Publications

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Below, by year, are the publications listed in the HAL open archive.

2009

Electrostatic solitary waves in current layers: from Cluster observations during a super-substorm to beam experiments at the LAPD
- Pickett J. S.
- Chen L.-J.
- Santolík O.
- Grimald S.
- Lavraud B.
- Verkhoglyadova O. P.
- Tsurutani B. T.
- Lefebvre B.
- Fazakerley A.
- Lakhina G. S.
- Ghosh S. S.
- Grison B.
- Décréau Pierrette
- Gurnett D. A.
- Torbert R.
- Cornilleau-Wehrlin Nicole
- Dandouras I.
- Lucek E.
Nonlinear Processes in Geophysics, European Geosciences Union (EGU), 2009, 16 (3), pp.431-442. Electrostatic Solitary Waves (ESWs) have been observed by several spacecraft in the current layers of Earth's magnetosphere since 1982. ESWs are manifested as isolated pulses (one wave period) in the high time resolution waveform data obtained on these spacecraft. They are thus nonlinear structures generated out of nonlinear instabilities and processes. We report the first observations of ESWs associated with the onset of a super-substorm that occurred on 24 August 2005 while the Cluster spacecraft were located in the magnetotail at around 18-19 RE and moving northward from the plasma sheet to the lobes. These ESWs were detected in the waveform data of the WBD plasma wave receiver on three of the Cluster spacecraft. The majority of the ESWs were detected about 5 min after the super-substorm onset during which time 1) the PEACE electron instrument detected significant field-aligned electron fluxes from a few 100 eV to 3.5 keV, 2) the EDI instrument detected bursts of field-aligned electron currents, 3) the FGM instrument detected substantial magnetic fluctuations and the presence of Alfvén waves, 4) the STAFF experiment detected broadband electric and magnetic waves, ion cyclotron waves and whistler mode waves, and 5) CIS detected nearly comparable densities of H and O ions and a large tailward H velocity. We compare the characteristics of the ESWs observed during this event to those created in the laboratory at the University of California-Los Angeles Plasma Device (LAPD) with an electron beam. We find that the time durations of both space and LAPD ESWs are only slightly larger than the respective local electron plasma periods, indicating that electron, and not ion, dynamics are responsible for generation of the ESWs. We have discussed possible mechanisms for generating the ESWs in space, including the beam and kinetic Buneman type instabilities and the acoustic instabilities. Future studies will examine these mechanisms in more detail using the space measurements as inputs to models, and better relate the ESW space measurements to the laboratory through PIC code models. (10.5194/npg-16-431-2009)
DOI : 10.5194/npg-16-431-2009
Influence of dielectric material in Dielectric Barrier Discharge (DBD) for chemistry reactivity control
- Youssef Joseph
- Bouamra K.
- Makarov M.
- Guaitella Olivier
- Rousseau Antoine
, 2009.
Oblique propagation of whistler mode waves in the chorus source region
- Santolík O.
- Gurnett D. A.
- Pickett J. S.
- Chum J.
