Electron – Air Molecule Collisions in Hypersonic Flows

  • Winifred M. Huo
  • Helmar T. Thümmel
Part of the NATO ASI Series book series (ASIC, volume 482)


At high vehicle velocity, the flow field surrounding a space vehicle becomes partially ionized, with the amount of ionization determined by the vehicle velocity. For a transatmospheric flight at an altitude of 80 km and a velocity of 10 km/sec, a maximum of 1% ionization is expected, whereas up to 30% of the atoms and molecules in the flow field will be ionized in a Mars return mission with a velocity of 12 – 17 km/sec. Even when the flow field is only slightly ionized, electron collisions still have an important role in determining the internal energy and state distribution of the atoms and molecules in the flow field. This in turn contributes to the flow characteristic and the amount of radiative heat load on the vehicle.


Vibrational Level Vibrational Excitation Excitation Cross Section Hypersonic Flow Dissociative Recombination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Huo, W.M. and Gianturco, F.A. (eds.) (1995) Computational Methods for Electron-Molecule Collisions, Plenum Press, New York.Google Scholar
  2. 2.
    Burke, P.G. and Berrington, K.A. (eds.) (1993) Atomic and Molecular Processes: An R-matrix Approach, Institute of Physics Publishing, Bristol.Google Scholar
  3. 3.
    A detailed description of the R-matrix method as applied to electron-molecule collisions are given in Chapters 8–14 in Ref. [1].Google Scholar
  4. 4.
    Partridge IL, Stallcop, J.R., and Levin, E. (1995) Potential energy curves and collision integrals of air components, in M. Capitelli, (ed.) Molecular Physics and Hypersonic Flows, Kluwer Academic Publishing (Dordrecht).Google Scholar
  5. 5.
    Shimamura, I. (1980) State-to-state rotational transition cross sections from unresolved energy-loss spectra, Chem. Phys. Lett. 73, 328–333.ADSCrossRefGoogle Scholar
  6. 6.
    Jackson J. L. (1951) A variational approach to nuclear reactions, Phys. Rev. 83 301–304.ADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Oberoi, R.S. and Nesbet, R.K. (1973) Variational formulation of the R-matrix method for multichannel scattering, Phys. Rev. A 8, 215–9.ADSCrossRefGoogle Scholar
  8. Oberoi, R.S. and Nesbet, R.K. (1974) Addendum to “Variational formulation of the R-matrix method for multichannel scattering”, Phys. Rev. A. 8, 2804–5.ADSCrossRefGoogle Scholar
  9. 8.
    Buttle, P.J.A. (1967) Solution of coupled equations by R-matrix techniques, Phys. Rev. A 180, 719–29.Google Scholar
  10. 9.
    Gillan, C.J., Tennyson, J., and Burke, P.G. (1995) The UK molecular R-matrix scattering package: a computational perspective, in Huo, W.M. and Gianturco, F.A. (eds.) Computational Methods for Electron-Molecule Collisions, Plenum Press, New York.Google Scholar
  11. 10.
    Morgan, L.A. (1995) Non-adiabatic effects in vibrational excitation and dissociative recombination, in Huo, W.M. and Gianturco, F.A. (eds.) Computational Methods for Electron-Molecule Collisions, Plenum Press, New York.Google Scholar
  12. Takatsuka, K. and McKoy, V. (1981) Extension of the Schwinger variational principle beyond the static-exchange approximation, Phys. Rev. A 24, 2473–2480;Google Scholar
  13. Takatsuka, K. and McKoy, V. (1984) Theory of electronically inelastic scattering of electrons by molecules, Phys. Rev. A 30, 1734–1740.ADSCrossRefGoogle Scholar
  14. 12.
    Domcke, W. (1991) Theory of resonance and threshold effects in electron-molecule collisions: the projection operator approach, Phys. Rep. 20897–188.ADSCrossRefGoogle Scholar
  15. 13.
    Feshbach, H. (1958) Unified theory of nuclear reactions, Ann. Phys. 5 357–390;MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. Feshbach, H. (1962) A unified theory of nuclear reactions, II, Ann. Phys. 19, 287–313.MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. 14.
    Rescigno, T.N., McCurdy, C.W., Orel, A.E., and Lengsfield, B.H., III (1995) The complex Kohn variational method, in Huo, W.M. and Gianturco, F.A. (eds.) Computational Methods for Electron-Molecule Collisions, Plenum Press, New York.Google Scholar
  18. 15.
    Rescigno, T.N., Lengsfield, B.H. III, and McCurdy, C.W. (1995) in Yarkony, D.R., (ed.) Modern Electronic Structure Theory, Part I, World Scientific, Singapore.Google Scholar
  19. 16.
    Abramowitz, M. and Stegun, I (1965) Handbook of Mathematical Functions, Dover, New York.Google Scholar
  20. 17.
    Heisenberg, A. (1984) Vibrational excitation of molecules by slow electrons, in Shimamura, I. and Takayanagi, K. (eds.) Electron-Molecule Collisions, Plenum Press, New York.Google Scholar
  21. 18.
