High-energy Events Research Articles

Search for directional associations between baikal gigaton volume detector neutrino-induced cascades and high-energy astrophysical sources

ABSTRACT Baikal-GVD has recently published its first measurement of the diffuse astrophysical neutrino flux, performed using high-energy cascade-like events. We further explore the Baikal-GVD cascade data set collected in 2018–2022, with the aim to identify possible associations between the Baikal-GVD neutrinos and known astrophysical sources. We leverage the relatively high angular resolution of the Baikal-GVD neutrino telescope (2–3 deg.), made possible by the use of liquid water as the detection medium, enabling the study of astrophysical point sources even with cascade events. We estimate the telescope’s sensitivity in the cascade channel for high-energy astrophysical sources and refine our analysis prescriptions using Monte-Carlo simulations. We primarily focus on cascades with energies exceeding 100 TeV, which we employ to search for correlation with radio-bright blazars. Although the currently limited neutrino sample size provides no statistically significant effects, our analysis suggests a number of possible associations with both extragalactic and Galactic sources. Specifically, we present an analysis of an observed triplet of neutrino candidate events in the Galactic plane, focusing on its potential connection with certain Galactic sources, and discuss the coincidence of cascades with several bright and flaring blazars.

Cross-Wavelet Analysis on Radiation Emitted by the plume of a small-size Solid Rocket Motor

This work follow a previous activity that developed a non-intrusive measurements technique for particles velocity ejected from a solid rocket motor based on wavelet analysis. The aim was to detect the particles passage and calculate the axial velocity through an auto-conditioned cross-correlation algorithm. In this study, a wavelet based processing techniques are applied and an innovative methodology based on the cross-wavelet analysis is presented. The objective is to detect the impulsive events associated to the particles crossing the field of view of the acquisition system. Starting from two synthetic signals characterized by a Gaussian peak, each one located at a different time instants, cross-wavelet analysis identify an increase of energy for all the correlation time producing a structure in the time scale comparable to the delay between the peaks. On the experimental database a continuous wavelet transform and a local intermittency measurement are performed to localize high energy events with randomic occurrence in the time series that are associated to the passage of allumina particles. Cross-wavelet analysis present several correlation structures localized in time between the events highlighted by the LIM maps. Results are very promising and could be a very interesting bases for deeper analysis based on wavelet, LIM and cross-wavelet.

Two Candidate Obscured Tidal Disruption Events Coincident with High-energy Neutrinos

Recently, three optical tidal disruption event (TDE) candidates discovered by the Zwicky Transient Facility (ZTF) have been suggested to be coincident with high-energy neutrinos. They all exhibit unusually strong dust infrared echoes, with their peak times matching the neutrino arrival time even better than the optical peaks. We hereby report on two new TDE candidates that are spatially and temporally coincident with neutrinos by matching our sample of mid-infrared outbursts in nearby galaxies (MIRONG) with Gold alerts of IceCube high-energy neutrino events up to 2022 June. The two candidates show negligible optical variability according to their ZTF light curves and can therefore be classified as part of the growing population of obscured TDE candidates. The chance probability of finding two such candidates is about ∼3% by redistributing the MIRONG sources randomly in the Sloan Digital Sky Survey footprint, which will be as low as ∼0.1% (or ∼0.2%) if we limit to sources with increased fluxes (or variability amplitudes) comparable with the two matched sources. Our findings further support the potential connection between high-energy neutrinos and TDEs in dusty environments by increasing the total number of neutrino-associated TDE and TDE candidates to five, although the underlying physics remains poorly understood.

Review of the online analyses of multi-messenger alerts and electromagnetic transient events with the ANTARES neutrino telescope

By constantly monitoring a very large portion of the sky, neutrino telescopes are well-designed to detect neutrinos emitted by transient astrophysical events. Real-time searches with the ANTARES telescope have been performed to look for neutrino candidates coincident with gamma-ray bursts detected by the Swift and Fermi satellites, high-energy neutrino events registered by IceCube, transient events from blazars monitored by HAWC, photon-neutrino coincidences by AMON notices and gravitational wave candidates observed by LIGO/Virgo. By requiring temporal coincidence, this approach increases the sensitivity and the significance of a potential discovery. This paper summarises the results of the follow-up performed of the ANTARES telescope between January 2014 and February 2022, which corresponds to the end of the data-taking period.

