Abstract

Laser-induced fluorescence of the Balmer–alpha (Hα) transition of atomic hydrogen was performed within the nozzle of a 1-kW class radiatively cooled arcjet thruster operating on hydrogen and synthesized-hydrazine propellants. Axial velocities were determined from the Doppler shift of the Hα line center relative to a stationary reference, whereas translational temperatures and electron number densities were determined from a line-shape analysis of the Hα transition. The results are compared with a numerical model and indicate excellent agreement with the velocities, as well as temperatures near the nozzle exit. There are discrepancies, however, in the temperatures far upstream of the exit and in the electron densities, suggesting needed improvements in the modeling of the recombination chemistry.

© 1998 Optical Society of America

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References

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  1. J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993).
    [CrossRef] [PubMed]
  2. W. M. Ruyten, D. Keefer, “Two-beam multiplexed laser-induced fluorescence measurements of an argon arcjet plume,” AIAA J. 31, 2083–2089 (1993).
    [CrossRef]
  3. J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
    [CrossRef]
  4. J. A. Pobst, I. J. Wysong, R. A. Spores, “Laser induced fluorescence of ground state hydrogen atoms at nozzle exit of an arcjet thruster,” AIAA-95-1973, 26th AIAA Plasmadynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, New York, 1995).
  5. D. M. Zube, R. M. Myers, “Thermal nonequilibrium in a low power arcjet nozzle,” J. Propuls. Power 9, 545–552 (1993).
    [CrossRef]
  6. W Hargus, M Micci, R Spores, “Interior spectroscopic investigation of the propellant energy modes in an arcjet nozzle,” Paper AIAA-94-3302, AIAA/ASME/SAE/ASEE 30th Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).
  7. H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
    [CrossRef]
  8. P. V. Storm, M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma—I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996).
    [CrossRef]
  9. M. A. Cappelli, P. V. Storm, “Interior plasma diagnostics of arcjet thrusters,” J. Propuls Power 12, 1070–1076 (1996).
    [CrossRef]
  10. P. V. Storm, M. A. Cappelli, “Fluorescence velocity measurements in the interior of a hydrogen arcjet nozzle,” AIAA J. 34, 853–855 (1996).
    [CrossRef]
  11. G. W. Butler, A. E. Kull, D. Q. King, “Single fluid simulations of low power hydrogen arcjets,” Paper AIAA-94-2870, 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).
  12. H. A. Bethe, E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer-Verlag, Berlin, 1957) Sec. 64, p. 274.
  13. H. R. Griem, Spectral Line Broadening by Plasmas (Academic, London, 1974).
  14. D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
    [CrossRef] [PubMed]
  15. H. Ehrich, D. E. Kelleher, “Experimental investigation of plasma-broadened hydrogen Balmer lines at low electron densities,” Phys. Rev. A 21, 319–334 (1980).
    [CrossRef]
  16. P. V. Storm, M. A. Cappelli, “LIF characterization of arcjet nozzle flows,” Paper AIAA-96-2987, 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1996).
  17. P. V. Storm, M. A. Cappelli, “Laser-induced fluorescence measurements within an arcjet thruster nozzle,” Paper AIAA-95-2381, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1995).
  18. M. Mitchner, C. H. Kruger, Partially Ionized Gases (Wiley, New York, 1973).

1996 (4)

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma—I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996).
[CrossRef]

M. A. Cappelli, P. V. Storm, “Interior plasma diagnostics of arcjet thrusters,” J. Propuls Power 12, 1070–1076 (1996).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Fluorescence velocity measurements in the interior of a hydrogen arcjet nozzle,” AIAA J. 34, 853–855 (1996).
[CrossRef]

1994 (1)

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
[CrossRef]

1993 (3)

D. M. Zube, R. M. Myers, “Thermal nonequilibrium in a low power arcjet nozzle,” J. Propuls. Power 9, 545–552 (1993).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993).
[CrossRef] [PubMed]

W. M. Ruyten, D. Keefer, “Two-beam multiplexed laser-induced fluorescence measurements of an argon arcjet plume,” AIAA J. 31, 2083–2089 (1993).
[CrossRef]

1988 (1)

D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
[CrossRef] [PubMed]

1980 (1)

H. Ehrich, D. E. Kelleher, “Experimental investigation of plasma-broadened hydrogen Balmer lines at low electron densities,” Phys. Rev. A 21, 319–334 (1980).
[CrossRef]

Andoh, Y.

