Large-scale Electric Field Research Articles

Acceleration mechanisms of energetic ion debris in laser-driven tin plasma EUV sources

Laser-driven tin plasmas are driving new-generation nanolithography as sources of extreme ultraviolet (EUV) radiation centered at 13.5 nm. A major challenge facing industrial EUV source development is predicting energetic ion debris produced during the plasma expansion that may damage the sensitive EUV channeling multilayer optics. Gaining a detailed understanding of the plasma dynamics and ion acceleration mechanisms in these sources could provide critical insights for designing debris mitigation strategies in future high-power EUV sources. We develop a fully kinetic model of tin-EUV sources using one-dimensional particle-in-cell simulations to study ion debris acceleration, which will be valuable for cross-validation of radiation-hydrodynamic simulations. An inverse-bremsstrahlung heating operator is used to model the interaction of a tin target with an Nd:YAG laser, and thermal conduction is included through a Monte Carlo Coulomb collision operator. While the large-scale evolution is in reasonable agreement with analogous hydrodynamic simulations, the significant timescale for collisional equilibration between electrons and ions allows for the development of prominent two-temperature features. A collimated flow of energetic ions is produced with a spectrum that is significantly enhanced at high energies compared to fluid simulations. The dominant acceleration mechanism is found to be a large-scale electric field supported mainly by the electron pressure gradient, which is enhanced in the kinetic simulations due to the increased electron temperature. We discuss the implications of these results for future modeling of tin-EUV sources and the development of debris mitigation schemes.

Dreicer Electric Field Definition and Runaway Electrons in Solar Flares

We analyze electron acceleration by a large-scale electric field E in a collisional hydrogen plasma under the solar flare coronal conditions based on approaches proposed by Dreicer and Spitzer for the dynamic friction force of electrons. The Dreicer electric field E Dr is determined as a critical electric field at which the entire electron population runs away. Two regimes of strong (E ≲ E Dr) and weak (E ≪ E Dr) electric field are discussed. It is shown that the commonly used formal definition of the Dreicer field leads to an overestimation of its value by about five times. The critical velocity at which the electrons of the “tail” of the Maxwell distribution become runaway under the action of the sub-Dreiser electric fields turns out to be underestimated by 3 times in some works because the Coulomb collisions between runaway and thermal electrons are not taken into account. The electron acceleration by sub-Dreicer electric fields generated in the solar corona faces difficulties.

Ionospheric longitudinal variability in the Northern Hemisphere during magnetic storms in March 2012 from ionosonde and GPS/GLONASS data

A comprehensive study of spatio-temporal variations of geomagnetic, ionospheric, and atmospheric parameters in the middle and high latitudes of the Northern Hemisphere during a series of magnetic storms in March 2012 has been expanded by including vertical total electronic content (TEC) data from measurements at the chains of dual-frequency phase receivers GPS/GLONASS in the analysis. The features of longitudinal variations in ionosphere ionization over mid-latitude Eurasia, found earlier from vertical sounding data, are confirmed by vertical TEC data. We emphasize the complex physics of the long magnetically disturbed period in March 2012 with switching between positive and negative effects of an ionospheric storm during the same magnetic storm phases for spaced mid-latitude regions of the Eastern Hemisphere. Such changes in the ionospheric storm effects might have been caused by the superposition of competing processes in the mid-latitude region of the Eastern Hemisphere due to variations in the thermospheric composition, thermospheric winds, and large-scale electric fields affecting ionospheric ionization. We have observed significant differences in the nature of the ionospheric ionization reaction between the Eastern and Western hemispheres to the prolonged geomagnetic disturbance in March 2012. According to TEC data, there was an effect of reduced ionization of the ionosphere at longitudes of the Western Hemisphere, unlike the Eastern one. The effect of a negative ionospheric storm was caused by the formation of vast areas of atmospheric gas with a reduced density ratio [O]/[N2] over the mid-latitude region of the Western Hemisphere in the zone of maximum penetration of geomagnetic disturbances from high latitudes to middle latitudes. According to the INTERMAGNET magnetometer chain data for the analyzed period of magnetic storms on March 7–20, 2012, at midlatitudes of the Northern Hemisphere the maximum geomagnetic field variations were observed in the Western Hemisphere.

