We examine a general solution to the associated linear homogeneous ordinary differential equations of the collisional radiative model, and survey the behavior of eigenvalues of the characteristic matrix. It is proved that the real part of each eigenvalue is negative with the help of the Gershgorin’s theorem. Consequently, the differential equations describing the CR model are exponentially stable. We also examine absolute values of the real part of eigenvalues for the argon CR model. Dependence of real part of the eigenvalue to determine the relaxation time is examined with respect to electron temperature and density for argon plasma with its electron temperature 0.1−10eV, electron density 109−1014cm−3, and discharge pressure 1−760Torr, including the effect of atomic collisional quenching.
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