What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?

It is shown that Steenbeck’s principle of minimum power, or voltage, for discharges with fixed current is not a corollary of the principle of minimum entropy production, in contrast to what is frequently assumed; besides, the latter principle itself does not provide a reasonable approximation in gas discharge physics. Similarly, Steenbeck’s principle is not a corollary of mathematical models of gas discharges. Hence, this principle contradicts the mathematical models. A methodically correct evaluation of the error caused by the use of Steenbeck’s principle requires a comparison of a solution obtained with the use of this principle with an exact solution to the same problem, rather than with experimental results or results deemed reasonable from the point of view of common sense. Such a comparison is performed for two examples from the theory of a cylindrical arc column. The examples show that the error incurred by the usage of Steenbeck’s principle is uncontrollable and may be unacceptably high.info:eu-repo/semantics/publishedVersio

Reply to the Comment on ‘What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?’

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Visualising gas heating from an RF plasma loudspeaker

In an electro-acoustic transduction mechanism, an ac modulation (here in the audio frequency range) of the electric field in an atmospheric pressure air plasma gives rise to a rapid increase in the gas temperature and dimensions of the gas volume. As in natural lightning, the rapid expansion in the ionised column though the air produces external pressure variations at the modulation frequency.  \ud Spatial and temporal measurement of the gas temperature can identify the nature of the thermal expansion and provide a direct approach to understanding its relationship to the sound pressure wave that is generated. However, the established method through spectroscopic measurement of rotational line emission from nitrogen molecules is limited to the main current channel where relaxation and subsequent optical emission of the excited nitrogen molecules occurs. The wider picture is revealed through the use of the Schlieren method where the refractive index gradients caused by gas heating in the plasma are imaged

Simulation of pre-breakdown discharges in high-pressure air: II. Effect of surface protrusions

Analysis of deviations from the similarity law, observed at high and very high pressures in experiments on discharge ignition and breakdown in corona-like configurations, can serve as a useful, albeit inevitably indirect, source of information about microprotrusions on the surface of the electrodes. In this work, such analysis was performed by means of 2D numerical modelling. Conical or cylindrical protrusions on the surface of the inner electrode were studied and the kinetic scheme includes the electrons, one species of positive ions, and negative ions O− 2 , O−, and O− 3 . It is shown that the deviations from the similarity law, observed in the experiment, may indeed be attributed to enhanced ionization of air molecules in regions of amplified electric field near the microprotrusions. A qualitative agreement with the experiment in all the cases is achieved for protrusion heights of the order of 50 µm. Such values may appear rather high, however there is no other explanation in sight at present. The enhancement of the field electron emission from the surface of the negative electrode due to the amplification of the electric field on the microprotrusion was estimated and found insignificant in the range of values of the protrusion aspect ratio where the enhanced ionization in the gas phase is already appreciable.info:eu-repo/semantics/publishedVersio

Modelling interaction of multispecies plasmas with thermionic cathodes

The model of the near-cathode plasma, developed previously for the case of a single-species plasma-producing gas, is generalized for the case of multiple plasma-producing species. Results are presented of calculation of a diffuse mode of current transfer to tungsten cathodes in a mercury plasma with an addition of sodium. It is found that the presence of 1% of sodium results in a considerable expansion of the range of stability of the diffuse mode.info:eu-repo/semantics/publishedVersio

Modelling current transfer to cathodes in metal halide plasmas

This work is concerned with investigation of the main features of current transfer to cathodes under conditions characteristic of metal halide (MH) lamps. It is found that the presence of MHs in the gas phase results in a small decrease of the cathode surface temperature and of the near-cathode voltage drop in the diffuse mode of current transfer; the range of stability of the diffuse mode expands. Effects caused by a variation of the work function of the cathode surface owing to formation of a monolayer of alkali metal atoms on the surface are studied for particular cases where the monolayer is composed of sodium or caesium. It is found that the formation of the sodium monolayer affects the diffuse mode of current transfer only moderately and in the same direction that the presence of metal atoms in the gas phase affects it. Formation of the caesium monolayer produces a dramatic effect: the cathode surface temperature decreases very strongly, the diffuse-mode current–voltage characteristic becomes N–S-shaped.info:eu-repo/semantics/publishedVersio

Comment on “Electric field measurements under DC corona discharges in ambient air by electric field induced second harmonic generation” [Appl. Phys. Lett. 115, 244101 (2019)]

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Simple computation of ignition voltage of self-sustaining gas discharges

A robust, fast, and accurate numerical method is proposed for finding the voltage of the ignition of DC self-sustaining gas discharges in a wide range of conditions. The method is based on physical grounds and builds up from the idea that the ignition of a self-sustaining gas discharge should be associated with a resonance that would occur in a non-self-sustained discharge in the same electrode configuration. Examples of the application of the method are shown for various configurations: parallel-plate discharge, coaxial and wire-to-plane corona discharges, and a discharge along a dielectric surface. The results conform to the conventional Townsend breakdown condition for the parallel-plate configuration and are in good agreement with existing experimental data for the other configurations. The method has the potential of providing a reference point for optimization of the hold-off capability of high-power switchgear operating in low-frequency fields.info:eu-repo/semantics/publishedVersio

A practical guide to modeling low-current quasi-stationary gas discharges: Eigenvalue, stationary, and time-dependent solvers

The work is concerned with the modeling of low-current quasi-stationary discharges, including the Townsend and corona discharges. The aim is to develop an integrated approach suitable for the computation of the whole range of existence of a quasi-stationary discharge from its inception to a non-stationary transition to another discharge form, such as a transition from the Townsend discharge to a normal glow discharge or the corona-to-streamer transition. This task includes three steps: (i) modeling of the ignition of a self-sustaining discharge, (ii) modeling of the quasi-stationary evolution of the discharge with increasing current, and (iii) the determination of the current range where the quasi-stationary discharge becomes unstable and the non-stationary transition to another discharge form begins. Each of these three steps is considered in some detail with a number of examples, referring mostly to discharges in high-pressure air.info:eu-repo/semantics/publishedVersio

Simulation of pre-breakdown discharges in high-pressure air. I: The model and its application to corona inception

A ‘minimal’ kinetic model of plasmachemical processes in low-current discharges in high pressure air is formulated, which takes into account electrons, an effective species of positive ions, and three species of negative ions. The model is implemented as a part of numerical model of low-current quasi-stationary discharges in high-pressure air based on the use of stationary solvers, which offer important advantages in simulations of steady-state discharges compared to standard approaches that rely on time-dependent solvers. The model is validated by comparison of the computed inception voltage of corona discharges with several sets of experimental data on glow coronas. A good agreement with the experiment has been obtained for positive coronas between concentric cylinders in a wide range of pressures and diameters of the cylinders. The sensitivity of the computation results with respect to different factors is illustrated. Inception voltages of negative coronas, computed using the values of the secondary electron emission coefficient of 10−4 –10−3 , agree well with the experimental data. A simplified kinetic model for corona discharges in air, which does not include conservation equations for negative ion species, has been proposed and validated. Modelling of positive coronas in rod-to-plane electrode configuration has been performed and the computed inception voltage was compared with experimental data.info:eu-repo/semantics/publishedVersio