The capability of water Cherenkov detectors arrays of the LAGO project to detect Gamma-Ray Burst and high energy astrophysics sources

Gamma-Ray Bursts (GRBs) are one of the brightest transient events detected, with energies in their prompt phase ranging from keV to GeV. Theoretical models predict emissions at higher energies in the early times of the afterglow emission, and recently GRB190114C was the first GRB detected at TeV energies by the MAGIC experiment. The Latin American Giant Observatory (LAGO) operates a network of water Cherenkov detectors (WCD) at different sites in Latin America. Spanning over different altitudes and geomagnetic rigidity cutoffs, the geographic distribution of the LAGO sites, combined with the new electronics for control, atmospheric sensing, and data acquisition, allows the realization of diverse astrophysics studies at a regional scale. LAGO WCDs located at high altitudes possess good sensitivity to electromagnetic secondary radiation, which is the main expected signature of this kind of high-energy event on the ground. Due to the characteristics of the WCD and the wide field of view, LAGO possesses a large aperture high-duty cycle. In this work, we present the results of the sensitivity of LAGO small arrays of WCDs for the detection of events like GRB190114C. Also, we extend the study to other TeV galactic emitters, such as pulsar wind nebulas, TeV-halos, and some additional sources with unidentified categorizations. These are interesting sources to study taking advantage of the long-term monitoring capabilities of LAGO. We use a dedicated simulation process: ARTI, a toolkit developed by LAGO for high-energy air showers, MEIGA, a framework to simulate the response of the detectors, and oneDataSim, the new high-performance computing and cloud-based implementation of our simulation framework.

Big flares from small stars: detecting flares from faint low-mass stars with NGTS full-frame images

ABSTRACT High-cadence observations of high-energy stellar flares from cool and ultracool dwarfs are often limited by the faint nature of their host stars. Many low-mass sources cannot be detected in quiescence by photometric surveys, meaning they are not targeted for high-cadence observations. This reduces the chances of detecting the rarest high-energy flare events. We used the 13-s cadence full-frame images of Next-Generation Transit Survey (NGTS) to search for flares from M and L dwarfs. This included stars that were too faint to detect in quiescence. We detect 160 flares from 135 stars, with spectral types ranging from M3 to L2.5. We use our sample to study the energies, amplitudes and durations of flares from M and L dwarfs. We measure bolometric flare energies up to 4.5 × 1034 erg for ultracool dwarfs, but conclude that we have not reached a maximum limit to the energy released during white-light flares. We use our results to study the incidence rate of flares of mid- and late-M stars, not accounting for age or binarity, and find that 1.4 ± 0.4 and $9^{+16}_{-3}$ per cent of mid- and late-M stars, respectively, exhibit flares with amplitudes above 1 mag in the NGTS bandpass. Future studies with greater numbers of NGTS fields will expand upon this work.

Adaptive surface code for quantum error correction in the presence of temporary or permanent defects

Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may correspond to individual qubits or to clusters and could potentially disrupt the code sufficiently to generate logical errors. In this paper, we explore a novel adaptive approach for surface code quantum error correction on a defective lattice. We show that combining an appropriate defect detection algorithm and a quarantine of the identified zone allows one to preserve the advantage of quantum error correction at finite code sizes, at the cost of a qubit overhead that scales with the size of the defect. Our numerics indicate that the code's threshold need not be significantly affected; for example, for a certain scenario where small defects repeatedly arise in each logical qubit, the noise threshold is 2.7% (versus the defect-free case of 2.9%). These results pave the way to the experimental implementation of large-scale quantum computers where defects will be inevitable.

