Introduction. The productivity of the wells at gas and gas condensate fields along with the wells at underground gas storage facilities, depends on such parameters as thermodynamic conditions, properties of the produced fluid, method of opening and completion, filtration-volumetric and geometrical characteristics of the formation. To identify the factors affecting the flow rate of wells, the information obtained as a result of the interpretation of the data of systematically conducted gas well tests is used. The development of mathematical models for assessing the factors affecting the technological regime of gas wells' operation, followed by the formation of a list of candidate wells for wells intervention is an urgent approach for increasing the productivity of underground gas storage facilities. Materials and research methods. The processing of the results of gas well tests is based on the theoretical provisions of the iltration of luids in a porous medium obeying to linear and nonlinear laws. The results of well tests under steady-state filtration modes provide the most reliable estimate of the numerical values of the coefficients of filtration resistances A and B. The paper analyzes the reasons for the change in the coefficients A, B, and their main parameters by the example of underground gas storage wells. The definition of the turbulence coefficient p, which is included in the quadratic term of the equation of gas filtration obeying to the nonlinear law, has been substantiated. Since the largest pressure drop in the producing formation occurs in the immediate vicinity of the wellbore, the main factors affecting the iltration resistance in the bottomhole formation zone are the radius and degree of change in the permeability coefficient of the contaminated zone, as well as the radius of influence and the height of the sandclay plug. Research results and their discussion. To identify the parameters of the bottomhole formation zone, mathematical models have been developed for assessing the values of skin factors for the coefficients A and B, characterizing the linear and turbulent filtration resistance factors under the nonlinear law of gas filtration, respectively. The obtained formulas for calculating skin factors for cases of the presence of contamination of the bottomhole formation zone or sand-clay plug make it possible to determine the radius and permeability coeficient of the contaminated zone, as well as the radius of influence and height of the sand-clay plug. Mathematical models have been tested on synthetic wells of underground gas storage facilities. For these wells, the conditions for the change in the fiiltration resistance coefficients from the initial values A and B (without skin factors) to the current As and Bs (with regard to skin factors) are modeled. Conclusions. The paper presents the methodological foundations for assessing the main parameters of the bottomhole formation zone which affect the productivity of gas wells. The developed methodology can also be used to assess well interventions already performed to increase the productivity of gas wells.

Introduction . Prospects for the development of deposits with hard-to-recover reserves are associated with the huge potential of hydrocarbon reserves concentrated in the formations of the Bazhenov and Tyumen deposits . 99% of all recoverable reserves of hard-to-recover oil of industrial categories are located on the territory of the West Siberian oil and gas complex. Therefore, increasing the efficiency of the development of such fields is undoubtedly an urgent task . One of the methods to ensure stable and profitable levels of oil production is the treatment of the bottomhole zone of wells with acid compositions to clean up and increase the iltration properties of the formation. Materials and methods of research. The article discusses various methods of acidizing the bottomhole zone of wells operating deposits with hard-to-recover reserves The main criteria to be met by the acid composition used are given Results and Discussion The results of acid treatments in the wells of the Bazhenov and Tyumen deposits are presented For the Bazhenov deposits, in order to restore and improve the permeability of the bottomhole zone of formations composed of terrigenous reservoirs with high carbonate content, it is recommended to carry out acidizing at the stage of well development For the Tyumen deposits, the efficiency of treatment of the bottomhole zone of the well for individual fields differs significantly and depends on the treatment method and the concentration of reagents Conclusion For sediments of the Bazhenov formation at the Salym field, the success rate of operations is 20-30%, which is associated with the complex mineralogical composition of the rocks, and with low values of reservoir parameters, as well as temperature and pressure conditions of occurrence For the deposits of the Tyumen suite at the Lovinskoye field, the effectiveness of acid treatments varies from 30 to 100%, At the Russkinskoye field, the success of the measures is estimated at 95%.

