A pilot channel electron density diagnostic system and method based on a slotted spectrum

Abstract

The present application relates to the technical field of high-voltage insulation prediction, and particularly relates to a leader channel electron density diagnosis system and method based on a slotted spectrum, which comprises an impulse voltage generator, a high-voltage electrode, a condenser lens, a slit, a first collimating lens, a second collimating lens, a VPHG, a high-speed camera, an electro-optical converter, an opto-electric converter, an oscilloscope and a computer; the present application can accurately obtain the electron density in the leader channel, can effectively describe the evolution characteristics of the physical characteristic parameters in the leader channel in the long-gap discharge process, and can realize high-precision calculation of the electron density without measuring the temperature; the time resolution and the spatial resolution are improved, the high diagnosis precision is ensured, the monitoring capability of the electron density change in the leader discharge channel is enhanced, the change of the electron density can be effectively monitored in time and space by the method, and the physical mechanism and characteristics in the leader discharge process can be understood in depth.

Description

Technical Field

[0001] This invention relates to the field of high-voltage insulation prediction technology, and in particular to a pilot channel electron density diagnostic system and method based on slit spectroscopy. Background Technology

[0002] The study of long air gap discharge is fundamental to the design of external insulation and lightning protection in high-voltage power transmission and transformation projects. Leader discharge is the most critical discharge mode in the long gap discharge process. Accurately obtaining the microscopic physical parameters in the leader discharge channel, especially the evolution characteristics of electron density, is of great significance for a deeper understanding of the physical mechanism of leader discharge and helps to realize the refined design of external insulation in power transmission and transformation projects, providing a theoretical basis for lightning protection design. Although electron density is one of the most important physical parameters in the leader discharge channel, existing technologies have not yet provided an ideal measurement method. Since electron density is difficult to measure directly, although the early probe method can infer the electron density in the plasma channel, it is only applicable to low electron density scenarios. In recent years, laser Townsend scattering and interferometry techniques have been used to measure electron density, but the measurement accuracy is still low.

[0003] Currently, the Saha equation and Stark broadening method are mainly used to calculate electron density using emission spectra. The Saha equation requires the discharge channel to meet the local thermodynamic equilibrium (LTE) condition and assumes that the discharge channel is an optical thin layer. However, the temperature of the leader discharge channel is high (1500-6000K) and does not meet the LTE condition. The difficulty in obtaining the temperature limits the application of the Saha equation. In contrast, the Stark broadening method only needs to measure the full width at half maximum (FWHM) of the target spectral line and calculate the electron density through the broadening formula. It does not depend on the temperature of the discharge channel and therefore has a wider range of application potential. Although these existing methods have made progress, they still face challenges in terms of accuracy and applicability.

[0004] The purpose of this invention is to provide a leader channel electron density diagnostic system and method based on slit spectroscopy, which can realize spatiotemporal continuous diagnosis of electron density in the leader discharge channel, and help to deepen the explanation of the development mechanism of long gap leader discharge. Summary of the Invention

[0005] This invention provides a pilot channel electron density diagnostic system and method based on slit spectroscopy.

[0006] A pilot channel electron density diagnostic system based on slit spectroscopy includes an impulse voltage generator, a high-voltage electrode, a focusing lens, a slit, a first collimating lens, a second collimating lens, a VPHG, a high-speed camera, an electro-optic converter, a photoelectric converter, an oscilloscope, and a computer, wherein;

[0007] The impulse voltage generator is connected to the high-voltage electrode via an exposed copper wire. The high-voltage electrode is 1m above the ground. The impulse voltage generator produces a 250 / 2500μs standard operating impulse voltage waveform, creating a pilot discharge channel below the high-voltage electrode.

[0008] The focusing lens is positioned 1-2m away from the high-voltage electrode, and the beam emitted from the pilot discharge channel is focused by the focusing lens to the left focal point;

[0009] The slit is positioned at the left focal point of the condenser lens, and the slit is placed vertically with its center on the same horizontal line as the center of the condenser lens.