Particle classification in the LAGO water Cherenkov detectors using clustering algorithms

The Latin American Giant Observatory (LAGO) is a ground-based observatory studying solar or high-energy astrophysics transient events. LAGO takes advantage of its distributed network of Water Cherenkov Detectors (WCDs) in Latin America as a tool to measure the secondary particle flux reaching the ground. These secondary particles are produced during the interaction between the modulated cosmic rays flux and the atmosphere.The LAGO WCDs are sensitive to secondary charged particles, high energy photons through pair creation and Compton scattering, and even neutrons thanks to, e.g., the deuteration of protons in the water volume. The pulse shape generated by these particles depends on several factors, such as the detector geometry, the water purity, the sensor response, or the reflectivity and diffusivity of the inner coating. Due to the decentralized nature of LAGO, these properties are different for each node. Additionally, the pulse shape depends on the convolution between the response of the central photomultiplier (PMT) to individual photons and the time distribution of the Cherenkov photons reaching the PMT. Typically, a WCD gives pulses with a sharp rise time (∼10ns) and a longer decay time (∼70ns).In this work, the WCD data used is acquired using the original LAGO data-acquisition system that digitizes pulses at a sampling rate of 40 MHz and 10 bits resolution on time windows of 400ns. Here, we apply unsupervised machine learning techniques to find patterns in the WCDs data and subsequently create groups, through clustering, that can be used to provide particle separation. We use data acquired from an individual WCD, showing that density-based clustering algorithms are suitable for automatic particle separation producing good candidate groups. Improved separation would help LAGO to reconstruct in situ the properties of primary cosmic rays flux. These results open the possibility to deploy machine learning-based models in our distributed detection network for onboard data analysis as an operative prototype, allowing detectors to be installed at very remote sites.

Heritage Stone 9. Tyndall Stone, Canada’s First Global Heritage Stone Resource: Geology, Paleontology, Ichnology and Architecture

Tyndall Stone is a distinctively mottled and strikingly fossiliferous dolomitic limestone that has been widely used for over a century in Canada, especially in the Prairie Provinces. It comprises 6–8 m within the lower part of the 43 m thick Selkirk Member of the Red River Formation, of Late Ordovician (Katian) age. It has been quarried exclusively at Garson, Manitoba, 37 km northeast of Winnipeg, since about 1895, and for the past half-century extraction has been carried out solely by Gillis Quarries Ltd. The upper beds tend to be more buff-coloured than the grey lower beds, as a result of groundwater weathering. Tyndall Stone, mostly with a smooth or sawn finish, has been put to a wide variety of uses, including exterior and interior cladding with coursed and random ashlar, and window casements and doorways. Split face finish and random ashlar using varicoloured blocks split along stylolites have become popular for commercial and residential buildings, respectively. Tyndall Stone lends itself to carving as well, being used in columns, coats of arms and sculptures. Many prominent buildings have been constructed using Tyndall Stone, including the provincial legislative buildings of Saskatchewan and Manitoba, the interior of the Centre Block of the House of Commons in Ottawa, courthouses, land titles buildings, post offices and other public buildings, along with train stations, banks, churches, department stores, museums, office buildings and university buildings. These exhibit a variety of architectural styles, from Beaux Arts to Art Deco, Châteauesque to Brutalist. The Canadian Museum of History and the Canadian Museum for Human Rights are two notable Expressionist buildings. The lower Selkirk Member is massive and consists of bioturbated, bioclastic wackestone to packstone, rich in crinoid ossicles. It was deposited in a low-energy marine environment within the photic zone, on the present-day eastern side of the shallow Williston Basin, which was part of the vast equatorial epicontinental sea that covered much of Laurentia at the time. Scattered thin bioclastic grainstone lenses record episodic, higher energy events. Tyndall Stone is spectacularly fossiliferous, and slabs bearing fossils have become increasingly popular. The most common macrofossils are receptaculitids, followed by corals, stromatoporoid sponges, nautiloid cephalopods, and gastropods. The relative abundance of the macrofossils varies stratigraphically, suggesting that subtle environmental changes took place over time. The distinctive mottles—‘tapestry’ in the trade—have been regarded as dolomitized burrows assigned to Thalassinoides and long thought to have been networks of galleries likely made by arthropods. In detail, however, the bioclastic muddy sediment underwent a protracted history of bioturbation, and the large burrows were mostly horizontal back-filled features that were never empty. They can be assigned to Planolites. The matrix and the sediment filling them were overprinted by several generations of smaller tubular burrows mostly referrable to Palaeophycus due to their distinctive laminated wall linings. Dolomite replaced the interiors of the larger burrows as well as smaller burrows and surrounding matrix during burial, which is why the mottling is so variable in shape.

What Do Halo CMEs Tell Us about Solar Cycle 25?