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

Bethe, H. A.

H. A. Bethe, E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer-Verlag, Berlin, 1957) Sec. 64, p. 274.

Butler, G. W.

G. W. Butler, A. E. Kull, D. Q. King, “Single fluid simulations of low power hydrogen arcjets,” Paper AIAA-94-2870, 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Cappelli, M. A.

P. V. Storm, M. A. Cappelli, “Fluorescence velocity measurements in the interior of a hydrogen arcjet nozzle,” AIAA J. 34, 853–855 (1996).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma—I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996).
[CrossRef]

M. A. Cappelli, P. V. Storm, “Interior plasma diagnostics of arcjet thrusters,” J. Propuls Power 12, 1070–1076 (1996).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993).
[CrossRef] [PubMed]

P. V. Storm, M. A. Cappelli, “LIF characterization of arcjet nozzle flows,” Paper AIAA-96-2987, 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1996).

P. V. Storm, M. A. Cappelli, “Laser-induced fluorescence measurements within an arcjet thruster nozzle,” Paper AIAA-95-2381, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

Ehrich, H.

H. Ehrich, D. E. Kelleher, “Experimental investigation of plasma-broadened hydrogen Balmer lines at low electron densities,” Phys. Rev. A 21, 319–334 (1980).
[CrossRef]

Greene, R. L.

D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
[CrossRef] [PubMed]

Griem, H. R.

H. R. Griem, Spectral Line Broadening by Plasmas (Academic, London, 1974).

Hanson, R. K.

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993).
[CrossRef] [PubMed]

Hargus, W

W Hargus, M Micci, R Spores, “Interior spectroscopic investigation of the propellant energy modes in an arcjet nozzle,” Paper AIAA-94-3302, AIAA/ASME/SAE/ASEE 30th Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Keefer, D.

W. M. Ruyten, D. Keefer, “Two-beam multiplexed laser-induced fluorescence measurements of an argon arcjet plume,” AIAA J. 31, 2083–2089 (1993).
[CrossRef]

Kelleher, D. E.

D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
[CrossRef] [PubMed]

H. Ehrich, D. E. Kelleher, “Experimental investigation of plasma-broadened hydrogen Balmer lines at low electron densities,” Phys. Rev. A 21, 319–334 (1980).
[CrossRef]

King, D. Q.

G. W. Butler, A. E. Kull, D. Q. King, “Single fluid simulations of low power hydrogen arcjets,” Paper AIAA-94-2870, 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Komiko, K.

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

Kruger, C. H.

M. Mitchner, C. H. Kruger, Partially Ionized Gases (Wiley, New York, 1973).

Kull, A. E.

G. W. Butler, A. E. Kull, D. Q. King, “Single fluid simulations of low power hydrogen arcjets,” Paper AIAA-94-2870, 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Liebeskind, J. G.

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Laser-induced fluorescence diagnostic for temperature and velocity measurements in a hydrogen arcjet plume,” Appl. Opt. 32, 6117–6127 (1993).
[CrossRef] [PubMed]

Micci, M

W Hargus, M Micci, R Spores, “Interior spectroscopic investigation of the propellant energy modes in an arcjet nozzle,” Paper AIAA-94-3302, AIAA/ASME/SAE/ASEE 30th Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Mitchner, M.

M. Mitchner, C. H. Kruger, Partially Ionized Gases (Wiley, New York, 1973).

Myers, R. M.

D. M. Zube, R. M. Myers, “Thermal nonequilibrium in a low power arcjet nozzle,” J. Propuls. Power 9, 545–552 (1993).
[CrossRef]

Oza, D. H.

D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
[CrossRef] [PubMed]

Pobst, J. A.

J. A. Pobst, I. J. Wysong, R. A. Spores, “Laser induced fluorescence of ground state hydrogen atoms at nozzle exit of an arcjet thruster,” AIAA-95-1973, 26th AIAA Plasmadynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

Ruyten, W. M.