Introduction. Over the past 70 years, there has been a radical restructuring of the landscapes of the region, affecting water systems as well. This study is an attempt to conduct a retrospective analysis of the transformation of the faunal complex of the territory. Materials and methods of research. To assess the state of the faunal complex, the materials contained in a number of works devoted to the faunal complex of the Egorlyk River were used. In addition to the literature data, materials collected in 2015-2020 were used. The accounting of the animal population was carried out according to the methods summarized in the “Field studies on the ecology of terrestrial vertebrates” by G.A. Novikov. Amphibians were accounted for by visual inspection of the territory. The species identity was established remotely. The identification of the species composition of reptiles and the study of the state of their populations was carried out during the survey of terrestrial biotopes. Identification of the species composition of birds and the study of the state of their populations was carried out by route accounting methods. The total length of the hiking routes was about 140 km. The names of bird species are given in accordance with the summary of L.S. Stepanyan. Rodent accounting was carried out by trap lines. The accounting of insectivores was carried out by the method of hunting grooves. The assessment of the condition of large mammals was carried out according to literature data, as well as visual observations. In total, 10 routes were conducted to study the fauna of birds, mammals, amphibians and reptiles. The total length of the routes was 130 km. The community of ter restrial vertebrates is represented by 1 species of amphibians, 2 species of reptiles, 16 species of birds, 2 species of mammals. The results and their discussions. In this study, the development of the ecosystem of the Egorlyk River from 1948 to the present, we will divide into three stages of formation. The first stage will include the period of the natural state of the territory and the faunal complex before flooding (until 1948). The second stage begins from the moment of flooding - from 1950 to 2000. The third stage will include the modern period, from 2000 to the present. Conclusions: Based on stock data, the species diversity of the animal population before the flooding of the river, characteristic of low-water steppe water systems, with bitter-salty water drying up in summer, has been established. After watering, the stenobiont species are actively replaced by eurybiont species. During this period, the greatest species diversity was most noted. River flooding is a process of primary succession, and its settlement by various species is a succession series. Currently, the formation of a climax community has been established, due to the stable availability of habitats, as well as the regulation of the number of species, the number and density of the animal population.

Introduction. The article describes and summarizes the experience of different countries in developing the information systems supporting the management of territories and their sustainable development. Some countries, such as the USA, Australia, Great Britain, and others, made great strides in developing such systems at the national level. The article also provides examples of spatial databases for the territories of Saudi Arabia, Hungary, coastal regions of Spain, etc. The basis for the territorial management support system is the spatial data infrastructure (SDI), which provides data storage, updating, access to data, as well as their visualization in the form of maps, graphs or tables. For a long time, geoportals were considered one of the most effective types of spatial data infrastructures, combining many functions necessary for displaying spatial information and effective management. However, now geoportals are being replaced by information and analytical systems of a new generation that goes beyond the SDI concept and are called geospatial ecosystems. Materials and research methods. The tasks of information support of territorial development projects from the perspective of sustainable development are set at all territorial levels, from global to local. At the global level, statistical data is collected by countries and regions of the world within the framework of the work of the largest international organizations: The United Nations, the World Bank, WHO, UNESCO, the International Labor Organization, the International Tourism Organization, etc. As a rule, this data is publicly available and published on the websites of organizations and in annual reports. The results of the study and their discussion: For a long time, geoportals were considered one of the most effective types of spatial data infrastructures, combining many functions necessary for effective territory management (Gamez et al., 2019). However, in recent years, geoportals have been replaced by new-generation information and analytical systems that go beyond the SDI concept and are called geospatial ecosystems. The metaphor "ecosystem" in this case conveys the fundamental concept of a dynamic, complexly organized, stable, adaptive multi-user geoinformation environment (Strobl, 2021; Shao et al., 2012).The transition from SDI to a geospatial ecosystem is driven by a continuous increase in the volume of generated spatial information, an increase in the number of platforms and services based on geodata, and the emergence of new challenges in data management, including in the field of data protection and cyber-security.

Ntroduction. The North Caucasus Federal District stands out against the background of Russia with a favorable demographic situation, which is reflected in population growth, a younger age structure and relatively higher total fertility rates. At the same time, the district is losing population in migration exchange with other territories of Russia. At the same time, it is obvious that the demographic situation in different subjects and even different settlements is not the same. The purpose of this study is to identify the territorial features of the demographic development of the North Caucasus Federal District. Materials and research methods. The informational basis of the study is the data of official statistics at the level of regions and cities-cores of urban agglomerations of the North Caucasus Federal District. Graphical-cartographic and statistical spatial analysis was used as the main research method. Research results and their discussion. The regional features of the modern dynamics of the population of the North Caucasus Federal District, the regional specificity of changes in the main indicators of population reproduction: the coeficients of natural growth / decline, migration growth / decline, general fertility rates, mortality, total fertility, and age structure are revealed. An important component of the study is to consider the impact of the pandemic on demographic processes. The role of migration processes in the demographic development of regions has been established. Conclusions. By demographic development, the regions of the North Caucasus Federal District are divided into three groups. The first group includes regions with stable population growth, mainly due to natural growth (republics in the eastern part of the okrug. The second group includes republics in which population growth has practically stopped. migration outflow predominates in all regions. the district is less critical than other Russian territories.