    Lofthus, A. and Krupenie, P.H. (1977) The spectrum of molecular nitrogen, J. Phys. Chem. Ref. Data 8, 113–307.ADSCrossRefGoogle Scholar
  22. 19.
    Huo, W.M., Lima, M.A.P., Gibson, T.L., and McKoy, V. (1987) Correlation effects in elastic e-N2 scattering, Phys. Rev. A 38, 1642–1648.ADSCrossRefGoogle Scholar
  23. 20.
    Kennerly, R.E. (1980) Absolute total electron scattering cross sections for N2 between 0.5 and 50 eV, Phys. Rev. A 21, 1876–1883.ADSCrossRefGoogle Scholar
  24. 21.
    Weatherford, C.A. and Temkin, A. (1994) Completion of a hybrid theory calculation of the Hs resonance in electron-N2 scattering, Phys. Rev. A 49, 2580–2586.ADSCrossRefGoogle Scholar
  25. 22.
    Gillan, C.J., Nagy, O., Burke, P.G., Morgan, L.A., and Noble, C.J. (1987) J. Phys. B 20, 4585.ADSCrossRefGoogle Scholar
  26. 23.
    Allan, M. (1985) Excitation of vibrational levels up to y = 17 in N2 by electron impact in the 0–5 eV region J. Phys. B 18, 4511–4517.ADSCrossRefGoogle Scholar
  27. 24.
    Jung, K., Antoni, Th., Müller, R., Kochum, K.-H., and Ehrhardt, H. (1982) Rotational excitation of N2, CO, and H2O by low-energy electron collisions, J. Phys. B 15, 3535–3555.ADSCrossRefGoogle Scholar
  28. 25.
    Huo, W.M., Gibson, T.L., Lima, M.A.P., and McKoy, V. (1987) Schwinger multichannel study of the ens shape resonance in N2, Phys. Rev. A 36, 1632–1641.ADSCrossRefGoogle Scholar
  29. 26.
    Morgan, L.A., (1986) Resonant vibrational excitation of N2 by low-energy electron impact, J. Phys. B 19, L439.ADSCrossRefGoogle Scholar
  30. 27.
    Huo, W.M., McKoy, V., Lima, M.A.P., and Gibson, T.L. (1986) Electron-nitrogen molecule collisions in high-temperature nonequilibrium air, in Moss J.N. and Scott, C.D. (eds.) Thermophysical Aspects of Re-entry Flows, AIAA, New York.Google Scholar
  31. 28.
    Krupenie, P. H. (1972) The spectrum of molecular oxygen, J. Phys. Chem. Ref. Data 1, 423–534.CrossRefGoogle Scholar
  32. 29.
    Higgins, K., Gillan, C.J., Burke, P.G., and Noble, C.J.. (1995) Low-energy electron scattering by oxygen molecules: II. vibrational excitation, J. Phys. B 28, 3391–3402.ADSCrossRefGoogle Scholar
  33. 30.
    Linder, F. and Schmidt, H. (1971) Experimental study of low energy e-Oz collision processes, Z. Naturf. 26a, 1617–1625.ADSGoogle Scholar
  34. 31.
    Land, J.E., and Raith, W. (1974) Phys. Rev. A 9, 1592–1602.ADSCrossRefGoogle Scholar
  35. 32.
    Parlant, G. and Fiquet-Fayard, F. (1976) The O; 2H, resonance: theoretical analysis of electron scattering data, J. Phys. B 9, 1617–1628.ADSCrossRefGoogle Scholar
  36. 33.
    Fiquet-Fayard, F. (1975) Angular distributions for pure resonant scattering of electrons by diatomic molecules in Hund’s cases a and bGoogle Scholar
  37. 34.
    Wigner, E.P. (1948) On the behavior of cross sections near thresholds, Phys. Rev. 73, 1002–1009.ADSzbMATHCrossRefGoogle Scholar
  38. Wigner, E.P. (1948) On the behavior of cross sections near thresholds J. Phys. B 8, 2880–2897.MathSciNetGoogle Scholar
  39. 35.
    Field, D., Mrotzek, G., Knight, D.W., Lunt, S., and Ziesel, J.P. (1988) High-resolution studies of electron scattering by molecular oxygen, J. Phys. B 21, 171–188.ADSCrossRefGoogle Scholar
  40. 36.
    This value is determined from the SMC cross sections at J = 0 [27].Google Scholar
  41. 37.
    Spence, D. and Schulz, G.J. (1971) Phys. Rev. 3, 1968–76.ADSGoogle Scholar
  42. 38.
    Tronc, M., Huets, A., Landau, M. Pichou, F. and Reinhardt, J. (1975) Resonant vibrational excitation of the NO ground state by electron impact in the 0.1–3 eV energy range, J. Phys. B 8, 1160–9.ADSCrossRefGoogle Scholar
  43. 39.