Долготная изменчивость ионосферы северного полушария во время магнитных бурь в марте 2012 года по данным ионозондов и GPS/ГЛОНАСС

A comprehensive study of spatio-temporal variations of geomagnetic, ionospheric, and atmospheric parameters in the middle and high latitudes of the Northern Hemisphere during a series of magnetic storms in March 2012 has been expanded by including vertical total electronic content (TEC) data from measurements at the chains of dual-frequency phase receivers GPS/GLONASS in the analysis. The features of longitudinal variations in ionosphere ionization over mid-latitude Eurasia, found earlier from vertical sounding data, are confirmed by vertical TEC data. We emphasize the complex physics of the long magnetically disturbed period in March 2012 with switching between positive and negative effects of an ionospheric storm during the same magnetic storm phases for spaced mid-latitude regions of the Eastern Hemisphere. Such changes in the ionospheric storm effects might have been caused by the superposition of competing processes in the mid-latitude region of the Eastern Hemisphere due to variations in the thermospheric composition, thermospheric winds, and large-scale electric fields affecting ionospheric ionization. We have observed significant differences in the nature of the ionospheric ionization reaction between the Eastern and Western hemispheres to the prolonged geomagnetic disturbance in March 2012. According to TEC data, there was an effect of reduced ionization of the ionosphere at longitudes of the Western Hemisphere, unlike the Eastern one. The effect of a negative ionospheric storm was caused by the formation of vast areas of atmospheric gas with a reduced density ratio [O]/[N2] over the mid-latitude region of the Western Hemisphere in the zone of maximum penetration of geomagnetic disturbances from high latitudes to middle latitudes. According to the INTERMAGNET magnetometer chain data for the analyzed period of magnetic storms on March 7–20, 2012, at midlatitudes of the Northern Hemisphere the maximum geomagnetic field variations were observed in the Western Hemisphere.

Estimating the corotation lag of the plasmasphere based on the electric field measurements of the Van Allen Probes

The corotation electric field driving the plasmasphere to corotate with the Earth body is important in establishing the topology of the inner magnetosphere and is usually calculated by assuming a 24 h corotation period. However, studies have found that a plasmasphere corotation lag exists, suggesting an overestimation of the electric field driving the plasmasphere to rotate with the planet in previous calculations. In this study, we use electric field measurements from the Van Allen Probes mission from 2012 to 2018 to obtain the distribution of the large-scale electric field in the inner magnetosphere. A new method is developed to extract plasmaspheric rotation information from electric field measurements. Our results show that the electric field driving the plasmaspheric rotation varies with magnetic activity, decreasing with increasing Kp index. It is thus suggested that the corotation lag of the plasmasphere is more significant during magnetically active periods.

Hydrodynamic cumulation mechanism caused by quantum shell effects.

The computational and theoretical analysis carried out in this article demonstrates the existence of a nontrivial mechanism for the compression of a submicron-sized gas bubble formed by a gas of classical ions and a gas of degenerate electrons. This mechanism fundamentally differs from conventional compression mechanisms. It is shown that taking into account the quantum effect of a large spatial scale in the distribution of electrons qualitatively changes the character of cumulative processes. Because of a large-scale electric field caused by quantum shell effects, the compression process is characterized by the formation of multiple shock waves. The values of gas temperature and pressure achieved during compression occur higher by two orders of magnitude as compared with the classical adiabatic regime. The analysis is carried out within the framework of the following model: the dynamics of the electron subsystem is described by equations of a quantum electron fluid, while the hydrodynamic approximation is adopted for the ionic subsystem. The large-scale effect is taken into account by means of effective external field acting on electrons. The theoretical analysis carried out within this approach clarifies the nature of the cumulative process in the system under consideration; some quantitative characteristics obtained with numerical simulation are presented. The possibility of experimental observation of this cumulative mechanism is analyzed. It is suggested that the manifestation of the effect can be observed during laser compression of a system of submicron targets by measuring the neutron yield.

