Derivation of a merging condition for two interacting streamers in air

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative ones. Moreover it is demonstrated that these ratios are practically independent of the applied electric field, the initial seed configuration, and the pressure

Influence of the pre-ionization background and simulation of the optical emission of a streamer discharge in preheated air at atmospheric pressure between two point electrodes

International audienceThis paper presents simulations of positive and negative streamers propagating between two point electrodes in preheated air at atmospheric pressure. As many discharges have occurred before the simulated one, seed charges are taken into account in the interelectrode gap. First, for a pre-ionization background of 109 cm−3, we have studied the influence of the data set used for transport parameters and reaction rates for air on the simulation results. We have compared results obtained in 1997 using input parameters from Morrow and Lowke and from Kulikovsky. Deviations as large as 20% of streamer characteristics (i.e. electric field in the streamer head and body, streamer velocity, streamer radius, streamer electron density) have been observed for this point-to-point configuration. Second, we have studied the influence of the pulsed voltage frequency on the discharge structure. For the studied discharge regime, a change in the applied voltage frequency corresponds to a change in the pre-ionization background. In this work, we have considered a wide range of pre-ionization values from 104 and up to 109 cm−3. We have noted that the value of the pre-ionization background has a small influence on the electron density, electric field and location of the negative streamer head. Conversely, it has a significant influence on the positive streamer characteristics. Finally, we have compared instantaneous and time-averaged optical emissions of the three band systems of N2 and {\rm N}_2^+ (1PN2, 2PN2 and {\rm 1NN}_2^+ ) during the discharge propagation. We have shown that the emission of the 2PN2 is the strongest of the three bands, in agreement with experimental observations. It is interesting to note that even with a short time averaging of a few nanoseconds, which corresponds to currently used instruments, the structure of the time-averaged emission of the 2PN2 is different from the instantaneous one and shows negative and positive streamers with smaller radial expansions and more diffuse streamer heads

Study on the conditions to obtain a diffuse nanosecond positive ionization wave in a point-to-plane geometry in atmospheric pressure air

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Electric field determination in streamer discharges in air at atmospheric pressure

International audienceThe electric field in streamer discharges in air can be easily determined by the ratio of luminous intensities emitted by N2(C) and N2+(B) if the steady-state assumption of the emitting states is fully justified. At ground pressure, the steady-state condition is not fulfilled and it is demonstrated that its direct use to determine the local and instantaneous peak electric field in the streamer head may overestimate this field by a factor of 2. However, when spatial and time-integrated optical emissions (OEs) are considered, the reported results show that it is possible to formulate a correction factor in the framework of the steady-state approximation and to accurately determine the peak electric field in an air discharge at atmospheric pressure. A correction factor is defined as G= Es/Ee, where Ee is the estimated electric field and Es is the true peak electric field in the streamer head. It is shown that this correction stems from (i) the shift between the location of the peak electric field and the maximum excitation rate for N2(C) and N2+(B) as proposed by Naidis (2009 Phys. Rev. E 79 057401) and (ii) from the cylindrical geometry of the streamers as stated by Celestin and Pasko (2010 Geophys. Res. Lett. 37 L07804). For instantaneous OEs integrated over the whole radiating plasma volume, a correction factor of G ∼ 1.4 has to be used. For time-integrated OEs, the reported results show that the ratio of intensities can be used to derive the electric field in discharges if the time of integration is sufficiently long (i.e. at least longer than the longest characteristic lifetime of excited species) to have the time to collect all the light from the emitting zones of the streamer. For OEs recorded using slits (i.e. a window with a small width but a sufficiently large radial extension to contain the total radial extension of the discharge) the calculated correction factor is G ∼ 1.4. As for OEs observed through pinholes, the reported results demonstrate that for local OEs, the G coefficient depends slightly on the radial position and is in a range [1.24, 1.28]. For line-integrated OEs, the radial variation of G is more significant and G is in the range [1.24, 1.38]. Finally, it is noted that the use of different sets of Einstein coefficients and quenching rates of excited states has negligible influence on the value of G

Study of the electric field in a diffuse nanosecond positive ionization wave generated in a pin-to-plane geometry in atmospheric pressure air