[0010] The first collimating lens is placed at a distance from the slit equal to its own focal length, and the light beam passing through the slit is emitted as a parallel light beam through the first collimating lens;

[0011] The VPHG is placed between the first collimating lens and the second collimating lens, and the distance from the vertical line of the center of the VPHG to the first collimating lens and the second collimating lens is the same. The parallel beam emitted by the first collimating lens is split by the VPHG, and the split beam exits the VPHG in parallel.

[0012] The second collimating lens (i.e., the high-speed camera lens) is used to converge the parallel beam of light emitted from the VPHG onto the CMOS plane of the high-speed camera for imaging.

[0013] The condenser lens, slit, first collimating lens, VPHG, second collimating lens and high-speed camera are placed on the same horizontal line;

[0014] The high-speed camera is used to record the raw spectrum;

[0015] The computer is connected to the high-speed camera via a network cable and is used to receive the time-domain continuous lead channel emission spectrum captured by the high-speed camera.

[0016] Optionally, the trigger signal transmission circuit of the high-speed camera includes:

[0017] The impulse voltage generator and the voltage divider are connected by a wire;

[0018] The voltage divider is connected to the oscilloscope via a coaxial cable;

[0019] The oscilloscope receives the voltage signal from the voltage divider, displays it, and stores the waveform.

[0020] The oscilloscope is set to trigger mode and trigger level. The trigger level is set to 500mV. When the voltage divider signal received by the oscilloscope reaches the trigger level, the oscilloscope outputs a trigger signal.

[0021] The trigger signal is converted into an optical signal by a photoelectric converter, and then converted into an electrical signal by an optical fiber connected to the photoelectric converter.

[0022] The high-speed camera receives a trigger signal converted by the photoelectric converter, which synchronously triggers the high-speed camera to capture the emission spectrum of the pilot channel.

[0023] A leader channel electron density diagnostic method based on slit spectroscopy, implemented by the aforementioned leader channel electron density diagnostic system based on slit spectroscopy, includes the following steps:

[0024] S1, obtain the time-continuous emission spectrum of the leader channel;

[0025] S2, based on the leader channel emission spectrum, the computer program identifies and locates the OI 777.4nm spectral line;

[0026] S3, extract the spectral data of the OI 777.4 nm spectral line at the height H position at time t, and fit the OI 777.4 nm atomic spectral line based on the Lorenz line shape function;

[0027] S4, calculate FWHM parameters based on the fitted OI 777.4nm spectral line;

[0028] S5. Based on the Stark broadening method for O atom spectral lines, calculate the leader channel electron density at height H at time t.

[0029] S6, update the calculation of the leader channel electron density at different times and different height positions, repeat S1-S5 until the leader channel enters the final jump stage and the electron density at that time is no longer calculated, and finally obtain the temporal and spatial distribution of the leader channel electron density in the development stage.

[0030] Optionally, S1 includes acquiring the raw emission spectrum of the pilot channel at the height H position at time t with a time resolution greater than 3 μs.

[0031] Optionally, S2 includes identifying and locating the OI 777.4 nm spectral line based on the acquired leader channel emission spectrum and the feature with the highest spectral line intensity.

[0032] Optionally, S3 includes:

[0033] Based on the identified and located OI 777.4nm spectral line, the channel portion in the leader channel that is vertical and has a spectral resolution greater than the resolution threshold is selected, and the number of spectral data points on both sides of the center wavelength of the OI 777.4nm spectral line is extracted in equal numbers.

[0034] The OI 777.4nm spectrum was fitted using the Lorenz function and is represented as follows:

[0035]

[0036] Where A is the area enclosed by the spectral line shape, ω is the FWHM parameter, and x c y is the center wavelength of the spectral line, y0 is the background value of the spectral line intensity, x is the wavelength value of the spectral line, and y is the intensity value of the spectral line.