It is known that the weak state of the heliosphere due to diminished solar activity in cycle 24 backreacted on coronal mass ejections (CMEs) to make them appear wider for a given speed. One of the consequences of the weak state of the heliosphere is that more CMEs appear as halo CMEs (HCMEs), and halos are formed at shorter heliocentric distances. Current predictions for the strength of solar cycle (SC) 25 range from half to twice the strength of SC 24. We compare the HCME occurrence rate and other properties during the rise phase of cycles 23, 24, and 25 to weigh in on the strength of SC 25. We find that HCME and solar wind properties in SC 25 are intermediate between SCs 23 and 24, but closer to SC 24. The HCME occurrence rate, normalized to the sunspot number, is higher in SCs 24 and 25 than in SC 23. The solar wind total pressure in SC 25 is ∼35% smaller than that in SC 23. Furthermore, the occurrence rates of high-energy solar energetic particle events and intense geomagnetic storms are well below the corresponding values in SC 23, but similar to those in SC 24. We conclude that cycle 25 is likely to be similar to or slightly stronger than cycle 24, in agreement with polar-field precursor methods for cycle 25 prediction.

Constraints on Populations of Neutrino Sources from Searches in the Directions of IceCube Neutrino Alerts

Beginning in 2016, the IceCube Neutrino Observatory has sent out alerts in real time containing the information of high-energy (E ≳ 100 TeV) neutrino candidate events with moderate to high (≳30%) probability of astrophysical origin. In this work, we use a recent catalog of such alert events, which, in addition to events announced in real time, includes events that were identified retroactively and covers the time period of 2011–2020. We also search for additional, lower-energy neutrinos from the arrival directions of these IceCube alerts. We show how performing such an analysis can constrain the contribution of rare populations of cosmic neutrino sources to the diffuse astrophysical neutrino flux. After searching for neutrino emission coincident with these alert events on various timescales, we find no significant evidence of either minute-scale or day-scale transient neutrino emission or of steady neutrino emission in the direction of these alert events. This study also shows how numerous a population of neutrino sources has to be to account for the complete astrophysical neutrino flux. Assuming that sources have the same luminosity, an E −2.5 neutrino spectrum, and number densities that follow star formation rates, the population of sources has to be more numerous than 7 × 10−9 Mpc−3. This number changes to 3 × 10−7 Mpc−3 if number densities instead have no cosmic evolution.

Effects of Accident Thermal Loading on In-Plane Shear Behavior of Steel-Plate Composite Walls

Structural walls in safety-related nuclear facilities are required to be designed for seismic and accident thermal (due to postulated high-energy pipe break events) loading combination. Current U.S. and international codes provide limited guidance for analysis and design of walls for this loading combination. This paper describes the experimental results and observations from tests conducted on a laboratory-scale (1:4 to 1:5) test unit representing steel-plate composite (SC) walls subjected to combined in-plane (seismic) and accident thermal loading. The test unit was subjected to surface temperatures of up to 450°F in combination with cyclic in-plane loading. Results of similar experiments recently conducted in Japan are also summarized (with surface temperatures up to 570°F). Surface heating combined with the low thermal conductivity and high specific heat of concrete resulted in nonlinear thermal gradients through the thickness of the specimens. These nonlinear thermal gradients and the associated self- or internal restraint led to extensive concrete cracking. This concrete cracking reduced the initial and secant stiffness of the specimens. The initial stiffness of the heated specimens reduced to 30 to 40% of the initial stiffness of the control (unheated) specimen. The secant stiffness of the heated specimens reduced up to 50% of the secant stiffness of the control (unheated) specimen. However, the in-plane shear strength of the heated SC specimens was still approximately 10 to 30% greater than the nominal in-plane shear strength calculated, for the limit state of steel plate von Mises yielding, using AISC N690 equations and measured material properties. Evaluation of the experimental results and observations suggests that the in-plane shear strength of SC walls subjected to typical accident surface temperatures (up to 570°F) can be estimated conservatively using the current provisions of AISC N690. The stiffness for accident thermal loading combinations can be considered to reduce from cracked composite stiffness at ambient temperature to fully cracked—that is, steel-only stiffness as the surface temperature increases up to typical accident value.

