding center approach, a qualitative picture of the equilibrium of a pure RE beam is elucidated. In a hot thermal plasma, none of the classical drifts of charged particles contribute to the net field-perpendicular current density, which is purely due to magnetization current. In the case of a runaway beam, however, the curvature drift of REs provides the Lorentz force needed to maintain the centripetal acceleration associated with the relativistic toroidal motion. Two different equilibrium formulations are derived for the general case consisting of a mix of thermal and RE current. At higher RE energies, the shift between flux-surfaces and surfaces of constant generalized angular momentum of REs in such equilibria can exceed the radial extent of a typical magnetohydrodynamic mode such that its stability properties could be altered. Simplified one-dimensional governing equations are derived for the absolute and relative orbit shifts in the case of a circular tokamak, enabling quick estimates of parameter dependencies.

Feasibility of the EDICAM camera for runaway electron detection in JT-60SA disruptions

The visible camera system EDICAM (Event Detection Intelligent Camera), recently installed on JT-60SA, is simulated to assess whether it can be used for measuring synchrotron radiation from relativistic runaway electrons. In this simulation, the SOFT synthetic synchrotron diagnostic framework is used to compute the synthetic synchrotron camera images from a JT-60SA-like disruption modelled with the DREAM disruption simulation code. In the studied scenario, a large amount of argon is added to the plasma, and a disruption is simulated by starting a prescribed exponential temperature drop and finishing with further cooling provided by the argon in a self-consistent simulation of the current quench. The background plasma evolution is calculated by DREAM self-consistently with the fast electron population, which is modelled kinetically. The resulting runaway electron distribution function along with the parameters of the EDICAM visible camera system are used as an input to the SOFT framework to assess the feasibility of the camera for runaway electron detection. We find that the runaway electron beam formed in the disruption can produce synchrotron radiation observable by the EDICAM system, thus enabling the use of the EDICAM for the characterization of runaway electron beams.

Ambient Conditions of Winter Thunderstorms in Japan to Reproduce Observed Gamma‐Ray Glow Energy Spectra

AbstractElectric field of thunderclouds modifies components and energy spectra of the cosmic‐ray air shower. In particular, thunderstorms accelerate charged particles, resulting in an enhancement of gamma‐ray fluxes on the ground, known as a gamma‐ray glow. This phenomenon has been observed in recent years by the Gamma‐Ray Observation of Winter THunderclouds collaboration from winter thunderstorms in the Hokuriku area of Japan. The present work examines the ambient conditions required to produce spectral features of the previously detected gamma‐ray glows, by using Monte Carlo simulations of particle interactions in the atmosphere. We focus on three parameters, the strength and length of the electric field, and the length of a null‐field attenuation region below the electrified region. The average spectrum of observed gamma‐ray glows in winter thunderstorms of Japan requires an electric field intensity close to 0.31 MV/m, slightly exceeding the Relativistic Runaway Electron Avalanche threshold of 0.284 MV/m. The vertical size of the electric field region should be comparable to 1 km. The estimated attenuation region size is 300–500 m, necessary to reduce the low‐energy photon flux of the average gamma‐ray glows. There is still a wide range of acceptable parameter sets with degeneracy to make a similar spectrum.

Conditions for Inception of Relativistic Runaway Discharges in Air

AbstractTerrestrial gamma‐ray flashes are linked to growth of long bidirectional lightning leader system consisting of positive and stepping negative leaders. The spatial extent of streamer zones of a typical lightning leader with tip potential exceeding several tens of megavolts is on the order of 10–100 m. The photoelectric absorption of bremsstrahlung radiation generated by avalanching relativistic runaway electrons occurs efficiently on the same spatial scales. The intense multiplication of these electrons is triggered when the size of the negative leader streamer zone crosses a threshold of approximately 100 m (for sea‐level air pressure conditions) allowing self‐replication of these avalanches due to the upstream relativistic electron seeds generated by the photoelectric absorption. The model results also highlight importance of electrode effects in interpretation of X‐ray emissions from centimeter to meter long laboratory discharges, in particular, a similar feedback effect produced by generation of runaway electrons from the cathode material.

Bayesian approach for validation of runaway electron simulations

Plasma-terminating disruptions in future fusion reactors may result in conversion of the initial current to a relativistic runaway electron beam. Validated predictive tools are required to optimise the scenarios and mitigation actuators to avoid the excessive damage that can be caused by such events. Many of the simulation tools applied in fusion energy research require the user to specify input parameters that are not constrained by the available experimental information. The conventional approach, where an expert modeller calibrates these input parameters based on domain knowledge, is prone to lead to an intractable validation challenge without systematic uncertainty quantification. Bayesian inference algorithms offer a promising alternative approach that naturally includes uncertainty quantification and is less subject to user bias in choosing the input parameters. The main challenge in using these methods is the computational cost of simulating enough samples to construct the posterior distributions for the uncertain input parameters. This challenge can be overcome by combining probabilistic surrogate modelling, such as Gaussian process regression, with Bayesian optimisation, which can reduce the number of required simulations by several orders of magnitude. Here, we implement this type of Bayesian optimisation framework for a model for analysis of disruption runaway electrons, and explore for simulations of current quench in a JET plasma discharge with an argon induced disruption. We use this proof-of-principle framework to explore the optimum input parameters with uncertainties in optimisation tasks ranging from one to seven dimensions. The relevant Python codes that are used in the analysis are available via https://github.com/aejarvin/BO_FOR_RE_SIMULATIONS/.