[0037] Optionally, S4 includes:

[0038] Based on the fitted OI 777.4nm spectrum, the FWHM parameters of the spectrum were obtained, and the electron density of the leader channel was calculated.

[0039] The wavelengths corresponding to half the intensity of the OI777.4nm spectral line at its center wavelength are Δω1 and Δω2, respectively. The difference between these two wavelengths is the FWHM parameter of the OI777.4nm spectral line, expressed as:

[0040] FWHM=Δω2-Δω1.

[0041] Optionally, S5 includes:

[0042] The electron density of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line.

[0043] The Stark broadening of the OI atomic spectral line at a wavelength of 777.4 nm is calculated and expressed as:

[0044]

[0045] The electron density n of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line. e , represented as:

[0046]

[0047] Where ω(T) is the Stark broadening factor.

[0048] The beneficial effects of this invention are:

[0049] This invention employs a spectrometer design combining a high-speed camera and a VPH grating, which improves both spectral resolution and spectral dispersion, and significantly enhances temporal resolution. This enables continuous temporal diagnosis of the electron density in the leader discharge channel. By processing the acquired continuous temporal spectral data using a computer and fitting an OI 777.4nm spectral line diagram, the FWHM parameters of the spectral line are further calculated, thereby accurately obtaining the electron density within the leader channel. This effectively describes the evolution of physical characteristic parameters within the leader channel during long-gap discharge, and achieves high-precision electron density calculation without requiring temperature measurement.

[0050] This invention provides a diagnostic system with a simple and easy-to-build structure, high device replaceability and integration, making it particularly suitable for discharge observation in laboratories. The system does not rely on a pilot channel to meet LTE requirements and can be widely applied to various discharge experiments. Furthermore, while providing high spectral resolution, the system also improves temporal and spatial resolution, ensuring high diagnostic accuracy and enhancing the ability to monitor changes in electron density within the discharge channel. This method enables comprehensive and real-time monitoring of electron density changes, contributing to a deeper understanding of the physical mechanisms and characteristics of the discharge process. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a schematic diagram of a pilot channel electron density diagnostic system based on slit spectroscopy, according to an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram illustrating the calculation of FWHM parameters in the leader channel electron density diagnostic method based on slit spectroscopy according to an embodiment of the present invention.

[0054] Figure 3 This is a schematic diagram of the diagnostic method according to an embodiment of the present invention. Detailed Implementation

[0055] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0056] It should be noted that the use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0057] Generally, terms can be understood at least partly from their use in context. For example, depending at least partly on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in a singular sense, or a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood not necessarily to convey an exclusive set of factors, but rather, alternatively, depending at least partly on the context, to allow for the presence of other factors that are not necessarily explicitly described.

[0058] like Figure 1 As shown, a pilot channel electron density diagnostic system based on slit spectroscopy includes an impulse voltage generator, a high-voltage electrode, a condenser lens, a slit, a first collimating lens, a second collimating lens, a VPHG, a high-speed camera, an electro-optic converter, a photoelectric converter, an oscilloscope, and a computer, wherein;

[0059] The impulse voltage generator is connected to the high-voltage electrode via an exposed copper wire. The high-voltage electrode is about 1m above the ground. The impulse voltage generator produces a 250 / 2500μs standard operating impulse voltage waveform, creating a pilot discharge channel below the high-voltage electrode.

[0060] The condenser lens is placed 1-2m away from the high-voltage electrode. The beam emitted from the pilot discharge channel is focused by the condenser lens to the left focal point so as to generate a uniform beam and reduce the generation of stray light.

[0061] The slit is placed at the left focal point of the condenser lens, the slit is placed vertically, and the center of the slit is on the same horizontal line as the center of the condenser lens;

[0062] The first collimating lens is placed at a distance from the slit equal to its own focal length, and the light beam passing through the slit is emitted as a parallel light beam through the first collimating lens.

