Plasma diagnostic techniques have been employed to determine particle densities and temperatures in a low-pressure argon plasma jet generated by a cascade arc. These measurements allow characterization of the extent to which the plasma jet deviates from thermodynamic equilibrium and provide a basis for predicting how reactive gases will interact with the excited and ionized species in the plasma jet. It was found that the distribution of atomic states in the plasma jet is not adequately described by either local thermodynamic equilibrium (LTE) or partial local thermodynamic equilibrium (pLTE), and the jet was optically thick for 3p-->4s transitions across the jet radius. Excited argon neutrals outnumber ions by a large ratio, and dominate subsequent dissociation/excitation phenomena. The rate of methane destruction in the plasma jet shows that estimates for particle densities, temperature, and jet velocity are self-consistent.