Investigation of the Electron Coefficients of (Ar, He, N 2 , O 2 ) Gases in the Ionosphere

: In this study, the electron coefficients; Mean energy < ε > , Mobility (μN) and Drift velocity (Vd) of different gases Ar, He, N 2 and O 2 in the ionosphere have been calculated using BOLSIG+ program to check the solution results of Boltzmann equation results, and effect of reduced electric field (E/N) on electronic coefficients. The electric field has been specified in the limited range 1-100 Td. The gases were in the ionosphere layer at an altitude frame 50-2000 km. Furthermore, the mean energy and drift velocity steadily increased with increases in the electric field, while mobility was reduced. It turns out that there is a significant and obvious decrease in mobility as a result of inelastic collisions and in addition little energy gained by the reduced electric field. A clear mathematical model was obtained to find out the electronic coefficient values without a simulation program (BOLSIG +). In addition, this model shows a strong correlation between the current work and the electronic transaction values calculated through the BOLSIG+ program.


Introduction:
Plasma is a quasi-neutral gas composed of positively and negatively charged particles that collide or ionize with neutral particles [1][2] .There are different applications of plasma such as solar cells, optical reagents, biomedical, optoelectronic devices and Ozone generation by micro plasma [3][4][5][6] .The ionosphere layer in the upper atmosphere is a primary source of a real ionization neutral particles plasma [7][8] .The ionosphere is made up of different layers due to the different wavelengths in the sun's ultraviolet spectrum 9 .During the day, the solar flux and electron density increase in the ionosphere.This allows the diffusion of higher frequencies for long distances, but at night, when the solar flux is low, radio energy is absorbed very little and lower frequencies are propagated stronger 10 .The word "Discharge" refers to any passage of electric field within an ionized gas and emits energy in the form of light 11 .Emphasis was placed on how O2 in the mixture would affect the resolved transport data and derive the transport properties that should be incorporated into the flow and discharge fluid model by considering the range (E/n): 0.01-1000 Td 12 .Electron transfer properties of a helium-xenon mixture at a reduced electric field E/N ∼15 Td were calculated 13 .The kinetic properties of electron drift in argon at reduced electric fields E/N = (1-100) Td were investigated 14 .BOLSIG+ was used to calculate the electronic coefficients and collapse voltage gradient for the environment of the planetary System, as well as solve the Boltzmann equation 15 .The ionosphere's layers differ due to different wavelengths in the sun's ultraviolet spectrum 9 .Earth's ionosphere is made up of three parts: D (50-90) km, E (90-150) km, and F (150-500 km) 12 .During day time, The F layer is divided into D regions (50-90) km, E region (90-150) km, and F region (150-500) km 16 .During the day, the F layer is frequently divided into sub-layers known as F1 (150-250) km and F2 (250-500) km, which are then combined into a single layer at night.The F region is thicker than the E region and more ionized, with maximum electron density in the 200-400 km range.The atomic species O+ and O predominate in this region 17 .
At an altitude of 60-300 km, ionization results from the absorption of solar energy by neutral gases, the most important of which is atomic oxygen (O, ionized to O+).Hydrogen (H, to H+) and nitrogen monoxide (NO, to NO+) are two other gases that can be ionized.As altitude decreases towards the Earth's surface, solar radiation encounters an increasing number of neutral atmospheric particles, resulting in increased absorption while decreasing radiation intensity.This results in a layer of maximum ionization, which typically occurs at altitudes between 200 and 400 km 18 .
BOLSIG + is an excellent application for solving the Boltzmann equation for electrons in a gas with low ionization in regular electric fields, which is seen in a majority of cold plasma when the energy distribution of electrons is calculated by an equilibrium between acceleration in the electric field, momentum, and power loss in collisions of gas molecules.BOLSIG+ solves the electron Boltzmann equation for field equilibrium with a homogeneous electric field and density, no boundaries, and a steady state 19 .The aim of this paper is to estimate the mathematical model that aptly depicts the activity of electronic coefficients by varying the reduced electric field.

Calculation and Methods: Boltzmann Equation
Equation. 1 explains the characteristics of ions in gases by the phase space functional form f (r, c, t) 20- 21 .
Where e, m, t, r, c are the electron's charge, electron's mass, time, position and velocity coordinate respectively.The electric field is assumed spatially homogeneous with magnitude E. J(f, f0) indicating the change rate for f because they collide with uncharged particles only 12 .

Transport coefficients
It is the process of transporting charged particles in a gas.The mathematical expressions used for calculating the output parameters are BOLSIG +, and they are somewhat clear with some additional brief explanations.As well as getting to know the mathematical symbols.It should be noted that all transfer coefficients are multiplied or divided by the product of BOLSIG + with N (total gas number density).This coefficient resulted in a reduction independent of N. All units are with SI units 20 .

Mean energy
The mean energy of electrons is field-dependent, and the value of the energy of the "mean" electron corresponds to energy gains compensated for by losses 22 .
Where: : Electron mean energy at eV.

Mobility *N
It indicates the velocity of the electron in the plasma and depends on the velocity of drift and decreases with the increase in collisions due to the electron losing its energy upon collision 23 .