[0063] The VPHG is placed between the first collimating lens and the second collimating lens, and the distance from the center vertical line of the VPHG to the two collimating lenses is the same. The parallel beam emitted by the first collimating lens is split by the VPHG, and the split beam exits the VPHG in parallel.

[0064] The second collimating lens, also known as the high-speed camera lens, is used to converge the parallel beam of light emitted from the VPHG onto the CMOS plane of the high-speed camera for imaging.

[0065] The condenser lens, slit, first collimating lens, VPHG, second collimating lens, and high-speed camera are placed on the same horizontal line;

[0066] High-speed cameras are used to record the raw spectrum;

[0067] The computer is connected to the high-speed camera via a network cable to receive the time-domain continuous lead channel emission spectrum captured by the high-speed camera. The high-speed camera needs a trigger signal to complete the spectral capture.

[0068] The following is the trigger signal transmission circuit for a high-speed camera:

[0069] The impulse voltage generator and the voltage divider are connected by a wire;

[0070] The voltage divider is connected to the oscilloscope via a coaxial cable;

[0071] The oscilloscope receives the voltage signal from the voltage divider, displays it, and stores the waveform.

[0072] The oscilloscope is set to trigger mode and trigger level. The trigger level is set to 500mV. When the voltage divider voltage signal received by the oscilloscope reaches the trigger level, the oscilloscope outputs a trigger signal.

[0073] The trigger signal is converted into an optical signal by a photoelectric converter, and then converted into an electrical signal by an optical fiber connected to the photoelectric converter.

[0074] The high-speed camera receives a trigger signal converted by the photoelectric converter, which synchronously triggers the high-speed camera to capture the emission spectrum of the pilot channel.

[0075] The condenser lens is a biconvex lens with a light-transmitting aperture of 10cm and a focal length of 0.5m, and the distance between the pilot discharge channel and the condenser lens is greater than 0.5m.

[0076] The slit is placed to the left of the condenser lens, 0.5m away from the central axis of the condenser lens.

[0077] The first collimating lens is a convex lens with a light-transmitting aperture of 10cm and a focal length of 10cm, and its distance from the slit is 1.0m.

[0078] The VPHG is positioned between the first and second collimating lenses, at a distance of 0.3m from both lenses.

[0079] The second collimating lens uses an objective lens adapted for high-speed cameras, with a focal length range of 50-100mm and an aperture of f / 1.2.

[0080] The high-speed camera was set to a shooting frequency of 300,000 frames / s, an exposure time of 3 μs, and a spectral response range of 400-1000 nm to acquire a temporally continuous leader channel emission spectrum.

[0081] like Figures 2-3 As shown, a leader channel electron density diagnostic method based on slit spectroscopy, implemented by the aforementioned leader channel electron density diagnostic system based on slit spectroscopy, includes the following steps:

[0082] S1, obtain the time-continuous raw emission spectrum of the leader channel;

[0083] S2, based on the leader channel emission spectrum, the computer program identifies and locates the OI 777.4nm spectral line;

[0084] S3, extract the spectral data of the OI 777.4 nm spectral line at the height H position at time t, and fit the OI 777.4 nm atomic spectral line based on the Lorenz line shape function;

[0085] S4, calculate FWHM parameters based on the fitted OI 777.4nm spectral line;

[0086] S5. Based on the Stark broadening method for O atom spectral lines, calculate the leader channel electron density at height H at time t.

[0087] S6, update the calculation of the leader channel electron density at different times and different height positions, repeat steps S1-S5 until the leader channel enters the final jump stage and the electron density at that time is no longer calculated, and finally obtain the temporal and spatial distribution of the leader channel electron density in the development stage.

[0088] Obtain the time-continuous raw emission spectrum of the leader channel, including:

[0089] Under certain atmospheric pressure and humidity conditions, the original emission spectrum of the leader channel, which is continuous in the time domain, is obtained through the aforementioned leader channel electron density diagnostic system. The diagnostic system obtains the original emission spectrum of the leader channel at the height H at time t with a time resolution better than 3 μs.