Introduction. Traditional sources of information that are commonly used for spatial analysis of geodemographic processes are not always able to provide an extensive understanding of the effects associated with the growth or decline in the population of cities and agglomerations. In this regard, data obtained with the help of Big Data technologies are of great help for spatial analysis. Modern GIS is an effective tool for solving the problem of processing and interpreting big data. GIS allows you to structure data and visualize it, thus obtaining a geographical interpretation of information. The approbation of the possibilities of using data corrupted by big data technology, based on integration with GIS, as well as the use of traditional information sources (goskomstat) was carried out on the example of cities and urban agglomerations of Lipetsk and Stavropol. Materials and research methods. To analyze the dynamics of the built-up areas of Lipetsk and Stavropol in the period from 2000 to 2020, satellite images from Sentinel-2 and Landsat-8 satellites were used. The capabilities of the ScanEx Image Processor software were used to process satellite images. Work on the allocation of building boundaries in different years was carried out by the method of reverse decryption. To analyze the population density of cities, heat maps provided by the Export Base service were used. The cost of residential premises was estimated by processing information from Internet services for placing ads (Avito and CIAN). Quantum GIS is used as the main geoinformation tool. The results of the study and their discussion. The approbation of integration technologies and research methods on the example of the core cities of Lipetsk and Stavropol revealed that the demographically favorable city of Stavropol has higher rates of development, has higher prices for residential real estate. This process leads to a concentration of the population, including in new neighborhoods, which is not so pronounced in depopulating Lipetsk. Suburban areas included in the half-hour and hourly transport accessibility are generally comparable in terms of the cost of residential premises within both agglomerations. Results. The development and integration of technologies for the collection, processing and analysis of spatial and temporal data contributes to the expansion of the methodological tools of geodemographic research and opens up wide opportunities to comprehensively approach the issue of the development of intra-agglomeration and intra-urban processes. Traditional sources made it possible to assess the dynamics of the number of cities, and the use of big data technology with GIS integrations revealed the features of the development of urban and suburban development, heat maps of density gave an idea of the features of population concentration, including newly built-up areas. An analysis of the cost of housing using data from Internet services for placing ads in central cities and their suburbs confirmed the main trends related to the centrality of places and the periphery.

Introduction. Dangerous convective weather phenomena have a pronounced tendency to increase, which necessitates the development of new approaches to their forecasting. This is favored by the operational availability of the Earth's atmospheremodelingresults. In this paper, the possibility of predicting the characteristics of hail intensity based on the atmospheric stratification values obtained by the global forecast model (GFS NCEP) is considered. Such characteristics of hail intensity as the area of dead crops and the maximum diameter of hail, which have found application in research of hail and the effectiveness of active effects on hail processes, are considered. Materials and methods of research. The research materials were the output data of the GFS NCEP global atmospheric model with a 24-hour lead time and the characteristics of hail intensity provided by paramilitary services for active impact within the radius of representativeness of the actual aerological sounding dataat the MineralnyeVody station. The parameters of the atmosphere were preliminarily calculated, the most informative ones were selected using a biserial correlation coeficient and factor analysis. The subsequent assessment of the characteristics of the hail intensity was carried out by the method of multiple regression analysis. The results of the research and their discussion. Regression equations were derived for the area of dead crops and the maximum diameter of hail. Estimation of the regression equation'sparameters characterizing the statistical significance and practical applicability of the model showed their compliance with the criteria imposed on them. Conclusions. The proposed approach to forecasting the characteristics of hail intensity according to the global atmospheric model has shown its eficiency and can be used in practice with a high-quality and sufficient amount of initial data.