Lightning Initiation as a Consequence of Natural Thundercloud Evolution. Part 3. Streamers and Transition from Streamers to a Leader Channel

This article presents the final part of the study devoted to description of the authors’ scenario of lightning initiation in a thundercloud, the first two parts of which are presented in [1, 2]. The first part shows that consideration of the electron detachment from negative ions results in that the air breakdown field reduces by 15–30 %. This partially simplifies but does not solve the problem of lightning initiation in a thundercloud, the maximum electric fields in which are approximately an order of magnitude lower than the dielectric strength of air. The second part describes the transition from millimeter corona discharges to decimeter-scale regions of elevated ionic conductivity, which becomes possible if the spatiotemporal frequency of corona discharges arising due to collisions (nearly collisions) of hydrometeors exceeds a quite moderate value of 0,1 m-3s-1. In turn, the regions of elevated ionic conductivity give rise to positive streamers. The article presents the lightning initiation process final stage, at which streamers oriented by the large-scale electric field are combined into a single plasma network, inside which a hot leader channel is generated. It is shown that, for the transition from streamers to a lightning leader seed to occur, a potential difference between the boundaries of the zone of a strong intracloud field is to exceed 3 MV. The article ends with a general conclusion summarizing the trilogy results.

Lightning Initiation as a Consequence of Natural Thundercloud Evolution. Part 2. Pre-Streamer Stage

The article presents the second part of the authors’ lightning initiation scenario, which is a continuation of the study [1]. In the first part it was shown that, if the detachment of electrons from negative ions is taken into account, the air breakdown field reduces by 15–30 %. This partially simplifies but does not solve the problem of lightning initiation in a thundercloud, the maximum electric fields in which are approximately an order of magnitude lower than the dielectric strength of air. This article addresses the lightning discharge inception scenario pre-streamer stage. It describes how a series of corona discharges that occur during collisions (nearly collisions) of hydrometeors seeds the cloud with decimeter-scale regions having increased ionic conductivity. The electric field at the poles of these regions enhances to a level necessary for positive streamers to appear. It is shown that, for a transition from millimeter-scale corona discharges to decimeter- or meter-scale streamers to occur, a spatiotemporal frequency of corona discharges on hydrometeors higher than 0,1 m-3s-1 is required, which may well be achieved in a typical thundercloud. The final stage, at which streamers oriented by the direction of a large-scale electric field are combined into a single plasma network, within which a hot leader channel forms, will be described in the coming part of the study.

Lightning Initiation as a Consequence of Natural Thundercloud Evolution. Part 1. The Role of Detachment in Reducing the Critical Air Breakdown Field

Direct measurements show that the maximum values of electric fields measured in thunderclouds are approximately an order of magnitude lower than the air breakdown (ionization threshold) field. At first glance, this means the impossibility of electron avalanches to form and, as a consequence, the impossibility of a lightning discharge to occur. This circumstance puts the question about the lightning origin physical mechanism on a par with the most amazing mysteries of the nature. For more than half a century of research, several mechanisms have been proposed to solve this problem, among which two main lines can be distinguished. The first group of approaches focuses on the possibility of a streamer or a system of streamers to initiate from the surface of one or several hydrometeors, while the second one interprets lightning initiation as a consequence of the runaway electrons breakdown emerging from the interaction between high-energy cosmic rays and the atmosphere. There are also hybrid scenarios that combine both the ideas. However, in view of certain limitations, none of the proposed approaches has been recognized as the final solution to the problem. The article describes a fundamentally new lightning initiation mechanism that develops sequentially on several spatiotemporal scales. The scenario proposed shows how a series of corona discharges occurring during collisions of hydrometeors seeds the cloud with decimeter-scale elevated ionic conductivity regions, the electric field at the poles of which increases to the level necessary for positive streamers to appear. At the next stage, multiple streamer discharges oriented by the direction of a large-scale electric field are combined into a single plasma network, within which a hot leader channel is formed. The mechanism discussed effectively utilizes small-scale and mesoscale electric field fluctuations arising in a thundercloud and can be implemented if the spatiotemporal frequency of corona discharges, accompanying collisions and near collisions of hydrometeors, and the potential difference between the strong intracloud field zone boundaries exceed 0.1 m-3s-1 and 3 MV, respectively. In contrast to alternative approaches, the proposed lightning initiation scenario can be implemented under the conditions of a typical thundercloud without the need to involve any external auxiliary factors. The study results are presented in three parts. This article gives an introductory part, which sets the general context of the narrative and determines the study aims, and describes the role the detachment of electrons from negative ions plays in the air breakdown field reduction. The authors' lightning initiation scenario based on the results described in the present paper is given in two subsequent publications.

Overall Surfacial Antenna Immobilization Boosts Carrier Migration for Visible Light Superoxide Generation.