Environmental controls on trace-fossil distribution in the Upper Jurassic-Lower Cretaceous Vaca Muerta Formation (Argentina): Implications for the analysis of fine-grained depositional systems

Over the past years, the interest in organic-rich, fine-grained depositional systems has been growing due to the increasing relevance of unconventional shale reservoirs and several breakthroughs in the study of mud. However, the paleoenvironmental application of ichnologic analyses of these systems is still hindered by the scarcity of discrete trace fossils, small burrow size, and difficulty in obtaining fresh rock samples. The Upper Jurassic-Lower Cretaceous, Vaca Muerta Formation is the most important fine-grained unconventional reservoir in South America, and hence, contains a large density of cores that provide fresh cross-section views with detailed information on mudstone. An ichnologic analysis was carried out on cores and outcrop to develop an integrated ichnologic-sedimentologic model and to understand environmental controls on trace-fossil distribution. The Vaca Muerta Formation shows indistinct bioturbation represented by biodeformational structures generating irregular-laminated and massive mudstone fabrics, and discrete bioturbation and biodeposition structures mostly associated with tuff and heterolithic successions. Trace fossils were grouped into nine ichnocoenoses that illustrate organism responses to environmental controls. Abundant biodeformational structures in mudstone are associated with soupy substrates, whereas a change to softgrounds or loosegrounds occurs during coarser-grained sedimentation (associated with contourite drift, fluid mud flow, slope hemipelagic, and volcanic ash sedimentation), enhancing preservation of discrete traces. Locally, higher-energy events associated with exhumation of consolidated sediment generated firmgrounds colonized by the producers of the Thalassinoides isp. ichnocoenosis. In terms of oxygen, increased bioturbation index, penetration depth, burrow size, and ichnodiversity record an increase in bottom and interstitial water oxygenation. Moreover, an overall food-rich environment precluded specialized feeding and the development of tiered communities. The present study provides a clear picture of the relationship between substrate and oxygen controls in trace-fossil composition and distribution, contributing to the understanding of taphonomic controls and paleoecologic dynamics in fine-grained depositional systems, and providing an additional tool to refine sedimentologic and sequence stratigraphic analyses in similar mudstone successions elsewhere.

Estimating source distances for high-energy neutrinos: A method for improving electromagnetic follow-up searches

High-energy neutrino telescopes such as ICECUBEor KM3NET issue public alerts describing the characteristics of possible astrophysical high-energy neutrino events. This information, particularly with respect to the arrival direction and the associated uncertainty of the neutrino candidates, is used by observatories to search for possible electromagnetic counterparts. Such searches are complicated by the size of localisation areas, which can be up to tens of squared degrees or more, coupled with the absence of constraints on the distance or nature of the possible source – in contrast to gravitational wave alerts issued by instruments such as LIGO/VIRGO. Here, we describe a method for deriving a probable distance interval for the astrophysical source that may possibly be associated with a high-energy neutrino event, which may then be used in a cross-matching with galaxy catalogues to search for plausible electromagnetic counterparts. This study is intended to serve as a guide for high-energy neutrino followup campaigns.

Growing evidence for high-energy neutrinos originating in radio blazars

ABSTRACT Evidence for bright-radio blazars being high-energy neutrino sources was found in recent years. However, specifics of how and where these particles get produced still need to be determined. In this paper, we add 14 new IceCube events from 2020–2022 to update our analysis of the neutrino-blazars connection. We test and refine earlier findings by utilizing the total of 71 track-like high-energy IceCube events from 2009–2022. We correlate them with the complete sample of 3412 extragalactic radio sources selected by their compact radio emission. We demonstrate that neutrinos are statistically associated with radio-bright blazars with a post-trial p-value of 3 · 10−4. In addition to this statistical study, we confirm previous individual neutrino-blazar associations, find and discuss several new ones. Notably, PKS 1741 − 038 was selected earlier and had a second neutrino detected from its direction in 2022; PKS 0735 + 168 has experienced a major flare across the whole electromagnetic spectrum coincidently with a neutrino arrival from that direction in 2021.

