A detailed nonstationary kinetic model of the Penning plasma laser based on neon in mixture He-Ne-Ar-H2 (λ = 585.3 nm) considering the influence of nitrogen admixtures has been developed. The model describes adequately the experimental results on e-beam and nuclear pumping of He-Ne-Ar, Ne-H2, and He-Ne-Ar-H2 mixtures obtained by different experimental groups and allows one to optimize the laser with a high degree of reliability.