The artificial photosynthesis efficiency is restricted for the covering of introduced light-absorbing antennas, where they could generally be immobilized at specific surface sites of semiconductors. Here, we highlight the emerging π-π interaction strategies in realizing overall surfacial antenna immobilization onto semiconductor supports, during which large-scale built-in electric fields are established, strongly driving photocarrier migration to catalytic centers accompanied with enhanced light absorption. By taking porphyrin and ZIF-8 as a prototype, both theoretical calculation and experimental results show that the photocatalytic systems with overall surfacial antennas could absorb broader visible light and form abundant photocarrier transport pathways from porphyrin to ZIF-8, boosting the generation of superoxide and organic synthesis efficiency. This work develops a universal strategy for design of efficient artificial photosynthetic systems.

Hot plasma channel network formation in thunderclouds

The main intrigue of lightning initiation is that electric fields measured in thunderclouds have peak values about an order of magnitude lower than the dielectric strength of air and do not even exceed the minimum field needed for positive streamers propagation. It was recently established that pronounced decimeter-scale electric field fluctuations appear against the background of a relatively weak thundercloud large-scale electric field owing to turbulent mixing and polarization of hydrometeors. In the course of thundercloud development these field enhancements reach a level sufficient for initiation of positive streamers and their propagation over the distances of the order of decimeters. Streamers initiate, develop, decay, and merge with each other, thereby providing the appearance of an extensive hierarchical system of interacting plasma channels at different stages of development with embedded and growing hot segments. In this study the renormalization group approach is employed to calculate the value of thundercloud electric field that provides hot plasma channel network explosive formation. The calculated threshold field is considerably less than the minimum field required for positive streamers propagation and may be viewed as the true lightning initiation field.

The criterion for self-sustaining production of relativistic runaway electron avalanches by the positron feedback in thunderstorms

Relativistic runaway electron avalanches (RREA) occurring in thunderstorm large-scale electric fields are one of the sources of atmospheric gamma radiation. Relativistic feedback is the generation of RREAs by positrons or backscattered gamma rays of the previously produced RREAs. In strong electric fields, relativistic feedback can make RREAs self-sustainable that hypothetically can cause a terrestrial gamma-ray flash (TGF). This paper introduces a kinetic approach to study the positron relativistic feedback, which is predominant for the directly observed conditions within thunderstorms. The criterion for self-sustaining production of RREAs by the positron feedback in thunderstorms is derived. The discovered criterion allows one to obtain the parameters of the thunderstorm electric field required for self-sustaining RREA development with positron feedback for any altitude. It is shown that the derived conditions of self-sustainable RREA development are not achieved for the parameters of electric field observed in real thunderclouds.

Modeling of the electrical interaction between desert dust particles and the Earth’s atmosphere

In the current work, the two distinct charging mechanisms of spherical dust particles settling in the Earth’s atmosphere, i.e. ion attachment and contact electrification, are studied in parallel. A novel 1D numerical model has been developed that parametrizes the charging processes in the presence of a large scale electric field, under stagnant atmospheric conditions where wind contribution is neglected. The model is able to self-consistently calculate the modification of atmospheric ion densities and the subsequent alteration of the large scale electric field, when dust particles are present and atmospheric ions attach to them, and is further updated to account for the particle charging due to the efficient collisions between particles of sizes ranging from fine (less than 1μm in radius) to giant mode (larger than 50μm in radius). Due to a lack of a rigorous mathematical expression for the quantification of the particle collision process, the mechanical and electrostatic effects are modeled independently, based on works in the past literature, and then are combined by a simple superposition principle. Additionally, the electrostatic effects are studied in the presence of weak external electric fields (less than 1–2 kV/m). Moreover, for the same reasons a simple superposition principle has been applied for the quantification of the ion attachment process. All these assumptions lead to an approximation of the actual mechanisms quantification, but this method can lead to physically reasonable results, highlighting the impact of several processes to the eventual charging of the dust particles. By binning integration of a realistic particle size distribution in the model, the acquired electrical charge on the dust particles is calculated in the range of 0.5 to 2000 elementary charges. The particles become on average negatively charged, but under specific conditions giant mode particles can be locally and temporarily positive, congruently to previously reported laboratory experiments. Moreover, the electrical force that is applied on the particles by each mechanism individually and through the superposition of both, is extracted and compared to the gravitational force acting on each particle. However, the 1D results indicate that the electrical force is not enough to significantly influence the gravitational settling of the charged particles, as it is more than one order of magnitude less than gravity. This designates that although the electrical processes alone are accounted for, significant meteorological processes such as updrafts, wind shears, or horizontal winds need to be included in the model to accurately represent the modulation of particle electrification and so as to represent the impact of electricity on particle dynamics in a more realistic way.

