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A two-dimensional and stationary magnetohydrodynamic model of a plasma spray torch operated with argon is developed to predict the plasma properties in a steady operating mode. The model couples a submodel of a refractory cathode and its non-equilibrium boundary layer to a submodel of the plasma in local thermodynamic equilibrium in a self-consistent manner. The Navier–Stokes equations for a laminar and compressible flow are solved in terms of low and high Mach number numerical approaches. The results show that the Mach number can reach values close to one. Simulations are performed for electric currents of 600 A and 800 A, and gas flow rates of 40, 60, and 80 NLPM. The plasma parameters obtained by the two approaches differ, and the differences become more pronounced for higher currents and gas flow rates. The arc voltage, the electric power, and the thermal efficiency from both the low and high Mach number models of the plasma agree well with experimental findings for a current of 600 A and a flow rate of 40 NLPM. For higher currents and gas flow rates, the results of the low and high Mach number models gradually differ and underline the greater appropriateness of the high Mach number model.

The heat convection generated by micro filaments of a self-organized non-thermal atmospheric pressure plasma jet in Ar is characterized by employing laser schlieren deflectometry (LSD). It is demonstrated as a proof of principle, that the spatial and temporal changes of the refractive index n in the optical beam path related to the neutral gas temperature of the plasma jet can be monitored and evaluated simultaneously. The refraction of a laser beam in a high gradient field of n(r) with cylindrical symmetry is given for a general real refraction index profile. However, the usually applied Abel approach represents an ill-posed problem and in particular for this plasma configuration. A simple analytical model is proposed in order to minimize the statistical error. Based on that, the temperature profile, specifically the absolute temperature in the filament core, the FWHM, and the frequencies of the collective filament dynamics are obtained for non-stationary conditions. For a gas temperature of 700 K inside the filament, the presented model predicts maximum deflection angles of the laser beam of 0.3 mrad which is in accordance to the experimental results obtained with LSD. Furthermore, the experimentally obtained FWHM of the temperature profile produced by the filament at the end of capillary is (1.5 ± 0.2) mm, which is about 10 times wider than the visual radius of the filament. The obtained maximum temperature in the effluent is (450 ± 30) K and is in consistence with results of other techniques. The study demonstrates that LSD represents a useful low-cost method for monitoring the spatiotemporal behaviour of microdischarges and allows to uncover their dynamic characteristics, e.g., the temperature profile even for challenging diagnostic conditions such as moving thin discharge filaments. The method is not restricted to the miniaturized and self-organized plasma studied here. Instead, it can be readily applied to other configurations that produce measurable gradients of refractive index by local gas heating and opens new diagnostics prospects particularly for microplasmas.

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