- Cornilleau-Wehrlin Nicole
Journal of Geophysical Research Space Physics, American Geophysical Union/Wiley, 2009, 114. Whistler mode chorus has been shown to play a role in the process of local acceleration of electrons in the outer Van Allen radiation belt. Most of the quasi-linear and nonlinear theoretical studies assume that the waves propagate parallel to the terrestrial magnetic field. We show a case where this assumption is invalid. We use data from the Cluster spacecraft to characterize propagation and spectral properties of chorus. The recorded high-resolution waveforms show that chorus in the source region can be formed by a succession of discrete wave packets with decreasing frequency that sometimes change into shapeless hiss. These changes occur at the same time in the entire source region. Multicomponent measurements show that waves in both these regimes can be found at large angles to the terrestrial magnetic field. The hiss intervals contain waves propagating less than one tenth of a degree from the resonance cone. In the regime of discrete wave packets the peak of the wave energy density is found at a few degrees from the resonance cone in a broad interval of azimuth angles. The wave intensity increases with the distance from the magnetic field minimum along a given field line, indicating a gradual amplification of chorus in the source region. (10.1029/2009JA014586)
DOI : 10.1029/2009JA014586
Self synchronization of surface discharges in a two electrodes device
- Allegraud Katia
- Rousseau Antoine
IEEE Transactions on Dielectrics and Electrical Insulation, Institute of Electrical and Electronics Engineers, 2009, 16 (2), pp.435-439. A twin electrode device coupled to the same high voltage power supply is used to study the propagation of surface streamers. These two identical electrodes are separated from the grounded one by a pyrex plate acting as a dielectric barrier. The gas is dry air, at atmospheric pressure. 1 ns time resolved imaging of the discharge propagation is performed to monitor the discharge ignition and propagation. The discharge consists in filaments which propagate on the dielectric as cathode directed streamers. Each filament transfers 1 nC. The propagation velocities vary from 3.4times107 cm/s at the beginning of the propagation to 7times106 cm/s at the end of the propagation. Ignition at one electrode triggers ignition at the other within 2 ns. (10.1109/TDEI.2009.4815175)
DOI : 10.1109/TDEI.2009.4815175
Time-dependent hydrodynamical simulations of slow solar wind, coronal inflows, and polar plumes
- Pinto Rui
- Grappin Roland
- Wang Y-M
- Léorat Jacques
Astronomy & Astrophysics - A&A, EDP Sciences, 2009, 497 (2), pp.537--543. Aims. We explore the effects of varying the areal expansion rate and coronal heating function on the solar wind flow. Methods. We use a one-dimensional, time-dependent hydrodynamical code. The computational domain extends from near the photosphere, where nonreflecting boundary conditions are applied, to 30 , and includes a transition region where heat conduction and radiative losses dominate. Results. We confirm that the observed inverse relationship between asymptotic wind speed and expansion factor is obtained if the coronal heating rate is a function of the local magnetic field strength. We show that inflows can be generated by suddenly increasing the rate of flux-tube expansion and suggest that this process may be involved in the closing-down of flux at coronal hole boundaries. We also simulate the formation and decay of a polar plume, by including an additional, time-dependent heating source near the base of the flux tube. (10.1051/0004-6361/200811183)
DOI : 10.1051/0004-6361/200811183
Physics of non-diffusive turbulent transport of momentum and the origins of spontaneous rotation in tokamaks
- Diamond P.H.
- Mcdevitt C.J.
- Gürcan Özgür D.
- Hahm T.S.
- Wang W.X.
- Yoon E.S.
- Holod I.
- Lin Z.
- Naulin V.
- Singh R.
Nuclear Fusion, IOP Publishing, 2009, 49, pp.045002. Recent results in the theory of turbulent momentum transport and the origins of intrinsic rotation are summarized. Special attention is focused on aspects of momentum transport critical to intrinsic rotation, namely the residual stress and the edge toroidal flow velocity pinch. Novel results include a systematic decomposition of the physical processes which drive intrinsic rotation, a calculation of the critical external torque necessary to hold the plasma stationary against the intrinsic residual stress, a simple model of net velocity scaling which recovers the salient features of the experimental trends and the elucidation of the impact of the particle flux on the net toroidal velocity pinch. Specific suggestions for future experiments are offered. (10.1088/0029-5515/49/4/045002)
DOI : 10.1088/0029-5515/49/4/045002
Investigation of InP etching mechanisms in a Cl2/H2 inductively coupled plasma by optical emission spectroscopy
- Gatilova L.
- Bouchoule S.
- Guilet S.
- Chabert Pascal
Journal of Vacuum Science & Technology A, American Vacuum Society, 2009, 27, pp.262. Optical emission spectroscopy (OES) has been used in order to investigate the InP etching mechanisms in a Cl2H2 inductively coupled plasma. The authors have previously shown that anisotropic etching of InP could be achieved for a H2 percentage in the 35%45% range where the InP etch rate also presents a local maximum [ J. Vac. Sci. Technol. B 24, 2381 (2006) ], and that anisotropic etching was due to an enhanced passivation of the etched sidewalls by a silicon oxide layer [ J. Vac. Sci. Technol. B 26, 666 (2008) ]. In this work, it is shown that this etching behavior is related to a maximum in the H atom concentration in the plasma. The possible enhancement of the sidewall passivation process in the presence of H is investigated by comparing OES measurements and etching results obtained for Cl2H2 and Cl2Ar gas mixtures. (10.1116/1.3071950)
DOI : 10.1116/1.3071950
Wave-Number Spectrum of Drift-Wave Turbulence
- Gürcan Özgür D.