Observation of variations in cosmic ray single count rates during thunderstorms and implications for large-scale electric field changes

We present the first observation by the Telescope Array Surface Detector (TASD) of the effect of thunderstorms on the development of cosmic ray single count rate intensity over a 700 km2 area. Observations of variations in the secondary low-energy cosmic ray counting rate, using the TASD, allow us to study the electric field inside thunderstorms, on a large scale, as it progresses on top of the 700 km2 detector, without dealing with the limitation of narrow exposure in time and space using balloons and aircraft detectors. In this work, variations in the cosmic ray intensity (single count rate) using the TASD, were studied and found to be on average at the ∼(0.5–1)% and up to 2% level. These observations were found to be both in excess and in deficit. They were also found to be correlated with lightning in addition to thunderstorms. These variations lasted for tens of minutes; their footprint on the ground ranged from 6 km to 24 km in diameter and moved in the same direction as the thunderstorm. With the use of simple electric field models inside the cloud and between cloud to ground, the observed variations in the cosmic ray single count rate were recreated using CORSIKA simulations. Depending on the electric field model used and the direction of the electric field in that model, the electric field magnitude that reproduces the observed low-energy cosmic ray single count rate variations was found to be approximately between 0.2 GV–0.4 GV. This in turn allows us to get a reasonable insight on the electric field and its effect on cosmic ray air showers inside thunderstorms.2 MoreReceived 19 November 2021Accepted 3 January 2022DOI:https://doi.org/10.1103/PhysRevD.105.062002© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric scienceCosmic rays & astroparticlesInterdisciplinary PhysicsParticles & Fields

The Stationary Electric Field in the Heliosphere and Its Possible Relation to Current Sheets

The nature of the large-scale electric field in the heliosphere is discussed in this paper. The electric potential along each line of the magnetic field should be constant in the ideally conductive solar wind. A high electric potential is supposed to be maintained by the rapidly flowing solar wind far from the Sun and, near the Sun, by the unipolar effect caused by the rotation of the Sun. Meanwhile, there is a discrepancy between observations and theoretical concepts. The ratio of the observed electric field and that calculated from a model employing the unipolar effect at the Sun was obtained for the 1994–2008 Ulysses data. It was found that the unipolar effect is insufficient to maintain equipotentiality of magnetic field lines throughout the heliosphere, suggesting the existence of additional sources of the electric field at the Sun. Since the strong electric field is stably observed at high heliolatitudes, its previously unknown sources may be associated with polar conic current sheets and current sheets at the edges of coronal holes.

The Criterion for Infinite Positron Feedback in Dynamics of Relativistic Runaway Electron Avalanches

Relativistic runaway electron avalanches (RREA) accelerated by thunderstorm large-scale electric fields are one of the sources of atmospheric gamma radiation. In strong electric fields, RREAs can multiply by the relativistic feedback. Infinite relativistic feedback makes avalanches self-sustainable and hypothetically can cause a terrestrial gamma-ray flash (TGF). This paper introduces a kinetic approach to study the relativistic feedback caused by positrons since positron feedback dominates for the directly observed electric field strengths. With this approach, the criterion for infinite positron feedback within thunderstorms is derived. Discovered criterion allows obtaining the thunderstorm electric field parameters required for infinite positron feedback for any altitude. The possibility of derived thunderstorm conditions is discussed.

Thermospheric Neutral Winds as the Cause of Drift Shell Distortion in Earth’s Inner Radiation Belt