    Teillet-Billy, D. and Fiquet-Fayard, F. (1977) The NO- 3Σ- and 1Δ resonances: theoretical analysis of electron scattering data, J. Phys. B 10, L111–117.ADSCrossRefGoogle Scholar
  44. 40.
    Tennyson, J. and Noble, C.J. (1986) Low-energy electron scattering by the NO molecule, J. Phys. B 19, 4025–4033.ADSCrossRefGoogle Scholar
  45. 41.
    This value is attributed to J. Reinhardt (1976) in Ref. [39].Google Scholar
  46. 42.
    Morgan, L.A. and Gillan, C.J. (1995) Low energy electron scattering by NO, in Mitchell, J.B.A., McConkey, J.W., and Brion, C.E., XIX ICPEAC Scientific Program and Abstracts of Contributed Papers, Whistler, Canada (1995).Google Scholar
  47. 43.
    Itikawa, Y. (1994) Electron collisions with N2, O2, and O: what we know and do not know, in Inokuti, M. (ed.) Advances in Atomic, Molecular, and Optical Physics Vol. 33, Cross Section Data, Academic Press (Boston).Google Scholar
  48. 44.
    Huo, W. (1990) Electron collisions cross sections involving excited states, in Capitelli, M. and Bardsley, J.N., (eds.) Nonequilibrium Processes in Partially Ionized Gases, Plenum, New York.Google Scholar
  49. 45.
    Cartwright, D.C., Trajmar, S., Chutjian, A., and Williams, W., (1977) Electron impact excitation of the electronic states of N2. II. Integral cross sections at incident energies from 10 to 50 eV. Phys. Rev. A 16, 1041–1051.ADSCrossRefGoogle Scholar
  50. 46.
    Trajmar, S., Register, D.F., and Chutjian, A., (1983) Electron scattering by molecules II. experimental methods and data, Phys. Rep. 97, 219–356.ADSCrossRefGoogle Scholar
  51. 47.
    Schappe, R.S., Schulman, M.B., Anderson, L.W., and Lin, C.C. (1994) Measurements of cross sections for electron-impact excitation into the metastable levels of argon and number densities of metastable argon atoms, Phys. Rev. A 50, 444–461.ADSCrossRefGoogle Scholar
  52. 48.
    Nobel, C.J. and Burke, P.G. (1992) R-matrix calculations of low-energy electron scattering by oxygen molecules, Phys. Rev. Lett. 68, 2011–2014.ADSCrossRefGoogle Scholar
  53. 49.
    Trajmar, S., Cartwright, D.C., and Williams, W. (1971) Differential and integral cross sections for the electron-impact excitation of the a’ A, and b’ E9 states of 02. Phys. Rev. A 4, 1482–1492.ADSCrossRefGoogle Scholar
  54. 50.
    Doering, J.P. (1992) Absolute differential and integral electron excitation cross sections for the O2 (alΔ g, ← X3Σg-) transition, J. Geophys. Res. 97, 12267–12270.ADSCrossRefGoogle Scholar
  55. 51.
    Middleton, A.G., Teubner, P.J.O., and Brunger, M.J. (1992) Experimental confirmation for resonance enhancement in the electron impact excitation cross sections of the a1Δ g, and b1Σg+ electronic states of O2, Phys. Rev. Lett. 892495–2498.ADSCrossRefGoogle Scholar
  56. 52.
    While curve crossing is considered the DR mechanism for N2+, O2+, and NO, DR can also proceed without curve crossing. See Sarpal, B.K, Tennyson, J, and Morgan, L.A., Dissociative recombination without curve crossing: study of HeH+, J. Phys. B 27, 5943–5953.Google Scholar
  57. See also Guberman, S.L. (1994) Dissociative recombination without a curve crossing, Phys. Rev. A 49, R4277–4280.ADSCrossRefGoogle Scholar
  58. 53.
    Johnsen, R. (1989) Recombination measurements of microwave discharge plasma afterglows, in Mitchell, J.B.A. and Guberman, S.L. (eds) Dissociative Recombination: Theory, Experiment, and Applications, World Scientific, Singapore.Google Scholar
  59. 54.
    Noren, C., Yousif, F.B., and Mitchell, J.B.A. (1989) The dissociative recombination and excitation of N2+ J. Chem. Soc. Faraday Trans. 285, 1697.Google Scholar
  60. 55.
    Guberman, S.L. and Giusti-Suzor, A. (1991) The generation of O(1S) from the dissociative recombination of O2+. J. Chem. Phys. 95, 2602–2613.ADSCrossRefGoogle Scholar
  61. 56.
    Guberman, S.L. (1991) Dissociative recombination of the ground state of N2+, Geophys. Research Lett. 18, 1051–1054.ADSCrossRefGoogle Scholar
  62. 57.
    Guberman, S.L. (1988) The production of O(1D)from dissociative recombination of O2+, Planet. SpaceSci. 36, 47–52.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Winifred M. Huo
    • 1
  • Helmar T. Thümmel
    • 1
  1. 1.NASA Ames Research CenterMoffett FieldUSA

Personalised recommendations