- Garbet X.
- Hennequin Pascale
- Diamond P.H.
- Casati A.
- Falchetto G. L.
Physical Review Letters, American Physical Society, 2009, 102, pp.255002. A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactions and midrange drive. On the other hand, when disparate scale interactions are dominant, a simple spectrum for the density fluctuations of the form |nk|2∝k−3/(1 k2)2 is obtained. This simple prediction is then compared to, and found to be in fair agreement with, Tore Supra CO2 laser scattering data. (10.1103/PhysRevLett.102.255002)
DOI : 10.1103/PhysRevLett.102.255002
Enhanced confinement with increased extent of the low magnetic shear region in tokamak plasmas
- Nasi L.
- Firpo Marie-Christine
Plasma Physics and Controlled Fusion, IOP Publishing, 2009, 51, pp.045006. The Hamiltonian representation of magnetic field lines enables one to study their confinement properties in tokamaks through the use of symplectic maps such as the symmetric tokamap and its bounded version, the latter being introduced here. In this time-independent purely magnetic framework, we observed the drastic improvement in the confinement of magnetic field lines produced by the local vanishing of the shear profile. This amounts to a non-twist condition that notably acts in the same way the safety profile being (non-strictly) monotonic or having a reversed shear. We single out the effect of the amount of flatness of the safety profile in the vicinity of its zero shear point. All other things being equal, the beneficial effect of the vanishing of the shear profile is shown to be increased if the radial extent of the low-shear region is increased. To be specific, the low-shear region induces the formation of a belt of robust KAM tori acting as an internal transport barrier whose width is all the larger as the extent of the low-shear region is broad. (10.1088/0741-3335/51/4/045006)
DOI : 10.1088/0741-3335/51/4/045006
Global distribution of whistler-mode chorus waves observed on the THEMIS spacecraft
- Li W.
- Thorne R. M.
- Angelopoulos V.
- Bortnik J.
- Cully C. M.
- Ni B.
- Le Contel Olivier
- Roux A.
- Auster U.
- Magnes W.
Geophysical Research Letters, American Geophysical Union, 2009, 36, pp.9104. Whistler mode chorus waves are receiving increased scientific attention due to their important roles in both acceleration and loss processes of radiation belt electrons. A new global survey of whistler-mode chorus waves is performed using magnetic field filter bank data from the THEMIS spacecraft with 5 probes in near-equatorial orbits. Our results confirm earlier analyses of the strong dependence of wave amplitudes on geomagnetic activity, confinement of nightside emissions to low magnetic latitudes, and extension of dayside emissions to high latitudes. An important new finding is the strong occurrence rate of chorus on the dayside at L > 7, where moderate dayside chorus is present >10% of the time and can persist even during periods of low geomagnetic activity. (10.1029/2009GL037595)
DOI : 10.1029/2009GL037595
Evidence of a Cascade and Dissipation of Solar-Wind Turbulence at the Electron Gyroscale
- Sahraoui Fouad
- Goldstein M. L.
- Robert Patrick
- Khotyaintsev Y. V.
Physical Review Letters, American Physical Society, 2009, 102 (23), pp.231102. We report the first direct determination of the dissipation range of magnetofluid turbulence in the solar wind at the electron scales. Combining high resolution magnetic and electric field data of the Cluster spacecraft, we computed the spectrum of turbulence and found two distinct breakpoints in the magnetic spectrum at 0.4 and 35 Hz, which correspond, respectively, to the Doppler-shifted proton and electron gyroscales, fρp and fρe. Below fρp, the spectrum follows a Kolmogorov scaling f−1.62, typical of spectra observed at 1 AU. Above fρp, a second inertial range is formed with a scaling f−2.3 down to fρe. Above fρe, the spectrum has a steeper power law ∼f−4.1 down to the noise level of the instrument. We interpret this as the dissipation range and show a remarkable agreement with theoretical predictions of a quasi-two-dimensional cascade into Kinetic Alfvén Waves (KAW). (10.1103/PhysRevLett.102.231102)
DOI : 10.1103/PhysRevLett.102.231102
Whistler wave radiation from a loop antenna located in a cylindrical density depletion
- Kudrin A. V.