[0090] Based on the leader channel emission spectrum, the computer program identified and located the OI 777.4 nm spectral line, including:

[0091] Based on the original emission spectrum of the acquired leader channel, the spectral line at OI 777.4 nm was identified and located according to the feature with the highest spectral line intensity.

[0092] The spectral data of the OI 777.4 nm atomic line at height H at time t were extracted, and the OI 777.4 nm atomic line was fitted based on the Lorenz line shape function, including:

[0093] Based on the identified and located OI 777.4nm spectral line, the channel portion of the leader channel that is vertical and has a spectral resolution greater than the resolution threshold was selected. An equal number of spectral data points were extracted to the left and right of the center wavelength of the OI 777.4nm spectral line, and the OI 777.4nm spectral line was fitted using the Lorenz function.

[0094]

[0095] Where A is the area enclosed by the spectral line shape; ω is the FWHM parameter; x c y is the center wavelength of the spectral line; y0 is the background value of the spectral line intensity; x is the wavelength value of the spectral line; y is the intensity value of the spectral line.

[0096] The FWHM parameters were calculated based on the fitted OI 777.4 nm spectral line, including:

[0097] Based on the fitted OI 777.4 nm spectrum, the electron density of the leader channel can be calculated by obtaining the FWHM parameters of the spectrum. The wavelengths corresponding to half the intensity of the spectral line at the center wavelength of the OI 777.4 nm spectrum are Δω1 and Δω2, respectively. The difference between the two wavelengths is the FWHM parameter of the OI 777.4 nm spectrum, i.e.:

[0098] FWHM = Δω2 - Δω1;

[0099] The leader channel electron density at height H at time t is calculated using the Stark broadening method based on O atom spectral lines, including:

[0100] The electron density of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line.

[0101] Stark broadening of the OI atomic spectral line at a wavelength of 777.4 nm was calculated.

[0102]

[0103] The electron density n of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line. e :

[0104]

[0105] Where ω(T) is the Stark broadening factor, which is a function of temperature T. Since the temperature of the pilot channel is basically maintained in the range of 3000-6000K, ω(T) can be regarded as a constant value, which is 0.00228nm.

[0106] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0107] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A pilot channel electron density diagnostic system based on slit spectroscopy, characterized in that, It includes an impulse voltage generator, high-voltage electrodes, a condenser lens, a slit, a first collimating lens, a second collimating lens, a VPHG, a high-speed camera, an electro-optical converter, a photoelectric converter, an oscilloscope, and a computer, among which; The impulse voltage generator is connected to the high-voltage electrode via an exposed copper wire. The high-voltage electrode is 1m above the ground. The impulse voltage generator produces a 250 / 2500μs standard operating impulse voltage waveform, creating a pilot discharge channel below the high-voltage electrode. The focusing lens is positioned 1-2m away from the high-voltage electrode, and the beam emitted from the pilot discharge channel is focused by the focusing lens to the left focal point; The slit is positioned at the left focal point of the condenser lens, and the slit is placed vertically with its center on the same horizontal line as the center of the condenser lens. The first collimating lens is placed at a distance from the slit equal to its own focal length, and the light beam passing through the slit is emitted as a parallel light beam through the first collimating lens; The VPHG is placed between the first collimating lens and the second collimating lens, and the distance from the vertical line of the center of the VPHG to the first collimating lens and the second collimating lens is the same. The parallel beam emitted by the first collimating lens is split by the VPHG, and the split beam exits the VPHG in parallel. The second collimating lens is used to converge the parallel beam of light emitted from the VPHG onto the CMOS plane of the high-speed camera for imaging. The condenser lens, slit, first collimating lens, VPHG, second collimating lens and high-speed camera are placed on the same horizontal line; The high-speed camera is used to record the raw spectrum; The computer is connected to the high-speed camera via a network cable and is used to receive the time-domain continuous lead channel emission spectrum captured by the high-speed camera.