Introduction. Against the background of global warming observed in recent decades, changes in all climatic characteristics are taking place. In the era of global warming, as the air temperature rises, the moisture content of the air masses also increases, therefore, the amount of snow falling increases in cold regions. This indicates a high sensitivity of the snow cover to any changes in the composition of the atmosphere and its circulation. Snow cover is an important component of the natural environment during the winter. In this work, the assessment of trends in the height of snow cover at three meteorological stations in the North Caucasus, located in different climatic zones, is carried out. For the analysis, data from observations of snow cover for the period 1961- 2018 were used. Materials and research methods: To obtain the results of changes in the snow cover regime from 1960/1961 to 2017/2018. On the territory of the Caucasus region, the averaged series of snow cover characteristics were studied according to data from 3 meteorological stations: Prokhladnaya, Nalchik and Teberda. Using the statistical software package SPSS 13.0, the following statistics were calculated: mean (standard error), standard deviation, minimum, maximum, range, skewness coefficient, kurtosis coefficient, extreme values, climatic norm, Kolmogorov-Smirnov test for normal distribution curve, T- test for comparing the equality of the mean with the climatic norm. Linear trends, the rate of change of the meteorological parameter were obtained, the stability of climatic changes was assessed, and anomalies were identiied for each series under study. Research results and their discussion: To assess the change in the characteristics of the snow cover, data from the series of the snow cover depth in the cold seasons of 1961-2018 were used (from October to April for 1960/612017/18). Seasons from October to April 1960/1961, 1961/1962, ... , 2017/2018 hereinafter, for brevity, they are written as 1961, 1962, 2018. When analyzing the average ten-day snow cover, for example, in 1961, data from October, November, December 1960 and January, February, March and April 1961 were used. In the course of the study, the sustainability of climatic changes was assessed. As its integral characteristic, the Hurst exponent (H) was used, which showed the trend stability and a stable tendency to increase the height of the snow cover at the studied m/stations. The standard deviation а was used as a measure of the typical variability of snow cover (SC) over the period 1960/61-2017/18. For each row of meteorological parameters, the minimum and maximum values of the SC altitude were calculated. To identify anomalies, deviations of the current values from the long-term average for the period 1961-1990 were investigated (climatic norm). The analysis of changes in the height of snow cover for the entire period of the study (1961-2018) and during the period of global warming (from 1976 to 2018) was carried out. Studies have shown that for the period from 1961 to 2018 at all m/stations, there was an increase in the growth rate of the average 10-day snow cover, with its subsequent increase in the period from 1976. The extreme values are revealed for all studied series. The analysis of the average 10-day SC altitude by months (October-April) was carried out in order to identify the medium-snow and little-snow months. Conclusions. Analysis of changes in the growth rate of the average ten-day snow cover showed that there was an increase, both in the baseline (19612018) and in the period 1976-2018. For all the studied series of mean ten-day snow cover, the Hurst exponent demonstrates a high trend resistance of the series. It was revealed that for the entire period of research there are fewer positive anomalies than negative ones. Over the entire observation period at the considered m/stations, 9 extreme values of the height of the snow cover were identified. In the modern period, there has been an increase in the number of extreme values of the average ten-day snow cover by 3.5 times (7: 2) compared to the base period.