- Bakharev P. V.
- Krafft C.
- Zaboronkova T. M.
Physics of Plasmas, American Institute of Physics, 2009, 16, pp.063502. Electromagnetic radiation from sources in a magnetoplasma containing a radially nonuniform cylindrical density depletion is considered. Using a rigorous solution for the total field comprising both the discrete and continuous parts of the spatial spectrum of excited waves, the radiation resistance of a loop antenna and the efficiency of excitation of different modes by such a source are determined in the whistler range. Based on the numerical results, conditions are revealed under which the power radiated from a loop antenna located in a density depletion is dominated by the contribution of either discrete- or continuous-spectrum modes. It is found that the radiation resistance of the loop antenna in a weakly nonuniform density depletion can be notably greater than that in a homogeneous magnetoplasma whose parameters coincide with those near the depletion axis. The results are relevant to the basic properties of whistler wave excitation in the presence of field-aligned plasma density irregularities and can be useful for wave diagnostics in laboratory and space plasmas. (10.1063/1.3142469)
DOI : 10.1063/1.3142469
Dispersion relations of electron density fluctuations in a Hall thruster plasma, observed by collective light scattering
- Tsikata Sedina
- Lemoine N.
- Pisarev V.
- Grésillon D.
Physics of Plasmas, American Institute of Physics, 2009, 16, pp.033506. Kinetic models and numerical simulations of E×B plasma discharges predict microfluctuations at the scales of the electron cyclotron drift radius and the ion plasma frequency. With the help of a specially designed collective scattering device, the first experimental observations of small-scale electron density fluctuations inside the plasma volume are obtained, and observed in the expected ranges of spatial and time scales. The anisotropy, dispersion relations, form factor, amplitude, and spatial distribution of these electron density fluctuations are described and compared to theoretical expectations. (10.1063/1.3093261)
DOI : 10.1063/1.3093261
A comment on the paper 'Solar activity and its influence on climate' Author C. de Jager Published in Netherlands Journal of Geosciences-Geologie en Mijnbouw, 87-3, pp 207213, 3 2008
- Amory-Mazaudier Christine
- Legrand J.P.
NETHERLANDS JOURNAL OF GEOSCIENCES-GEOLOGIE EN MIJNBOUW, 2009, [88-3] 177, pp.[88-3] 177. The purpose of this comment is not to criticize the results obtained by Dr C. de Jager, and we agree for example with his prediction of the next sunspot cycle amplitude - 68 with σ= 17.
Slow Solar Wind From Open Regions with Strong Low-Coronal Heating
- Wang Y-M
- Ko Y-K
- Grappin Roland
The Astrophysical Journal, American Astronomical Society, 2009, 691 (1), pp.760--769. By comparing solar wind data taken by the Advanced Composition Explorer during 1998-2007 with extrapolations of the observed photospheric magnetic field, we verify that high O7 /O6 and Fe/O ratios are associated with low wind speeds, large expansion factors, strong footpoint fields, and high mass and energy flux densities at the coronal base. As demonstrated by model calculations, these correlations are consistent with the idea that the bulk of the slow wind originates from regions of rapidly diverging open flux, where the coronal heating is concentrated at low heights. We identify two main components of the slow wind, one emanating from small coronal holes near active regions and characterized by particularly strong low-coronal heating, the other coming from just inside the polar-hole boundaries and characterized by weaker low-coronal heating and intermediate O7 /O6 and Fe/O ratios. (10.1088/0004-637X/691/1/760)
DOI : 10.1088/0004-637X/691/1/760
Toroidal Rotation Driven by the Polarization Drift
- Mcdevitt C.J.
- Diamond P.H.
- Gürcan Özgür D.
- Hahm T.S.
Physical Review Letters, American Physical Society, 2009, 103, pp.205003. Starting from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers a novel mechanism by which microturbulence may drive intrinsic rotation. This mechanism, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the polarization drift. The derivation and physical discussion of this mechanism will be pursued throughout this Letter. (10.1103/PhysRevLett.103.205003)
DOI : 10.1103/PhysRevLett.103.205003
Quasi-parallel whistler mode waves observed by THEMIS during near-earth dipolarizations
- Le Contel Olivier
- Roux A.