W. M. Ruyten, D. Keefer, “Two-beam multiplexed laser-induced fluorescence measurements of an argon arcjet plume,” AIAA J. 31, 2083–2089 (1993).
[CrossRef]

Salpeter, E. E.

H. A. Bethe, E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer-Verlag, Berlin, 1957) Sec. 64, p. 274.

Spores, R

W Hargus, M Micci, R Spores, “Interior spectroscopic investigation of the propellant energy modes in an arcjet nozzle,” Paper AIAA-94-3302, AIAA/ASME/SAE/ASEE 30th Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

Spores, R. A.

J. A. Pobst, I. J. Wysong, R. A. Spores, “Laser induced fluorescence of ground state hydrogen atoms at nozzle exit of an arcjet thruster,” AIAA-95-1973, 26th AIAA Plasmadynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

Storm, P. V.

P. V. Storm, M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma—I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996).
[CrossRef]

M. A. Cappelli, P. V. Storm, “Interior plasma diagnostics of arcjet thrusters,” J. Propuls Power 12, 1070–1076 (1996).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Fluorescence velocity measurements in the interior of a hydrogen arcjet nozzle,” AIAA J. 34, 853–855 (1996).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Laser-induced fluorescence measurements within an arcjet thruster nozzle,” Paper AIAA-95-2381, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

P. V. Storm, M. A. Cappelli, “LIF characterization of arcjet nozzle flows,” Paper AIAA-96-2987, 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1996).

Tahara, H.

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

Wysong, I. J.

J. A. Pobst, I. J. Wysong, R. A. Spores, “Laser induced fluorescence of ground state hydrogen atoms at nozzle exit of an arcjet thruster,” AIAA-95-1973, 26th AIAA Plasmadynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

Yonezawa, T.

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

Yoshikawa, T.

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

Zube, D. M.

D. M. Zube, R. M. Myers, “Thermal nonequilibrium in a low power arcjet nozzle,” J. Propuls. Power 9, 545–552 (1993).
[CrossRef]

AIAA J. (3)

W. M. Ruyten, D. Keefer, “Two-beam multiplexed laser-induced fluorescence measurements of an argon arcjet plume,” AIAA J. 31, 2083–2089 (1993).
[CrossRef]

J. G. Liebeskind, R. K. Hanson, M. A. Cappelli, “Experimental investigation of velocity slip near an arcjet exit plane,” AIAA J. 33, 373–375 (1994).
[CrossRef]

P. V. Storm, M. A. Cappelli, “Fluorescence velocity measurements in the interior of a hydrogen arcjet nozzle,” AIAA J. 34, 853–855 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Plasma Sci. (1)

H. Tahara, K. Komiko, T. Yonezawa, Y. Andoh, T. Yoshikawa, “Thermodynamic nonequilibrium nitrogen plasmas in a direct-current arcjet engine nozzle,” IEEE Trans. Plasma Sci. 24, 218–225 (1996).
[CrossRef]

J. Propuls Power (1)

M. A. Cappelli, P. V. Storm, “Interior plasma diagnostics of arcjet thrusters,” J. Propuls Power 12, 1070–1076 (1996).
[CrossRef]

J. Propuls. Power (1)

D. M. Zube, R. M. Myers, “Thermal nonequilibrium in a low power arcjet nozzle,” J. Propuls. Power 9, 545–552 (1993).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

P. V. Storm, M. A. Cappelli, “Radiative emission analysis of an expanding hydrogen arc plasma—I. Arc region diagnostics through axial emission,” J. Quant. Spectrosc. Radiat. Transfer 56, 901–918 (1996).
[CrossRef]

Phys. Rev. A (2)

D. H. Oza, R. L. Greene, D. E. Kelleher, “Collisional broadening of the Balmer-α transition of H and He+ in plasmas,” Phys. Rev. A 37, 531–536 (1988).
[CrossRef] [PubMed]

H. Ehrich, D. E. Kelleher, “Experimental investigation of plasma-broadened hydrogen Balmer lines at low electron densities,” Phys. Rev. A 21, 319–334 (1980).
[CrossRef]

Other (8)

P. V. Storm, M. A. Cappelli, “LIF characterization of arcjet nozzle flows,” Paper AIAA-96-2987, 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1996).

