Sebastien Celestin

Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP3) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by S´ egur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 <p O2 R< 150 Torr cm, where pO2 is the partial pressure of molecular oxygen in air in units of Torr (pO2 = 150 Torr at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of boundary conditions represents an important task needed for a successful extension of the proposed formulations to two- and three-dimensional physical systems with obstacles of complex geometry (i.e. electrodes, dust particles, aerosols, etc), which are opaque for the photoionizing UV photons.

Energy and fluxes of thermal runaway electrons produced by exponential growth of streamers during the stepping of lightning leaders and in transient luminous events

[1] In the present paper, we demonstrate that the exponential expansion of streamers propagating in fields higher than the critical fields for stable propagation of streamers of a given polarity leads to the exponential growth of electric potential differences in streamer heads. These electric potential differences are directly related to the energy that thermal runaway electrons can gain once created. Using full energy range relativistic Monte Carlo simulations, we show that the exponential growth of potential differences in streamers gives rise to the production of runaway electrons with energies as high as ∼100 keV, with most of electrons residing in energy range around several tens of keVs. We apply these concepts in the case of lightning stepped leaders during the stage of negative corona flash. The computation of electric field produced by stepped leaders demonstrates for the first time that those energetic electrons are capable of further acceleration up to the MeV energies. Moreover, the flux of runaway electrons produced by streamers suggests that stepped leaders produce a considerable number of energetic electrons, which is in agreement with the number of energetic photons observed from satellites in terrestrial gamma ray flashes (TGFs). The results suggest that previously proposed process of relativistic runaway electron avalanche is difficult to sustain in the low‐electric fields observed in thunderclouds and is generally not needed for explanation of TGFs. The present work also gives insights on relations between physical properties of energetic electrons produced in streamers and the internal electrical properties of streamer discharges, which can further help development and interpretation of X‐ray diagnostics of these discharges.

Application of photoionization models based on radiative transfer and the Helmholtz equations to studies of streamers in weak electric fields

Recent advances in development of photoionization models in air based on radiative transfer and Helmholtz equations open new perspectives for efficient solution of nonthermal gas discharge problems involving complex geometries. Many practical applications require accurate modeling of streamer discharges developing in weak electric fields, in which the photoionization process significantly contributes to discharge dynamics. This paper (1) reports original studies, which demonstrate the validity and accuracy of the recently proposed photoionization models for studies of streamers in weak electric fields, and (2) introduces efficient boundary conditions for the photoinization models based on radiative transfer theory.

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

This paper presents the application of the ghost fluid method (GFM) to solve Poissons 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.

Soft collisions in relativistic runaway electron avalanches

This paper reports the first application of the relativistic binary-encounter-Bethe (RBEB) electron impact ionization model for studies of relativistic runaway electron avalanches (RREA) phenomenon at different pressures in air, which is believed to be the root cause of the hard x-rays and terrestrial gamma-ray flashes observed in the Earths atmosphere in association with lightning activity. The model allows robust and accurate description of ionization over a wide range of energies (from the ionization threshold to megaelectronvolts), that is especially important for studies of thermal runaway electrons. A direct comparison between RREA rates obtained using classic M?ller and the new RBEB differential ionization cross sections demonstrates that the dipole interaction between primary electrons and K-shell electrons of oxygen and nitrogen has an impact on the rates for relatively low applied electric fields comparable to or higher than 20?kV?cm?1 at ground pressure. Implications of non-similarity of the runaway process developing at different altitudes due to the Swann?Fermi density effect are discussed.

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 + −

Optical emissions associated with terrestrial gamma ray flashes

In this paper, we present modeling studies on optical emissions resulting from the excitation of air molecules produced by the large population of electrons involved in TGF events based on two production mechanisms: relativistic runaway electron avalanches (RREA) and production of thermal runaway electrons by high-potential +IC lightning leaders. Numerical models used in this study are first validated through comparison with available laboratory observations. Using Monte Carlo simulations, we show that electron energy distributions established from the two TGF production mechanisms are inherently different over the full energy range, mainly because of the difference in the driving electric fields. Furthermore, we show that TGFs are most likely accompanied with detectable levels of optical emissions. We also demonstrate that, due to the fundamental difference in the acceleration and avalanche multiplication processes undergone by runaway electrons, optical emissions generated by the two viable TGF production mechanisms are intrinsically different. These distinct optical features are of significant interests for constraining and validating current TGF production models.

Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4

This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ/Ne. We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ε). In addition, we present comparisons of GEANT4 simulations performed with a “standard” and a “low-energy” physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results. Key Points Testing the feedback mechanism with GEANT4 Validating the GEANT4 programming toolkit Study the ratio of bremsstrahlung photons to electrons at TGF source altitude

Modeling of X-ray emissions produced by stepping lightning leaders

Intense and brief bursts of X-ray emissions have been measured during the stepping process of both natural cloud-to-ground (CG) and rocket-triggered lightning flashes. In this paper, we investigate theoretically the energy spectra of X-rays produced by the bremsstrahlung emission of thermal runaway electrons accelerated in the inhomogeneous electric field produced around lightning leader tips. The X-ray energy spectrum depends on the physical properties of the associated lightning leaders. Consequently, X-ray measurements can be used for diagnostics of the electrical properties of lightning stepped leaders. We report simulation results of the photon energy spectra produced by 5 and 10 MV negative CG lightning discharges that would be measured from the ground using ideal detectors. We also quantify theoretically the radial dependence of X-ray energy spectra received at ground level during the leader stepping process. Moreover, it is found that the ground radiation generated in this process is harmless to humans.