Elastic electron scattering and rovibrational excitation of N<sub>2</sub>at low incident energies

A model for the electron-vibration energy exchange in nitrogen based on a Landau-Teller-type rate equation is presented. Analytical expressions of relaxation times are derived for cutoff harmonic oscillator and Morse oscillator approximations, assuming that the relaxation proceeds by way of a continuous series of Boltzmann distributions over the vibrational states. Comparisons with the direct numerical integration of the master equation have shown that the use of a two-temperature relaxation time allows accurate modeling of the nitrogen vibrational energy relaxation rate for various conditions encountered in high-enthalpy ows with electron and vibrational temperatures up to 40,000 K. Nomenclature a = constant in the analytical expression of rate coef cients for v > 0 ! w > v transitions dE n v / dt = nondimensionalvibrational energy relaxation rate E v = vibrational energy per unit volume, J/m 3 E ¤ v = vibrational energy calculated with vibrational levels in Boltzmann equilibrium at the electron temperature T e , J/m 3 E v, init = vibrational energy at 0-s time, J/m 3 J = rotational quantum number k B = Boltzmann constant, J/K k v,w = electron-vibration(E-V) rate coef cient of the v ! w transition, m 3 /s N t = total N 2 number density, N v , m ¡ 3 N v = number density of the vibrational level v of N 2 , m ¡ 3 n e = electron number density, m ¡ 3 p e = electron partial pressure, n e k B T e , atm T e = electron temperature, K T v , T exci = vibrational temperature, K t = time, s t n = nondimensionaltime v m = total number of excited vibrational levels D ² = constant of the Morse oscillator, cm ¡ 1 ²(v) = energy of the vibrational level v of N 2 , J ² 1 = energy of the rst vibrational level of N 2 , J r v, w = E-V cross section of the v ! w transition, m 2 s e = E-V relaxation time, s Supercripts HO = truncated harmonic oscillator MO = Morse oscillator

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“…In this case, the number density of a vibrational level w is given by Eq. (11) and the vibrational energy of the system at a given t is…”

Section: B Anharmonic Casementioning

confidence: 99%

“…By the use of Eq (11). and the expressions of E v (t ) and E ¤ v (T e ), the rate of change of the vibrational energy [Eq.…”

mentioning

confidence: 99%

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

Bourdon

Vervisch

2000

Journal of Thermophysics and Heat Transfer

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“…[56], Brennan et al. [57], and Shi, Stephen, and Burrow [58]; comparisons of 1050-2947/95/52(2)/1229{28)/$06. 00 1229 Qc1995 The American Physical Society the data from many of these experiments appear in the latter two papers.…”

Section: Intrqductiqnmentioning

confidence: 99%

Detailed theoretical and experimental analysis of low-energy electron-N2scattering

et al. 1995

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We have carried out a comprehensive theoretical and experimental study of electron scattering from molecular nitrogen at energies below 10.0 eV. In the theoretical component of this project we have generated differential and integral cross sections for elastic scattering and vibrational excitation in converged vibrational close-coupling calculations. In the experiments, we have measured dift'erential cross sections for these processes at scattering angles from 20' to 130 in a crossed-beam experiment at a large number of energies between 0.55 and 10 eV and, in a complementary time-of-Right experiment, total cross sections at energies between 0.08 and 10.0 eV. The measured angular distributions have been extrapolated to 0 and 180 using a procedure based on a nonlinear least-squares fit constrained by known physical properties of the e-Nz scattering matrix; numerical integration of the resulting extrapolated distributions yields integrated cross sections with almost no error beyond that inherent in the measured angular data. We find generally good agreement between the present experimental and theoretical cross section, particularly at energies near the H~r esonance near 2.39 eV. In previous studies of scattering in this region, such comparisons have been made problematical by the difhculty of ascertaining the appropriate theoretical scattering energy. We recommend here a protocol for resolving this problem for both elastic scattering and vibrational excitation.PACS number(s): 34.80.6s

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“…The discussion given in these papers showed that the positions and shapes of resonant peaks in DCS depend sensitively on both the ®nal vibrational state and the scattering angle. However, the measurements of DCS by Brennan et al (1992) were performed at only a few energies and used a normalization technique which was revised by Sun et al (1995). Robertson et al (1997) used this new technique to calculate vibrational excitation cross sections of N 2 and found that their results are in excellent agreement with the cross sections derived from previous swarm analysis and crossed beam studies at energies above 1.5±1.7 eV, but not compatible with the drift velocity data at energies up to about 1 eV.…”

Section: Introductionmentioning

confidence: 97%

“…Comparisons of DCS for N 2 v 0 3 N 2 v 1 scattering from many of these experiments have been carried out by Brennan et al (1992) and Sun et al (1995). The discussion given in these papers showed that the positions and shapes of resonant peaks in DCS depend sensitively on both the ®nal vibrational state and the scattering angle.…”

Section: Introductionmentioning

confidence: 99%

New electron energy transfer rates for vibrational excitation of N<sub>2</sub>

Павлов¹

1998

Ann. Geophys.

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Abstract. In this paper we present the results of a study of the electron cooling rate, the production rates of vibrationally excited N 2 v , and the production frequency of the N 2 vibrational quanta arising from the collisions of electrons with unexcited N 2 0 and vibrationally excited N 2 1 molecules as functions of the electron temperature. The electron energy transfer rates for vibrational excitation of N 2 have been calculated and ®t to analytical expressions by use of the revised vibrationally excited N 2 cross sections. These new analytical expressions are available to the researcher for quick reference and accurate computer modeling with a minimum of calculations.

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Elastic electron scattering and rovibrational excitation of N₂at low incident energies

Cited by 44 publications

References 22 publications

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

Detailed theoretical and experimental analysis of low-energy electron-N2scattering

New electron energy transfer rates for vibrational excitation of N<sub>2</sub>

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Elastic electron scattering and rovibrational excitation of N2at low incident energies

Cited by 44 publications

References 22 publications

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

Detailed theoretical and experimental analysis of low-energy electron-N2scattering

New electron energy transfer rates for vibrational excitation of N&lt;sub&gt;2&lt;/sub&gt;

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Product

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Elastic electron scattering and rovibrational excitation of N₂at low incident energies

New electron energy transfer rates for vibrational excitation of N<sub>2</sub>