Swarm of Electron Simulation in Carbon Dioxide Parameters for Intermediate E/N Values

The rotational excitation and transfer of low-energy electrons cross-sections in carbon dioxide have been obtained to compare in the theoretical & experimental values of the kinetic and diffusion coefficient. the transport coefficients theoretical values of were gained by calculating the delicate electron energy distribution functions using a putative elastic and inelastic cross-sections combination. The values for movement, drift speed, average electron energy, and power noticeable with experimental data were compared. Alteration were made to the default cross sections until obtaining good agreement. Transport coefficients were calculated for values between (6 × 10−17 - 6×10−15 )V cm2 with energy zoning 0.035 eV at 300k° temperature.


Introduction
Information in details of the parameters transportation that organize the gas discharges development were necessary for optimum operating requirements for the CO 2 laser. Several researches were made to find out the leakage parameter in uncontaminated gases. The importance of these factors lies in providing a connection among the cross-sections of the electronic gas conflict, the decomposition and degradation observable fact. Swarm factors are calculated in a straight line from a the impact cross-sections utilizing Boltzmann numerical 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020) IOP Conf. Series: Materials Science and Engineering 928 (2020) 072083 IOP Publishing doi:10.1088/1757-899X/928/7/072083 2 transport solution. calculations results were the allocation of the electron energy, that was a vital characteristic but hard to calculate empirically [1].
The electron swarm parameter for E/N drop where E denotes the applied electric field (V/cm) and N denotes the density number of the total gas (cm -3 ) minutes until the start of ionization (10 -15 ) Vcm 2 .It was previously considered utilizing Boltzmann transport factor to be compared with the experimental values [2]. The work's aim is calculating the swarm of electron parameters in carbon dioxide and match the obtained values with investigational records utilizing an appropriately selected set of cross sections. [3,4].

Numerical solution
By consider an electron's swarm drift during a gas subjected to a temperature (T) in the arrangement of the electric filed influential (E) at (V/ Centimetre).
Stead-state distribution function is then given by the solution of the Boltzmann equation [5,6 and7]: (1) where: represent f (r, ν, t) adjusts with point in time at v set values, (r ) while (ν) stands for the charged particles velocity, (a) represents charged particle acceleration, Fj being the velocity sharing occupation of the unbiased types (j), ν rj =|ν-V j | |represents the charge particles' relative taking into account the unbiased gas types (j) , V j represents neutral types velocity j ,σ j (,ν rj ) represents the degree of difference charged particles microscopic cross-section that interacts through V j , and d=sindd represents the robust angularity , Where  and  are the polar and azimuthally angles respectively.
The allocation purpose of electrons f(r,ν,t ) was approximated by f(ν) because it was considered the electric filed E, was not depend on the space and time and furthermore the interactions of electrons were specially  [5,8,9 and 10]. Whether the velocity dependence distribution function is represented by the legendry sequence growth where: (2)

Calculation procedures and analysis
The velocity distribution function for electrons diffusing in the gas temperature in (T) at the uniform electric filed controlling, (E) has been performed during the explanation of the numerical Boltzmann transport equation [11,12]. According to the above, the detailed analysis of transfer coefficients It was calculated for comparison with experimental data and included the velocity of drift Vd (cm / s), the characteristic energy  k (eV) the electron energy average <ϵ> (eV) the electron mobility μ (cm 2 /V. sec) and the diffusion coefficient D (cm 2 /sec). These parameters are [12 and 13]: where: with: finally: with (8) where is the energy rate obtained by the dc filed electrons, n o represents the electron number density (cm -3 ), n k is electrons number Each unit has a volume, per unit of energy in space ( k+1 + k ), m denotes the mass of the electron (gm), ϵ k is the energy of electron (eV), f k is the regularized distribution function,   refers to the energy zoning (eV), q s is the types concentration N s , σ s It is the elastic dispersion cross-section species (s), <ϵ> is the average energy electron (eV ), σ represents the cross section.

Numerical results and discussion
Equation (1) is solved numerically in excess of a rage of E/N for carbon dioxide gas using the Finite-Difference Method and through the equations between 3 to 8 were obtaining the swarm parameters [12], which could be simply evaluated to the earlier authors. Figure-1 exhibits the computed electron energy allocation task, the electron energy allocation was powerfully affected by parameter change E/ N [14].      Figure 5-the relationship between the electron energy average vs. the ratio of the applied electric field function to the total gas number density for CO 2 gas.