International audienceThe dynamics of a nanosecond positive ionization front generated in a pin-to-plane geometry inatmospheric pressure air is simulated using a 2D axisymmetric drift-diffusion fluid model. For a16 mm gap and a sharp pin electrode, the plateau of the applied voltage is varied between 40and 60 kV and the rise time is varied between 0.5 and 1.5 ns or a DC voltage is applied. Thedischarge ignition time and the voltage at ignition are shown to depend mostly on the voltagerise time. The connection time, i.e. the time for the ionization wave to ignite, propagate andconnect to the plane is shown to strongly depend on both the values of the voltage plateau andrise time. For all cases, the discharge has a conical shape with a maximal radius of about 8 mmas it connects to the grounded plane. The average propagation velocity of the ionization front isfound to vary in the range 3.1 to 8.5 mm ns−1. These values are in rather good agreement withexperiments. Temporal evolutions of the electric field are recorded on the symmetry axis atdifferent positions in the gap. At each location, an increase and decrease of the electric field isobserved as the ionization front, propagating from the pin to the plane, passes the studied point,in accordance with experimental observations. Finally, for a voltage plateau of 55 kV and a risetime of 0.5 ns, a temporal sampling of 100 ps is shown to be sufficient to capture the dynamicsof the electric field during the ionization front propagation when it passes close to the middle ofthe gap. Conversely, a temporal sampling of 10 ps is required when the ionization wave is closeto both electrodes, or during the fast redistribution of the electric field after the connection of theionization front at the cathode

Morphology of positive ionization waves in atmospheric pressure air: influence of electrode set-up geometry

International audienceA numerical parametric study on positive diffuse discharges in pointto-plane geometry in air at atmospheric pressure is presented. Different discharge characteristics are studied: ignition time, connection time to the grounded cathode plane, shape of the discharge and its maximum radius at the connection time, evolution of the maximum electric field in the discharge front and velocity of the ionization front during its propagation. First, a case at a DC voltage of 50 kV applied on a rod anode ended by a semi-sphere with a radius of 100 µm set at 1.6 cm from a grounded cathode plane is considered. The influence of the rod radius, the position of a disc holder, the shape of the anode electrode and the radial extension of the computational domain are studied. The radius of curvature of the anode tip (varied between 100 and 1000 µm) and the shape of the anode electrode (rod or hyperbola) are shown to have a negligible influence on discharge characteristics. Conversely, the presence of a disc holder or a small radial computational domain lead to a decrease of the maximum discharge radius at the connection time and a change in the discharge shape from a conical to an ellipsoidal shape. These changes on the discharge morphology have only a limited impact on the propagation velocity of the discharge front and maximum electric field on the discharge axis. Then, a point-to-plane geometry with a rod electrode of 50 µm radius, in a 1.6 cm gap, with a 100 kV voltage applied with a rise time of 1 ns is studied. The influence of a disc holder on the discharge characteristics is the same as for lower DC voltages. Finally, the time evolution of the absolute value of the electric field at different test points on the discharge axis is studied. Close to the anode tip, rapidly after the peak of electric field due to the passage of the ionization front, the electric field in the discharge channel is shown to increase to values higher than the breakdown field

A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations

International audienceWe develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used to solve hyperbolic and parabolic time-dependent PDEs. Such an approach guarantees a numerical solution of the Poisson equation within a user-defined accuracy tolerance. Most adaptive meshing approaches in the literature solve elliptic PDEs level-wise and hence at uniform resolution throughout the set of adapted grids. Here we introduce a numerical procedure to represent the elliptic operators on the adapted grid, strongly coupling inter grid relations that guarantee the conservation and accuracy properties of multiresolution finite volume schemes. The discrete Poisson equation is solved at once over the entire computational domain as a completely separate process. The accuracy and numerical performance of the method is assessed in the context of streamer discharge simulations

Recent advances in modeling low-temperature kHz atmospheric pressure plasma jets and their interactions with surfaces

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The use of the ghost fluid method for Poisson's equation to simulate streamer propagation in point-to-plane and point-to-point geometries

International audienceThis paper presents the application of the ghost fluid method (GFM) to solve Poisson's equation for streamer discharge simulations between electrodes of complex geometries. This approach allows one to use a simple rectilinear grid and nevertheless take into account the influence of the exact shape of the electrode on the calculation of the potential and the electric field. First, the validity of the GFM approach concerning the computation of the electric field is demonstrated by performing direct comparisons in a point-to-plane geometry of the Laplacian potential and electric field calculated with this method and given by the analytical solution. Second, the GFM is applied to the simulation of a positive streamer propagation in a hyperboloid-to-plane configuration studied by Kulikovsky (1998 Phys. Rev. E 57 7066–74). Very good agreement is obtained with the results of Kulikovsky (1998) on all positive streamer characteristics during its propagation in the interelectrode gap. Then the GFM is applied to simulate the discharge in preheated air at atmospheric pressure in point-to-point geometry. The propagation of positive and negative streamers from both point electrodes is observed. After the interaction of both discharges, the very rapid propagation of the positive streamer towards the cathode in the volume pre-ionized by the negative streamer is presented. This structure of the discharge is in qualitative agreement with the experiment

Effect of jet polarity on charging of a dielectric target: simulations and experiments

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