Abstract

The heating of a laser-irradiated solid aluminum particle to boiling or to temperatures that exceed boiling is analyzed theoretically and numerically by solution of the heat-transport equation. Two different criteria of particle destruction are considered. The temperature distributions inside the particles depending on the intensity values and particle sizes are presented. It is shown that at the start of heating the contribution of heat exchange plays the dominant role, but as the boiling point is approached the contribution of vaporization plays the main role.

© 1996 Optical Society of America

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References

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  1. V. A. Besprozvanyich, V. A. Ermakov, A. A. Razdobreev, “The explosion of metallic particles in the field of laser radiation,” in The Combustion of Heterogeneous and Gaseous Systems, Proceedings of the Eighth All-Union Symposium on Combustion and Explosion (Ob’yedineny Institut Chimicheskoy Fiziki AN SSSR, Chernogolovka, USSR, 1986), pp. 58–62.
  2. A. V. Baranov, I. L. Klukach, S.A. Ubogov, “Laser heating of small metallic particles in inert gas,” in Interaction of Radiation with Material, A. Yglov, ed. (Kuibyishev Gosuniversitet, Kuibyishev, Russia, 1988), pp. 106–115.
  3. D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
    [CrossRef]
  4. R. L. Armstrong, A. Zardecki, “Propagation of high energy laser beams through metallic aerosols,” Appl. Opt. 29, 1786–1792 (1990).
    [CrossRef] [PubMed]
  5. V. K. Pustovalov, D. S. Bobuchenko, “Heating, evaporation and combustion of a solid aerosol particles in a gas exposed to optical radiation,” Int. J. Heat Mass Transfer 3, 3–17 (1989).
    [CrossRef]
  6. L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).
  7. L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).
  8. L. G. Astafieva, A. P. Prishivalko, “Heating of solid aluminium particles by intense laser radiation with λ = 0.53 μm,” Metallofizika 13, 122–126 (1991).
  9. L. G. Astafieva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh. Fiz. J. 66, 340–344 (1994).
  10. E. M. Lifshitch, L. P. Pitaevski, Physical Kinetics (Nauka, Moscow, 1979).
  11. S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).
  12. B. S. Park, R. L. Armstrong, “Laser droplet heating: fast and slow heating regimes,” Appl. Opt. 28, 3671–3680 (1989).
    [CrossRef] [PubMed]
  13. A. V. Burmistrov, “About role of bubble during interaction of high intense flux of energy with medium,” J. Appl. Mech. Theoret. Physics 3, 35–44 (1979).
  14. J. E. Hatch, ed., Aluminium Properties and Physical Metallo-conduct Handbook (Metalurgiya, Moscow, 1989).
  15. H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
    [CrossRef]
  16. F. W. Dabby, U.-C. Paek, “High-intensity laser-induced vaporization and explosion of solid material,” IEEE J. Quantum Electron. QE-8, 106–111 (1972).
    [CrossRef]
  17. G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
    [CrossRef]

1994 (1)

L. G. Astafieva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh. Fiz. J. 66, 340–344 (1994).

1992 (1)

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).

1991 (2)

L. G. Astafieva, A. P. Prishivalko, “Heating of solid aluminium particles by intense laser radiation with λ = 0.53 μm,” Metallofizika 13, 122–126 (1991).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).

1990 (2)

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

R. L. Armstrong, A. Zardecki, “Propagation of high energy laser beams through metallic aerosols,” Appl. Opt. 29, 1786–1792 (1990).
[CrossRef] [PubMed]

1989 (2)

V. K. Pustovalov, D. S. Bobuchenko, “Heating, evaporation and combustion of a solid aerosol particles in a gas exposed to optical radiation,” Int. J. Heat Mass Transfer 3, 3–17 (1989).
[CrossRef]

B. S. Park, R. L. Armstrong, “Laser droplet heating: fast and slow heating regimes,” Appl. Opt. 28, 3671–3680 (1989).
[CrossRef] [PubMed]

1986 (1)

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

1984 (1)

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

1979 (1)

A. V. Burmistrov, “About role of bubble during interaction of high intense flux of energy with medium,” J. Appl. Mech. Theoret. Physics 3, 35–44 (1979).

1972 (1)

F. W. Dabby, U.-C. Paek, “High-intensity laser-induced vaporization and explosion of solid material,” IEEE J. Quantum Electron. QE-8, 106–111 (1972).
[CrossRef]

Alexander, D. R.

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

Anisimov, S.

S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).

Armstrong, R. L.

Astafieva, L. G.

L. G. Astafieva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh. Fiz. J. 66, 340–344 (1994).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).

L. G. Astafieva, A. P. Prishivalko, “Heating of solid aluminium particles by intense laser radiation with λ = 0.53 μm,” Metallofizika 13, 122–126 (1991).

Baranov, A. V.

A. V. Baranov, I. L. Klukach, S.A. Ubogov, “Laser heating of small metallic particles in inert gas,” in Interaction of Radiation with Material, A. Yglov, ed. (Kuibyishev Gosuniversitet, Kuibyishev, Russia, 1988), pp. 106–115.