Ntroduction. The current state of issues related to the study of the processes of dynamics of atmospheric phenomena, which are quite complex multiparameter in nature, requires a comprehensive approach. This direction of research is determined by the application, along with the analytical method, of numerical methods for obtaining solutions to the problems under consideration. The use of these methods allows you to get a solution to the problem in a general form, expressed through certain coefficients, the finding of which, of course, requires the imposition of additional conditions. However, the use of numerical methods allows to a greater extent to conduct a mathematical analysis of the solutions obtained, as well as the behavior of these dependencies under various speciied parameters, which in turn allows you to form a holistic view of the dynamics of processes when changing certain parameters. Materials and methods of the research. Methods of mathematical modeling of the processes of air particle movement. The basis of these methods are equations describing the dynamics of air, as well as the processes of transfer of radiant energy, heat and moisture in the atmosphere. When constructing the boundary problem of the dynamics of the environment under consideration, it is necessary to set boundary conditions that determine the scope of determining the problem to be solved, as well as the state of the system at the boundaries of this region. In the work, the solution of the problem under study is carried out by numerical methods using a set of tools of the computer program Maple 2021, which allows solving a system of partial differential equations of the second order. Also, using the numerical methods of the program, equations of trajectories and current lines of the air particle were obtained, as well as corresponding graphs were constructed. The results of the study and their discussion. The paper conducts a study, as well as a mathematical and numerical analysis of the mathematical model of dry air dynamics in the presence of small pressure perturbations in the atmosphere, which leads to a violation of the stationary state of the environment and the emergence of convection movements. The main task of the study was to find a general solution to the system of equations describing the dynamics of dry air without taking into account the viscosity of the medium, to obtain an equation of the trajectory of the air particle, as well as to conduct a qualitative analysis of the type of expressions obtained at different values of constant integration. The analysis of the obtained results allows to obtain numerical values of critical constants, included as parameters in the obtained equations of the trajectory of the air particle, and responsible for the occurrence of convective movements of the medium under consideration. Conclusions. In this paper, using the mathematical package Maple 2021, a general solution of the problem of determining the current function describing the motion of an air particle when a pressure disturbance occurs in the atmosphere, as well as the components of the speed of movement in the vertical plane, is obtained. A numerical analysis of the obtained solutions characterizing the migration processes in the environment is carried out. The expressions for the equation of trajectories and current lines of air particles are obtained in general form. At the given values of constant integration, the types of the obtained dependencies were graphically presented. Analysis of graphs shows that under certain conditions associated with some critical values of constant integration, closed curvilinear trajectories of motion are observed. Deviations from the speciied values of these constant data in the direction of greater or smaller values lead either to the non-closure of the trajectory, or to a change in the shape and size of the closed cell.

Introduction. An R/S analysis of the persistence of trends in climatic variables was carried out in the article using the normalized range method, which is one of the nonparametric approaches for studying series that do not satisfy all the conditions of standard Gaussian statistics. To study the stability of a system behaving not as a random variable, but passing a longer path (shifted Brownian motion with the presence of a trend), the Hurst indicator Н was used. Materials and methods of research. The trend stability (persistence) of air temperature changes was assessed using the normalized range method (R/S analysis). The method for determining the Hurst indicator H is based on in order to analyze the range of the parameter (the largest and the smallest values on the period of the segment) and the standard deviation and its dependence on the period of the studied time T, more or less than the current one. The use of long-term data of average, maximum and minimum surface air temperature of 20 meteorological stations of different climatic southern Russia (according to the state observational network of Roshydromet of the North Caucasian Directorate of the Hydrometeorological Service) is used. Results of the study and their discussion. When analyzing the climate, the initial data are time series containing the values of certain climatic indicators (temperature, precipitation, humidity, etc.) for a certain period. Traditionally, trends are used to analyze data for a number of climatic parameters. This solves the problem of predicting future values of the series. At the same time, the trend does not say anything about how stable the series is. Thus, classical methods of analysis are not very informative and have many methodological limitations for their application. The paper presents the results of time series analysis using the method of the normalized range R/S. It was found that the indicators of stability H characterize the stability and long-term changes in the time series of annual and summer average temperatures (H = 0.80), as well as autumn average temperatures (H = 0.73). Series of annual, summer (H = 0.75) and autumn maximum temperatures (H = 0.70), as well as spring minimum temperatures (H = 0.72) also had stable trends. Conclusions. The results of the R/S-analysis showed that the temperature series is not an ideal Poisson process (without memory), on the contrary, there is some long-term correlation between the last events and the initial ones. Change in climatic variables. as a phenomenon, it bears the dual characteristics of randomness and regularity, and the more the Hurst indicator H deviates from 0.5, the more regularity appears in the time series, and vice versa.