Drift velocity
Drift velocity Vd is the greatest electronic transport parameter used to describe the behavior of electrons in gas, this parameter is determined by the type of gas and the value of the electric field reducer E / N 21 , which is an important parameter in the swarm, as it is useful for controlling energy and used as well to describe the conductivity of a weakly ionized gas 24 .
Vd = μ E 4 Where: E: Electric field at Td

Influence of reduced electric field on mean energy
From Fig. 1, (E/N) affects obviously on < ε > of electrons for different gases He, N2, O2 and Ar, because the reduced electric field affects the crosssectional area, there is an increase in mean energy with an increase in E/N, and as a result, the rate of elastic and inelastic collisions increases, resulting in an increase in E/N 18 .In other words, the mean energy increases as the reduced electric field increases due to elastic collisions and electrons gaining energy due to the electric field.We can also see from the figure that the He element has the highest mean energy value due to the effect of the higher elastic collisions, whereas this effect is less for N element, as the mean energy values are less than possible.According to Fig. 2, a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) indicates the general behavior of the mean energy for He, N2 and O2 gases in the Earth's ionosphere with increasing electric field (E/N) This relationship is described by Eq. 6 with values of constants and the percentage of the highest match mentioned in Table .2:

Mean energy modeling
) 5 6  Influence of reduced electric field on mobility Fig. 3, shows that the electron mobility is inversely proportional to the electric field.We observed that the mobility is low at 0-10 Td, due to the energy loss of electrons in the elastic collisions, but the decrease in mobility from 10-100 Td, is very negligible due to the inelastic collisions 25 .

Mobility modeling
According to Fig. 3, a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) indicates the general behavior of the electron mobility for Ar, N2 and O2 gases in the Earth's ionosphere with increasing electric field (E/N).This relationship is described by Eq. 7 with values of constants and percentage of highest match mentioned in Table .3: According to Fig. 3, a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) indicates the general behavior of the electron mobility for He gas in the Earth's ionosphere with increasing electric field (E/N).
This relationship is described by Eq. 8, with values of constants and percentage of highest match mentioned in Table .4:

Influence of electric field on drift velocity
The drift velocities increase as a function of E/N, and at lower E/N, the increase is linear.It is also observed that the drift velocity is lower because the elastic collision cross section is large.Because energy depends on the cross-sectional area of the elastic collision, this effect is also caused by the loss of energy caused by ionization and excitement in gases 26 .Fig. 5, shows the increasing drift velocity as the electric field increases, where we note that the drift velocity is high at 5 and 20 Td, which is due to elastic collisions, but the drift velocity from 20-100 Td, the increase is progressively due to the inelastic collision.In this figure, we notice that the drift velocity values increase significantly by increasing in (E/N), due to the high impact of elastic collisions as a result of electrons gaining energy.We observed that the He element has the highest drift velocity value at 45-100 Td due to the effect of higher elastic collisions, whereas this effect is less for Ar because the drift velocity values are less than possible.

Drift velocity modeling
According to Fig. 6, a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) indicates the general behavior of the electron mobility for Ar, N2, O2 gases in the Earth's ionosphere with an increasing electric field (E/N).This relationship is described by Eq. 9, with values of constants and the percentage of the highest match mentioned in Table .5: Table 5. Show the relationship between constants I1, I2, Q0 and R and the drift velocity (Vd) for Ar, N2, O2 and He gases, where represented by Eq. 9.

Conclusion:
This study has proved the value of electronic coefficients shifted due to the change in crosssectional area as the electric field increased.There was a positive relationship between (E/N) and the electronic transport coefficients (mean energy and drift velocity) for Ar, He, N2 and O2 gases.A negative correlation between (E/N) and electrons' mobility was explained for all gases.The correlation between drift velocity and the reduced electric field is linear.Logistic and polynomial functions in this research showed a higher matching than other functions.

Figure 1 .
Figure 1.The relationship between the mean energy and increase electric field (E/N) for different gases He, N2, O2 and Ar in Earth's ionosphere.

Fig. 2 ,
Fig. 2, depicts a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) that indicates the general behavior of the mean energy for Ar gas in the Earth's ionosphere with increasing electric field (E/N).This relationship is described by Equation 5 with values of the constants and percentage of highest match mentioned in Table.1: Fig. 2, depicts a high fitting/matching ratio between the original data (utilizing Bolsig+ program) and our simulation model (utilizing Origin program) that indicates the general behavior of the mean energy for Ar gas in the Earth's ionosphere with increasing electric field (E/N).This relationship is described by Equation 5 with values of the constants and percentage of highest match mentioned in Table.1:< ε >= Z 1 e ((−E N ⁄ ) t 1 ) ⁄ + Z 2 e ((−E N ⁄ ) t 1 ) ⁄ + I 0 5 Where, E/N= (1-100) Td

Figure 3 .
Figure 3.The relationship between the electron mobility and increase electric field (E/N) for different gases He, N2, O2 and Ar in Earth's ionosphere.

Figure 5 .
Figure 5.The relationship between the drift velocity and increase electric field (E/N) for different gases He, N2, O2 and Ar in Earth's ionosphere.