Recent analysis of energetic electron measurements from the Magnetic Electron Ion Spectrometer instruments onboard the Van Allen Probes showed a local time variation of the equatorial electron intensity in the Earth’s inner radiation belt. The local time asymmetry was interpreted as evidence of drift shell distortion by a large-scale electric field. It was also demonstrated that the inclusion of a simple dawn-to-dusk electric field model improved the agreement between observations and theoretical expectations. Yet, exactly what drives this electric field was left unexplained. We combine in-situ field and particle observations, together with a physics-based coupled model, the Rice Convection Model (RCM) Coupled Thermosphere-Ionosphere-Plasmasphere-electrodynamics (CTIPe), to revisit the local time asymmetry of the equatorial electron intensity observed in the innermost radiation belt. The study is based on the dawn-dusk difference in equatorial electron intensity measured at L = 1.30 during the first 60 days of the year 2014. Analysis of measured equatorial electron intensity in the 150–400 keV energy range, in-situ DC electric field measurements and wind dynamo modeling outputs provide consistent estimates of the order of 6–8 kV for the average dawn-to-dusk electric potential variation. This suggests that the dynamo electric fields produced by tidal motion of upper atmospheric winds flowing across Earth’s magnetic field lines - the quiet time ionospheric wind dynamo - are the main drivers of the drift shell distortion in the Earth’s inner radiation belt.

Three-Dimensional Au/Ag Nanoparticle/Crossed Carbon Nanotube SERS Substrate for the Detection of Mixed Toxic Molecules.

Research on engineering “hotspots” in the field of surface-enhanced Raman scattering (SERS) is at the forefront of contributing to the best sensing indicators. Currently, there is still an urgent need to design a high-strength and large-scale electric field distribution method in order to obtain an ideal SERS sensor. Here, we designed a three-dimensional (3D) Au/Ag nanoparticle (NP)/crossed carbon nanotube film SERS substrate. The proposed structure formed by the simple preparation process can perfectly coordinate the interaction between the SERS substrates, lasers, and molecules. The denser “hotspots” can be induced and then distributed in holes enclosed by Au/AgNPs and the gaps between them. This process was verified by numerical simulations. The experimental results show that the proposed SERS substrate possesses an excellent sensitivity of 10−12 M (rhodamine 6G (R6G)), an enhancement factor of 1.60 × 109, and a good signal reproducibility (the relative standard deviation is ~6.03%). We further use a Au/AgNP/crossed CNT substrate to detect complex solutions composed of toxic molecules, which shows that our proposed SERS substrate has a wide range of application potentials, especially in food safety.

Modeling of Spherical Dust Particle Charging due to Ion Attachment

The attachment of positive and negative ions to settling spherical dust particles is studied. A novel 1D numerical model has been developed to parameterize the charging process in the presence of a large-scale electric field. The model is able to self-consistently calculate the modification of atmospheric ion densities in the presence of the dust particles, and the consequent alteration of the atmospheric electrical conductivity and the large-scale electric field. Moreover, the model estimates the acquired electrical charge on the dust particles and calculates the electrical force that is applied on them. Using observed dust size distributions, we find that the particles can acquire electrical charge in the range of 1–1,000 elementary charges depending on their size and number density. The particles become mainly negatively charged, but under specific conditions giant mode particles (larger than 50 μm radius) can be positive. Moreover, the large-scale electric field can increase up to 20 times as much as the fair weather value. However, our approach shows that the resultant electrical force is not enough to significantly influence their gravitational settling, as the ratio between the electrical force magnitude and the gravity magnitude does not exceed the value of 0.01. This indicates that the process of ion attachment alone is not sufficient to create strong electrical effects for the modification of particle dynamics. Therefore, other processes, such as the triboelectric effect and updrafts, must be included in the model to fully represent the impact of electricity on particle dynamics.

Statistics of variations in atmospheric electrical parameters based on a three-dimensional model and field observations

In this work, we study the space-time statistical features of variations in the atmospheric electric field (Ez) and space charge in the atmospheric boundary layer using a three-dimensional model and analysis of observational data. The model is a combination of large-eddy simulation supplemented with a subgrid kinematic model for scalar and the three-dimensional Poisson equation for the electric potential. Based on the calculated evolution of three-dimensional distributions of the space charge and electric potential, the variability of the spectral slopes of variations in the space charge, vertical potential difference, and the vertical component of the electric field Ez is investigated. The vertical profiles of Ez and the frequency power spectra of Ez variations at different heights computed are in reasonable agreement with the observed ones. It is shown that the cross-correlation of Ez at spatially separated points located on one straight line near the earth's surface decreases with increasing distance with a characteristic scale of a few tens meters and has a dependence on the angle between this line and the direction of the wind. Mean large-scale horizontal electric field defined through the position and amplitude of the potential extrema at the same height depends on height non-monotonically having a maximum value of about 5 V/m. Scaling exponents of structure functions for Ez variations are found to be significantly larger than those for space charge variations.