P. V. Storm, M. A. Cappelli, “Laser-induced fluorescence measurements within an arcjet thruster nozzle,” Paper AIAA-95-2381, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

M. Mitchner, C. H. Kruger, Partially Ionized Gases (Wiley, New York, 1973).

G. W. Butler, A. E. Kull, D. Q. King, “Single fluid simulations of low power hydrogen arcjets,” Paper AIAA-94-2870, 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

H. A. Bethe, E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer-Verlag, Berlin, 1957) Sec. 64, p. 274.

H. R. Griem, Spectral Line Broadening by Plasmas (Academic, London, 1974).

W Hargus, M Micci, R Spores, “Interior spectroscopic investigation of the propellant energy modes in an arcjet nozzle,” Paper AIAA-94-3302, AIAA/ASME/SAE/ASEE 30th Joint Propulsion Conference (American Institute of Aeronautics and Astronautics, New York, 1994).

J. A. Pobst, I. J. Wysong, R. A. Spores, “Laser induced fluorescence of ground state hydrogen atoms at nozzle exit of an arcjet thruster,” AIAA-95-1973, 26th AIAA Plasmadynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, New York, 1995).

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Figures (11)

Fig. 1
Fig. 1

Energy-level diagram of the atomic hydrogen n = 2 and n = 3 states showing the spin-orbit splitting and the allowable transitions constituting the Hα spectral line.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup.

Fig. 3
Fig. 3

Schematic cross section of the 1-kW arcjet thruster nozzle. All the dimensions are in millimeters. The cross hatching indicates the positions where the measurements were taken.

Fig. 4
Fig. 4

Typical LIF scan of the Hα transition at the arcjet exit-plane center line, obtained by piecing together three overlapping 30-GHz scans. Also shown is the best-fit line shape consisting of a sum of five Voigt functions.

Fig. 5
Fig. 5

Fluorescence saturation behavior at the arcjet exit-plane center line.

Fig. 6
Fig. 6

Center-line axial velocity in the arcjet nozzle plotted in nondimensional form.

Fig. 7
Fig. 7

Comparison of the modeled and measured axial velocities along the nozzle center line with hydrogen propellant at a mass flow rate of 14.2 mg/s and an arcjet power of 1.4 kW. The model results are from Ref. 11.

Fig. 8
Fig. 8

Radial profiles of axial velocity at three axial locations within the hydrogen nozzle at the same conditions as in Fig. 7. The dashed curves give the results of the arcjet model described in Ref. 11.

Fig. 9
Fig. 9

Comparison of axial velocity along the arcjet nozzle center line for hydrogen and synthesized-hydrazine propellants at an arcjet power of 1.2 kW.

Fig. 10
Fig. 10

Comparison of plasma translational temperature along the arcjet nozzle center line for hydrogen and synthesized-hydrazine propellants at an arcjet power of 1.2 kW.

Fig. 11
Fig. 11

Comparison of plasma-electron number density along the arcjet nozzle center line for hydrogen and synthesized-hydrazine propellants at an arcjet power of 1.2 kW.

Tables (2)

Tables Icon

Table 1 Components of the Hα Transition and Their Propertiesa

Tables Icon

Table 2 Summary of Arcjet Operating Conditions, Laser Scan Ranges, and Measurements

Equations (8)

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N p nV η   Ω 4 π A ul A ul + Q u   B lu , λ   Φ λ I laser ,
I sat = π 2   Δ λ   g u g u + g l A ul + Q u B lu , λ ,
Δ λ D FWHM = λ 0 8 kT   ln 2 mc 2 1 / 2 ,
log   Δ λ S FWHM = 0.0272   n e 0.090 - 3.29 ,
u c = Δ λ 0 λ 0 , ref ,
m ˙ h i + P = m ˙ h e + 1 2   u e 2 ,
u e = 2 P / m ˙ 1 / 2 .
σ SH = 1.53 × 10 - 2 T e 3 / 2 ln   Λ ,

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