On the vertical and horizontal profiles of the atmospheric electric field during thunderstorms

We present the first results of a new experiment on Mt. Aragats for measuring the horizontal profile of atmospheric electric fields during thunderstorms. Networks of advanced particle spectrometers operated on the slopes of Mt. Aragats continuously measure fluxes of charged and neutral particles, periodically registering impulsive enhancements, so-called Thunderstorm Ground Enhancements (TGEs). This gives the possibility to estimate the strength of the electric field in the lower atmosphere. Relativistic Runaway Electron Avalanches (RREAs) are registered by the particle detectors located on the Earth's surface as TGEs sometimes exceeding the fair-weather fluxes up to a hundred times. The strong accelerating electric field can reach 1.7-2.2 kV/cm at altitudes 3-6 km, and extend down to 50-150 m above the Earth's surface. The horizontal extent of the electric field can reach 10 km and more.

Thunderstorm ground enhancements: Multivariate analysis of 12 years of observations

We present a survey of more than a half-thousand thunderstorm ground enhancements (TGEs, fluxes of electrons, and gamma rays associated with thunderstorms) registered in 2008--2022 at Aragats space environmental center (ASEC). We analyze correlations between various measured parameters characterizing TGEs measured on Aragats. Two special cases of TGE events are considered: one, terminated by nearby lightning flashes, and another one---with a sufficiently large ratio of electrons to gamma rays. On the basis of the analysis, we summarize the most important results obtained during 12 years of TGE study, which include the following statements: (i) TGEs originated from multiple relativistic runaway electron avalanches starting with seed electrons from the ambient population of cosmic rays, which enter an extended region of the electric field with strength exceeding the critical value; (ii) quite frequently, TGEs occur prior to lightning flashes and are terminated by them; (iii) the energy spectra of avalanche electrons observed on Aragats indicate that the strong electric field region can extend very low above the ground covering a large area on the earth's surface.

Calculation of collisionless pitch-angle scattering of runaway electrons with synchrotron radiation via high-order guiding-centre equation

Recently, the collisionless pitch-angle scattering for relativistic runaway electrons (REs) in toroidal geometries such as tokamaks was discovered through a full orbit simulation approach (Liu et al., Nucl. Fusion, vol. 56, 2016, p. 064002), and it was then theoretically investigated that a new expression for the magnetic moment, including the second-order corrections, could essentially reproduce the so-called collisionless pitch-angle scattering process (Liu et al., Nucl. Fusion, vol. 58, 2018, p. 106018). In this paper, with synchrotron radiation, extensive numerical verification of the validity of the high-order guiding-centre theory is given for simulations involving REs by incorporating such an expression for the magnetic moment into our particle tracing code. A high-order guiding-centre simulation approach with synchrotron radiation (HGSA) is applied. Synchrotron radiation plays an essential role in the life cycle of REs. The energy of REs first increases and then becomes saturated until the electric field acceleration is balanced by the radiation dissipation. Unfortunately, the process cannot be simulated accurately with the standard guiding-centre model, i.e. the first-order guiding-centre model. Remarkably, it is found that the HGSA can effectively produce the fundamental process of REs. Since the time scale of the energy saturation of REs is close to seconds, the computational cost becomes significant. In order to save costs, it is necessary to estimate the time of energy saturation. An analytical estimate is derived for the time it takes for synchrotron drag to balance an accelerating electric field and the provided formula has been numerically verified. Test calculations reveal that HGSA is favourable for exploiting the dynamics of REs in tokamak plasmas.

The horizontal profile of the atmospheric electric fields as measured during thunderstorms by the network of NaI spectrometers located on the slopes of Mt. Aragats

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 between modification of the cosmic ray electron energy spectra (MOS) and relativistic runaway electron avalanche (RREA) processes, on the energy of the seed electrons, and on the strength and elongation of an atmospheric electric field. The network of large NaI spectrometers on slopes of Mt. Aragats 24/7 monitored secondary particle fluxes from 2013 until now, highly contributed to the understanding of the ways how RREAs are developed in the atmosphere. In 2022 we enlarge the NaI network with 2 remote detectors located at altitudes 2000 and 1700 m, and 13 and 16 km apart from the Aragats station to investigate the horizontal profile of the atmospheric electric field. We found, that the previously estimated values of the regions in the atmosphere, where RREA emerges, were highly underestimated. In the present report, we describe the NaI particle detector's network and present the first results of the experiment demonstrating that the particle fluxes from the atmospheric electron accelerators can cover large areas on the earth's (up to tens of km2).

Development of the relativistic runaway avalanches in the lower atmosphere above mountain altitudes

The comparative analysis of three thunderstorms on Aragats in May 2021 demonstrates that relativistic runaway electron avalanches (RREAs) can reach very low altitudes above the Earth’s surface on mountain altitudes. RREAs which reach the Earth’s surface are registered by the particle detectors as thunderstorm ground enhancements (TGEs) —large enhancements of electron and gamma ray fluxes, sometimes exceeding the fair-weather background fluxes up to a hundred times. By comparing the energy spectra of electrons and gamma rays it is possible to estimate the height above the ground where an RREA terminates and avalanche particles exit the accelerating field. For the several TGEs registered on Aragats, this estimate varied between 50 and 150 meters. The threshold electric field can reach on heights of . When a lightning’s active zone is above particle detectors RREAs last tens of seconds to a few minutes, until lightning flashes terminate electron acceleration. If the lightning activity is far from the detector site, TGEs are extended for a few tens of minutes and smoothly decay and TGE has a more or less symmetrical shape.

Calculation of Parameters of a Relativistic Runaway Electron Avalanche by the Group Equation Method for Moments of the Electron Distribution Function

Calculation of Parameters of a Relativistic Runaway Electron Avalanche by the Group Equation Method for Moments of the Electron Distribution Function