The role of neutral gas molecules in the Scrape-off Layer (SOL) region of tokamak plasma is important as it is expected to modify the plasma turbulence. Two-dimensional model has been used that consists of electron continuity, molecular ion continuity, quasi-neutrality, electron energy, and neutral molecular gas continuity equations in the presence of electron impact molecular ionizations and other non-ionizing collisions. The growth rate obtained from these equations has been presented using linear theory. It is observed that the growth rate increases with the neutral gas ionization coefficients. The nonlinear equations are solved numerically in the presence and absence of the neutral gas molecules. Radial profiles of plasma density, electron temperature, and electric field have been obtained. It is found that the neutral gas reduces electric fields. More significant reduction of the poloidal electric field has been found by the neutral gas. Time series obtained from the numerical data has been analyzed. A strong decrease in fluctuation of the plasma density, electron temperature, and potential has been found at the outer region the SOL plasma in the presence of the gas molecules.

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