Light speed variation from GRB 221009A

It is postulated in Einstein’s relativity that the speed of light in vacuum is a constant for all observers. However, the effect of quantum gravity could bring an energy dependence of light speed, and a series of studies on high-energy photon events from gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) suggest a light speed variation with E LV = 3.6 × 1017 GeV or a bound E LV ≥ 3.6 × 1017 GeV. From the newly observed gamma-ray burst GRB 221009A, we find that a 99.3 GeV photon detected by Fermi-Large Area Telescope (LAT) is coincident with the sharp spike in the light curves detected by both Fermi-Gamma-ray Burst Monitor (GBM) and HEBS under the above scenario of light speed variation, suggesting an option that this high-energy photon was emitted at the same time as a sharp spike of low-energy photon emission at the GRB source. Thus this highest energy photon event detected by Fermi-LAT during the prompt emission of GRBs might be considered as an optional signal for the linear form modification of light speed in cosmological space.

Ground Motion Prediction of High-Energy Mining Seismic Events: A Bootstrap Approach

Induced seismicity has been a serious problem for many coal mines in the Upper Silesian Coal Basin in Poland for many decades. The occurring mining tremors of the rock mass generate seismic vibrations that cause concern to the local population and in some rare cases lead to partial damage to buildings on the surface. The estimation of peak ground acceleration values caused by high energy mining seismic tremors is an important part of seismic hazard assessment in mining areas. A specially designed bootstrapping procedure has been applied to estimate the ground motion prediction model and makes it possible to calculate the confidence intervals of these peak ground acceleration values with no assumptions about the statistical distribution of the recorded seismic data. Monte Carlo sampling with the replacement for 132 seismic records measured for mining seismic tremors exceeding 150 mm/s2 have been performed to estimate the mean peak ground acceleration values and the corresponding upper limits of 95% confidence intervals. The specially designed bootstrap procedure and obtained ground motion prediction model reflect much better the observed PGA values and therefore provide more accurate PGA estimators compared to the GMPE model from multiple regression analysis. The bootstrap analysis of recorded peak ground acceleration values of high-energy mining tremors provides significant information on the level of seismic hazard on the surface infrastructure. A new tool has been proposed that allows for more reliable determination of PGA estimators and identification in the areas in coal mines that are prone to high-energy seismic activity.

The burst observer and optical transient exploring system in the multi-messenger astronomy era

The Burst Observer and Optical Transient Exploring System (BOOTES) was first designed as an asset of autonomous telescopes that started to be deployed in 1998, taking 24 years to be fully developed around the earth. Nowadays BOOTES has became a global network of robotic telescopes, being the first one present in all continents, as of 2022. Here we present the details of the network and review its achievements over the last 2 decades regarding follow-up observations of high-energy transient events. Moreover, considering the recent operations of neutrino and gravitational wave detectors, some hot-topic expectations related to robotic astronomy are discussed within the framework of multi-wavelength astrophysics.

Youth Hackathons in Computing for the Community: A Design Case.

As schools endeavor to provide all students with access to computational thinking and computer science, the hackathon emerges as a competitive and high-energy event that uses authentic problems to motivate learners to engage in the domain of computing. This article presents the design case of a hackathon for teenagers as enacted over five iterations by faculty and staff at a Southeastern public university in the United States. Given a problem in the local community, participating teenagers collaborated in a mentor-supported environment to design, develop, and communicate software-based solutions. Using trustworthiness from naturalistic inquiry as a guiding approach to build the design case, our methods draw on multiple data sources, peer debriefing, member checks, and thick description. This design case contributes detailed descriptions and design rationales related to the youth hackathon's evolving features. It provides all levels of designers with useful pedagogical and logistical resources to support efforts to enact hackathons in novel settings.

Synergistic Effect of Temperature and Operating Voltage on Deep Charging of PEEK in the Space Solar Power Station

When the Space Solar Power Station operates in its geostationary orbit, deep dielectric charging may occur due to the implantation of the space electrons into the dielectrics and destroy the electronic devices. In this work, during the high-energy electron storms event, the deep dielectric charging characteristics of the poly-ether-ether-ketone flat plate have been studied by the Geant4 simulation as a function of temperature. It is found that the maximum electric field strength decreases when the temperature of the space environment increases, which is due to the increasing dark conductivity. When the front plate of the poly-ether-ether-ketone is biased at 10,000 V, and the back plate is grounded, the electrostatic discharge is the most likely to occur, while the case of 10,000 V on the front plate with the back plate suspended (ungrounded) is the safest. It is well analyzed through the influence of the initial electric field generated by the bias voltage on the electric field induced by the electron deposition.