- Jacquey C.
- Robert Patrick
- Berthomier Matthieu
- Chust Thomas
- Grison B.
- Angelopoulos V.
- Sibeck David G.
- Chaston C. C.
- Cully C. M.
- Ergun B.
- Glassmeier K.-H.
- Auster U.
- Mcfadden J. P.
- Carlson C. W.
- Larson D. E.
- Bonnell J. W.
- Mende S. B.
- Russell C. T.
- Donovan E.
- Mann I. R.
- Singer H.
Annales Geophysicae, European Geosciences Union, 2009, 27, pp.2259-2275. We report on quasi-parallel whistler emissions detected by the near-earth satellites of the THEMIS mission before, during, and after local dipolarization. These emissions are associated with an electron temperature anisotropy alpha=T⊥e/T||e>1 consistent with the linear theory of whistler mode anisotropy instability. When the whistler mode emissions are observed the measured electron anisotropy varies inversely with beta||e (the ratio of the electron parallel pressure to the magnetic pressure) as predicted by Gary and Wang (1996). Narrow band whistler emissions correspond to the small alpha existing before dipolarization whereas the broad band emissions correspond to large alpha observed during and after dipolarization. The energy in the whistler mode is leaving the current sheet and is propagating along the background magnetic field, towards the Earth. A simple time-independent description based on the Liouville's theorem indicates that the electron temperature anisotropy decreases with the distance along the magnetic field from the equator. Once this variation of alpha is taken into account, the linear theory predicts an equatorial origin for the whistler mode. The linear theory is also consistent with the observed bandwidth of wave emissions. Yet, the anisotropy required to be fully consistent with the observations is somewhat larger than the measured one. Although the discrepancy remains within the instrumental error bars, this could be due to time-dependent effects which have been neglected. The possible role of the whistler waves in the substorm process is discussed. (10.5194/angeo-27-2259-2009)
DOI : 10.5194/angeo-27-2259-2009
International Heliophysical Year: GPS Network in Africa
- Amory-Mazaudier Christine
- Basu S.
- Bock Olivier
- Combrink A.
- Groves K.
- Fuller Rowell T.
- Lassudrie-Duchesne Patrick
- Petitdidier Monique
- Yizengaw E.
Earth, Moon, and Planets, Springer Verlag, 2009, 104 (1-4), pp.263-270. The main scientific objectives of the International Heliophysical Year are to discover and study all the physical processes coupling the Earth to the Sun. During the IHY a number of scientific instruments are being deployed all over the world. This brief report presents the scientific objectives, the GPS receiver network over Africa and the long lasting research planned for the next decades in Africa (10.1007/s11038-008-9273-8)
DOI : 10.1007/s11038-008-9273-8
Dielectric Barrier Discharge (DBD) and Zeolite Coupling: Butane case
- Youssef Joseph
- Bouamra K.
- Makarov M.
- Guaitella Olivier
- Rousseau Antoine
, 2009.
Time resolved shadow imaging of a pulsed corona in water
- Ceccato P H
- Guaitella Olivier
- Rousseau Antoine
, 2009.
Quantum Cascade Laser Absorption Spectroscopy Study on the Influence of Plasma Stimulated Surface Adsorptions to the NO Destruction Kinetics
- Hübner M.
- Guaitella Olivier
- Rousseau Antoine
- Welzel S.
- Roepcke J.
, 2009.
