Zdeněk Bonaventura

Simulation of the discharge propagation in a capillary tube in air at atmospheric pressure

This paper presents simulations of an air plasma discharge at atmospheric pressure initiated by a needle anode set inside a dielectric capillary tube. We have studied the influence of the tube inner radius and its relative permittivity ?r on the discharge structure and dynamics. As a reference, we have used a relative permittivity ?r = 1 to study only the influence of the cylindrical constraint of the tube on the discharge. For a tube radius of 100??m and ?r = 1, we have shown that the discharge fills the tube during its propagation and is rather homogeneous behind the discharge front. When the radius of the tube is in the range 300?600??m, the discharge structure is tubular with peak values of electric field and electron density close to the dielectric surface. When the radius of the tube is larger than 700??m, the tube has no influence on the discharge which propagates axially. For a tube radius of 100??m, when ?r increases from 1 to 10, the discharge structure becomes tubular. We have noted that the velocity of propagation of the discharge in the tube increases when the front is more homogeneous and then, the discharge velocity increases with the decrease in the tube radius and ?r. Then, we have compared the relative influence of the value of the tube radius and ?r on the discharge characteristics. Our simulations indicate that the geometrical constraint of the cylindrical tube has more influence than the value of ?r on the discharge structure and dynamics. Finally, we have studied the influence of photoemission processes on the discharge structure by varying the photoemission coefficient. As expected, we have shown that photoemission, as it increases the number of secondary electrons close to the dielectric surface, promotes the tubular structure of the discharge.

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

This 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 (1PN2, 2PN2 and ) 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.

Electric field determination in streamer discharges in air at atmospheric pressure

The electric field in streamer discharges in air can be easily determined by the ratio of luminous intensities emitted by N2(C 3 � u) and N + (B 2 � + u ) 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 � = 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 3 � u) and N + (B 2 � + u ) 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 � ∼ 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 � ∼ 1.4. As for OEs observed through pinholes, the reported results demonstrate that for + −

Solution of time-dependent Boltzmann equation for electrons in non-thermal plasma

The time development of the electron distribution function and electron macroscopic parameters was studied by solving the time-dependent Boltzmann equation for low temperature plasma. A new technique for solving the time-dependent Boltzmann equation was developed. This technique is based on a multi-term approximation of the electron distribution function expansion in Legendre polynomials. The results for electron relaxation in Reids ramp model and argon plasma are presented. The effect of negative mobility was studied and is discussed for argon plasma. Finally, the time-dependent Boltzmann equation was solved for pulsed microwave discharge in nitrogen. The accuracy of all results was confirmed by the Monte Carlo simulation.

Electron density measurements in afterglow of high power pulsed microwave discharge

In the paper we study, be means of microwave interferometry, the evolution of electron density in afterglow of pulsed driven nitrogen discharge. Recombination coeffients are derived, too.

Influence of the angular scattering of electrons on the runaway threshold in air

The runaway electron mechanism is of great importance for the understanding of the generation of x- and gamma rays in atmospheric discharges. In 1991, terrestrial gamma-ray flashes (TGFs) were discovered by the Compton Gamma-Ray Observatory. Those emissions are bremsstrahlung from high energy electrons that run away in electric fields associated with thunderstorms. In this paper, we discuss the runaway threshold definition with a particular interest in the influence of the angular scattering for electron energy close to the threshold. In order to understand the mechanism of runaway, we compare the outcome of different Fokker–Planck and Monte Carlo models with increasing complexity in the description of the scattering. The results show that the inclusion of the stochastic nature of collisions smooths the probability to run away around the threshold. Furthermore, we observe that a significant number of electrons diffuse out of the runaway regime when we take into account the diffusion in angle due to the scattering. Those results suggest using a runaway threshold energy based on the Fokker–Planck model assuming the angular equilibrium that is 1.6 to 1.8 times higher than the one proposed by [1, 2], depending on the magnitude of the ambient electric field. The threshold also is found to be 5 to 26 times higher than the one assuming forward scattering. We give a fitted formula for the threshold field valid over a large range of electric fields. Furthermore, we have shown that the assumption of forward scattering is not valid below 1 MeV where the runaway threshold usually is defined. These results are important for the thermal runaway and the runaway electron avalanche discharge mechanisms suggested to participate in the TGF generation.

An experimental study of high power microwave pulsed discharge in nitrogen

We investigated a plasma excited by high power pulsed microwaves (MWs) (pulse duration 2.5 µs, repetition rate 400 Hz, peak power 105 W, frequency 9.4 GHz) in nitrogen at reduced pressure (pressure range 10–2000 Pa) with the aim of a better understanding of such types of discharge. The construction of the experimental device suppresses the plasma–wall interactions and therefore the volume processes are predominant. To obtain the temporal evolution of the electron density we used two MW interferometers at frequencies of 15 and 35 GHz with dielectric rod waveguides which gives them the capability of localized measurements. We estimated the effective collision frequency from the absorption of a measurement beam. Time resolved optical emission spectroscopy of the 1st negative system and the 2nd positive system was carried out, too. Due to a high power input the discharge dynamics was fast and the steady state was typically reached in 1 µs. We found that the effective collision frequency has the same temporal behaviour as the 2nd positive system of N2, including a characteristic maximum at the beginning of the pulse.

Theoretical study of pulsed microwave discharge in nitrogen

A pulsed microwave discharge burning in pure nitrogen was studied theoretically. The time-dependent Boltzmann equation for electrons was solved numerically in multi-term approximation. It was assumed that the discharge was ignited by a 100 kW microwave (f = 9.4 GHz) pulses with 2.5 µs duration; the repetition frequency was 400 Hz. It was shown that the electron distribution function approaches very quickly the steady state distribution function after a change of the amplitude of electric field intensity. The steady state time averaged values of electron mean energy, diffusion and rate coefficients and drift velocity were calculated for different values of electric field intensity. With these values the actual values of electric field intensity from a previous experiment were determined from the measured time dependence of electron concentration. The calculated values were compared with previous experimental results.

Self-consistent spatio-temporal simulation of pulsed microwave discharge

A spatio-temporal theoretical model of pulsed microwave discharge was developed. This model is based on the macroscopic continuity equation for electrons and on the wave equation for an electromagnetic wave passing through the discharge plasma. These equations were solved together and in a self-consistent manner. For simplicity, the continuity equation was solved in one dimension only and the electromagnetic wave was assumed to be plane and transversal. Both equations were solved numerically and the spatio-temporal dependences of electron concentration and the amplitude of the microwave electric field were obtained. It was found that the discharge development depends, significantly, on the initial spatial distribution of electron concentration. Two different cases were studied: the discharge development during the first microwave pulse only and after several successive pulses. The calculations were performed particularly for the discharge in nitrogen. The results were compared with experimental data from our previous work.

Study of “source sheath” problem in PIC/MC simulation: Spherical geometry

A method for treatment of boundary conditions and particle loading in a self-consistent semi-infinite Particle-In-Cell/Monte Carlo simulation is presented. A non-ionizing, collisional plasma in contact with an electrode was assumed. The simulation was performed for a spherical probe with constant probe potential. The motion of charged particles was calculated in three dimensions, but only the radial charge distribution and thus only radial electric field were assumed. The particle loading has to be done with an appropriate velocity distribution with a radial drift velocity. This drift velocity has to be calculated from the probe current, and therefore, a self-consistent (iterative) approach is necessary. Furthermore, correct values of particle densities and electric field potential at the outer boundary of the computational domain have to be set using asymptotic formulae for particle density and electric field potential. This approach removes the “source sheath” which is created artificially, if incorrect...