Introduction. Hailing processes cause significant damage to agriculture, lead to damage to buildings, the death of animals and human casualties. To reduce the negative consequences of hail phenomena, work is being carried out to actively influence hail processes. In this work, an assessment of changes in the spectral and energy characteristics of hail is carried out during an active action according to the data of the hail-gauge network and radiosonding of the atmosphere. Materials and research methods. In the study of the ground characteristics of hail damage, we used the data obtained on the hail-gauge network during the Comprehensive hail experiment High Mountain Geophysical Institute (1983-1997), the data of the North Caucasian paramilitary service on active impacts on hydrometeorological processes (NC PS) about hailstorm for the period 2011-2012 and data from radiosonding of the atmosphere. Using the method of cluster analysis (statistical program SPSS), all processes with active impact (AI) and without active impact (91 processes in total) were divided from 2 to 5 clusters to identify the maximum inluence of atmospheric parameters on the characteristics of hail processes and further select the optimal number of clusters. Further, a correlation analysis was carried out to identify the relationship between the terrestrial characteristics of hail and atmospheric parameters. Multiple linear regression equations were constructed for the relationship between the ground characteristics of hail (average diameter, average surface density of kinetic energy, average concentration) and atmospheric parameters. The obtained equations can be used to analyze changes in the spectral and energy characteristics of hailstorms during active exposure. Research results and discussion. Analysis of data on the ground characteristics of hail processes with and without AI showed that the samples are not equal. More powerful hail processes most likely got into the processes with AI, therefore, for their correct comparison with the processes without AI, it is necessary to divide them into clusters. To carry out the cluster analysis, we used the characteristics of the atmosphere obtained from the data of radio sounding performed at the time instant closest to the time of the hail. The results of cluster analysis, confirmed by the T-test, showed that division into 2 clusters is optimal. From the characteristics of the parameters of the atmosphere in two clusters of clusters, it follows that 1 cluster includes the parameters of the atmosphere, leading to more powerful hail processes. To investigate the relationship between the parameters characterizing the state of the atmosphere and the terrestrial characteristics of hail, the dependent and independent variables were determined. In the processes assigned to cluster 1 and cluster 2, significant correlations of the ground characteristics of hail with atmospheric parameters were selected at significance levels < 0.05 and close to it. Multiple regression analysis was carried out using the selected characteristics and regression equations for the relationship between the ground characteristics of hail and atmospheric parameters for processes 1 and 2 of the cluster were constructed. The resulting equations were used to analyze changes in the spectral and energy characteristics of hail hits as a result of active exposure. Conclusions. The analysis of changes in the spectral and energy characteristics of hailstorms as a result of active exposure using the obtained regression equations for the relationship between the ground characteristics of hail and atmospheric parameters has been carried out. The analysis showed that changes in the ground characteristics of hail precipitation as a result of AI in the processes of cluster 1, which includes more powerful hail processes, does not lead to a signiicant change in the ground characteristics of hail. For processes of cluster 2 (weak processes), active impact leads to a decrease in the values of the ground characteristics of hail precipitation.

Introduction. Until now, despite the fact that reagents have long been used to control cloudy processes, issues related to the influence of an electric field on their ice-forming properties have not been fully studied. Studies carried out in this direction show that the growth of seed particles depends on the electric field strength, the charge of the crystallizing nucleus, and on the implementation of one or another growth mechanism [1]. The presence of an electric ield and a charge on the reagent particles in the atmosphere can affect the specific yield of ice-forming nuclei during work on active action on cloud systems. In this regard, studies related to the study of the effect of the electric ield strength on the speciic charge on the reagent particles formed during the sublimation of pyrotechnic compositions seem relevant and practically significant for determining the dosage of reagents when exposed to cloudy processes. Materials and methods of the research. This article presents the results of laboratory experiments on testing the equipment and methods for determining the effect of the electric field strength on the speciic charge on the reagent particles formed during the sublimation of pyrotechnic compositions. The method for measuring charged particles is based on the use of the delection of reagent particles in the electric field of a flat capacitor. The preliminary results obtained in the course of research made it possible to establish that the particles are charged during the sublimation of pyrotechnic compositions. pyrotechnic compositions used in anti-hail devices such as «Alazan-6» and «Alazan-9» [2, 3, 4] were considered as a working material for laboratory research. The results of the study and their discussion. The article presents the equipment, methodology and preliminary results of the study of the inluence of the electric ield strength on the speciic charge on the reagent particles formed during the sublimation of pyrotechnic compositions. Laboratory experiments were carried out on High-Mountain Geophysical Institute laboratory facilities. Conclusions. The experiments have shown that an increase in the negative speciic charge on the reagent particles slightly increases the speciic yield of ice-forming nuclei (by 20%) from the AD-1 pyrotechnic composition. With an electric field strength of -8,4 х 10^-4 V/m and a specific charge on the reagent particles of 3,0 х 10⁵ C/kg, the specific yield of ice-forming nuclei from the AD-1 pyrotechnic composition is 2.7 times higher than without an electric ield