2. The pilot channel electron density diagnostic system based on slit spectroscopy according to claim 1, characterized in that, The trigger signal transmission circuit of the high-speed camera includes: The impulse voltage generator and the voltage divider are connected by a wire; The voltage divider is connected to the oscilloscope via a coaxial cable; The oscilloscope receives the voltage signal from the voltage divider, displays it, and stores the waveform. The oscilloscope is set to trigger mode and trigger level. The trigger level is set to 500mV. When the voltage divider voltage signal received by the oscilloscope reaches the trigger level, the oscilloscope outputs a trigger signal. The trigger signal is converted into an optical signal by a photoelectric converter, and then converted into an electrical signal by an optical fiber connected to the photoelectric converter. The high-speed camera receives a trigger signal converted by the photoelectric converter, which synchronously triggers the high-speed camera to capture the emission spectrum of the pilot channel.

3. A method for diagnosing leader channel electron density based on slit spectroscopy, implemented by the leader channel electron density diagnostic system based on slit spectroscopy as described in any one of claims 1-2, characterized in that, Includes the following steps: S1, obtain the time-continuous emission spectrum of the leader channel; S2, based on the leader channel emission spectrum, the computer program identifies and locates the OI 777.4nm spectral line; S3, extract the spectral data of the OI 777.4 nm spectral line at the height H position at time t, and fit the OI 777.4 nm atomic spectral line based on the Lorenz line shape function; S4, calculate FWHM parameters based on the fitted OI 777.4nm spectral line; S5. Based on the Stark broadening method for O atom spectral lines, calculate the leader channel electron density at height H at time t. S6, update the calculation of the leader channel electron density at different times and different height positions, repeat S1-S5 until the leader channel enters the final jump stage and the electron density at that time is no longer calculated, and finally obtain the temporal and spatial distribution of the leader channel electron density in the development stage.

4. The method for diagnosing the electron density of a leader channel based on slit spectroscopy according to claim 3, characterized in that, S1 includes acquiring the raw emission spectrum of the pilot channel at the height H position at time t with a time resolution of more than 3 μs.

5. The method for diagnosing the electron density of a leader channel based on slit spectroscopy according to claim 4, characterized in that, S2 includes identifying and locating the OI 777.4nm spectral line based on the obtained leader channel emission spectrum and the feature with the highest spectral line intensity.

6. The method for diagnosing the electron density of a leader channel based on slit spectroscopy according to claim 5, characterized in that, S3 includes: Based on the identified and located OI 777.4nm spectral line, the channel portion in the leader channel that is vertical and has a spectral resolution greater than the resolution threshold is selected, and the number of spectral data points on both sides of the center wavelength of the OI 777.4nm spectral line is extracted in equal numbers. The OI 777.4nm spectrum was fitted using the Lorenz function and is represented as follows: Where A is the area enclosed by the spectral line shape, ω is the FWHM parameter, and x c y is the center wavelength of the spectral line, y0 is the background value of the spectral line intensity, x is the wavelength value of the spectral line, and y is the intensity value of the spectral line.

7. The method for diagnosing the electron density of a leader channel based on slit spectroscopy according to claim 6, characterized in that, S4 includes: Based on the fitted OI 777.4nm spectrum, the FWHM parameters of the spectrum were obtained, and the electron density of the leader channel was calculated. The wavelengths corresponding to half the intensity of the OI777.4nm spectral line at its center wavelength are Δω1 and Δω2, respectively. The difference between these two wavelengths is the FWHM parameter of the OI777.4nm spectral line, expressed as: FWHM=Δω2-Δω1.

8. The method for diagnosing the electron density of a leader channel based on slit spectroscopy according to claim 7, characterized in that, S5 includes: The electron density of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line. The Stark broadening of the OI atomic spectral line at a wavelength of 777.4 nm is calculated and expressed as: The electron density n of the leader channel was calculated based on the FWHM parameters of the OI 777.4 nm spectral line. e , is represented as: Where ω(T) is the Stark broadening factor.

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