Disk formation during collapse of magnetized protostellar cores
- Hennebelle Patrick
- Ciardi Andrea
Astronomy & Astrophysics - A&A, EDP Sciences, 2009, 506, pp.L29-L32. Context: In the context of star and planet formation, understanding the formation of disks is of fundamental importance. Aims: Previous studies found that the magnetic field has a very strong impact on the collapse of a prestellar cloud, by possibly suppressing the formation of a disk even for relatively modest values of the magnetic intensity. Since observations infer that cores have a substantial level of magnetization, this raises the question of how disks form. However, most studies have been restricted to the case in which the initial angle, alpha, between the magnetic field and the rotation axis equals 0°. Here we explore and analyse the influence of non aligned configurations on disk formation. Methods: We perform 3D ideal MHD, AMR numerical simulations for various values of mu, the ratio of the mass-to-flux to the critical mass-to-flux, and various values of alpha. Results: We find that disks form more easily as alpha increases from 0 to 90°. We propose that as the magnetized pseudo-disks become thicker with increasing alpha, the magnetic braking efficiency is lowered. We also find that even small values of alpha (~=10-20°) show significant differences with the aligned case. Conclusions: Within the framework of ideal MHD, and for our choice of initial conditions, centrifugally supported disks cannot form for values of mu smaller than ~=3 when the magnetic field and the rotation axis are perpendicular, and smaller than about ~=5-10 when they are perfectly aligned. (10.1051/0004-6361/200913008)
DOI : 10.1051/0004-6361/200913008
Universality of Solar-Wind Turbulent Spectrum from MHD to Electron Scales
- Alexandrova Olga
- Saur J.
- Lacombe C.
- Mangeney Anne
- Mitchell J.
- Schwartz S. J.
- Robert Patrick
Physical Review Letters, American Physical Society, 2009, 103, pp.165003. To investigate the universality of magnetic turbulence in space plasmas, we analyze seven time periods in the free solar wind under different plasma conditions. Three instruments on Cluster spacecraft operating in different frequency ranges give us the possibility to resolve spectra up to 300 Hz. We show that the spectra form a quasiuniversal spectrum following the Kolmogorovs law ∼k−5/3 at MHD scales, a ∼k−2.8 power law at ion scales, and an exponential ∼exp[−√kρe] at scales kρe∼[0.1,1], where ρe is the electron gyroradius. This is the first observation of an exponential magnetic spectrum in space plasmas that may indicate the onset of dissipation. We distinguish for the first time between the role of different spatial kinetic plasma scales and show that the electron Larmor radius plays the role of a dissipation scale in space plasma turbulence. (10.1103/PhysRevLett.103.165003)
DOI : 10.1103/PhysRevLett.103.165003
Mechanism of ignition by non-equilibrium plasma
- Aleksandrov N.L.
- Kindysheva S.V.
- Kosarev I.N.
- Starikovskaia Svetlana
- Starikovskii A.Yu.
Proceedings of the Combustion Institute, Elsevier, 2009, 32 (1), pp.205-212. The kinetics of ignition in stoichiometric CnH2n 2:O2:Ar mixtures with 90% dilution for n = 15 has been studied experimentally and numerically under the action of a high-voltage nanosecond discharge. It was shown that the initiation of the discharge by a high-voltage pulse 115 kV in amplitude with a specific deposited energy of 1030 mJ/cm3 leads to more than an order of magnitude decrease in the ignition delay time. The generation of atoms, radicals and excited and charged particles by the discharge was numerically described. The role of different atoms and radicals (O, H and CnH2n 1) was analyzed. The temporal evolution of the densities of intermediate components in the plasma assisted ignition was discussed. (10.1016/j.proci.2008.06.124)
DOI : 10.1016/j.proci.2008.06.124
Simulation of the ignition of a methane-air mixture by a high-voltage nanosecond discharge
- Aleksandrov N.L.
- Kindysheva S.V.
- Kukaev E. N.
- Starikovskaia Svetlana
- Starikovskii A.Yu.
Fizika Plazmy / Plasma Physics Reports, MAIK Nauka/Interperiodica, 2009, 35 (10), pp.867-882. The ignition dynamics of a CH4: O2: N2: Ar = 1: 4: 15: 80 mixture by a high-voltage nanosecond discharge is simulated numerically with allowance for experimental data on the dynamics of the discharge current and discharge electric field. The calculated induction time agrees well with experimental data. It is shown that active particles produced in the discharge at a relatively low deposited energy can reduce the induction time by two orders of magnitude. Comparison of simulation results for mixtures with and without nitrogen shows that addition of nitrogen to the mixture leads to a decrease in the average electron energy in the discharge and gives rise to new mechanisms for accumulation of oxygen atoms due to the excitation of nitrogen electronic states and their subsequent quenching in collisions with oxygen molecules. Acceleration of the discharge-initiated ignition is caused by a faster initiation of chain reactions due to the production of active particles, first of all oxygen atoms, in the discharge. (10.1134/S1063780X09100109)
DOI : 10.1134/S1063780X09100109

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