Barton, J. P.

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

Besprozvanyich, V. A.

V. A. Besprozvanyich, V. A. Ermakov, A. A. Razdobreev, “The explosion of metallic particles in the field of laser radiation,” in The Combustion of Heterogeneous and Gaseous Systems, Proceedings of the Eighth All-Union Symposium on Combustion and Explosion (Ob’yedineny Institut Chimicheskoy Fiziki AN SSSR, Chernogolovka, USSR, 1986), pp. 58–62.

Bobuchenko, D. S.

V. K. Pustovalov, D. S. Bobuchenko, “Heating, evaporation and combustion of a solid aerosol particles in a gas exposed to optical radiation,” Int. J. Heat Mass Transfer 3, 3–17 (1989).
[CrossRef]

Burmistrov, A. V.

A. V. Burmistrov, “About role of bubble during interaction of high intense flux of energy with medium,” J. Appl. Mech. Theoret. Physics 3, 35–44 (1979).

Dabby, F. W.

F. W. Dabby, U.-C. Paek, “High-intensity laser-induced vaporization and explosion of solid material,” IEEE J. Quantum Electron. QE-8, 106–111 (1972).
[CrossRef]

Dreehsen, H. G.

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

Ermakov, V. A.

V. A. Besprozvanyich, V. A. Ermakov, A. A. Razdobreev, “The explosion of metallic particles in the field of laser radiation,” in The Combustion of Heterogeneous and Gaseous Systems, Proceedings of the Eighth All-Union Symposium on Combustion and Explosion (Ob’yedineny Institut Chimicheskoy Fiziki AN SSSR, Chernogolovka, USSR, 1986), pp. 58–62.

Hartwich, C.

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

Imas, Ya.

S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).

Khodyko, Yu.

S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).

Klukach, I. L.

A. V. Baranov, I. L. Klukach, S.A. Ubogov, “Laser heating of small metallic particles in inert gas,” in Interaction of Radiation with Material, A. Yglov, ed. (Kuibyishev Gosuniversitet, Kuibyishev, Russia, 1988), pp. 106–115.

Leiko, S. T.

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).

Lifshitch, E. M.

E. M. Lifshitch, L. P. Pitaevski, Physical Kinetics (Nauka, Moscow, 1979).

Paek, U.-C.

F. W. Dabby, U.-C. Paek, “High-intensity laser-induced vaporization and explosion of solid material,” IEEE J. Quantum Electron. QE-8, 106–111 (1972).
[CrossRef]

Park, B. S.

Pitaevski, L. P.

E. M. Lifshitch, L. P. Pitaevski, Physical Kinetics (Nauka, Moscow, 1979).

Poulain, D. E.

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

Prishivalko, A. P.

L. G. Astafieva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh. Fiz. J. 66, 340–344 (1994).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).

L. G. Astafieva, A. P. Prishivalko, “Heating of solid aluminium particles by intense laser radiation with λ = 0.53 μm,” Metallofizika 13, 122–126 (1991).

Pustovalov, V. K.

V. K. Pustovalov, D. S. Bobuchenko, “Heating, evaporation and combustion of a solid aerosol particles in a gas exposed to optical radiation,” Int. J. Heat Mass Transfer 3, 3–17 (1989).
[CrossRef]

Razdobreev, A. A.

V. A. Besprozvanyich, V. A. Ermakov, A. A. Razdobreev, “The explosion of metallic particles in the field of laser radiation,” in The Combustion of Heterogeneous and Gaseous Systems, Proceedings of the Eighth All-Union Symposium on Combustion and Explosion (Ob’yedineny Institut Chimicheskoy Fiziki AN SSSR, Chernogolovka, USSR, 1986), pp. 58–62.

Romanov, G.

S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).

Sauertbrey, R.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Schaefer, J. H.

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

Schaub, S. A.

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

Shinn, G. B.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Steigerwald, F.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Stiegler, H.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Tittel, F. K.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Ubogov, S.A.

A. V. Baranov, I. L. Klukach, S.A. Ubogov, “Laser heating of small metallic particles in inert gas,” in Interaction of Radiation with Material, A. Yglov, ed. (Kuibyishev Gosuniversitet, Kuibyishev, Russia, 1988), pp. 106–115.

Uhlen-busch, J.

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

Wilson, W. L.

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Zardecki, A.

Zhang, J.

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

Appl. Opt. (2)

Fiz. Khim. Obrab. Mater. (1)

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of metallic particles by laser radiation,” Fiz. Khim. Obrab. Mater. n2, 64–69 (1991).

IEEE J. Quantum Electron. (1)

F. W. Dabby, U.-C. Paek, “High-intensity laser-induced vaporization and explosion of solid material,” IEEE J. Quantum Electron. QE-8, 106–111 (1972).
[CrossRef]

Int. J. Heat Mass Transfer (1)

V. K. Pustovalov, D. S. Bobuchenko, “Heating, evaporation and combustion of a solid aerosol particles in a gas exposed to optical radiation,” Int. J. Heat Mass Transfer 3, 3–17 (1989).
[CrossRef]

Inzh. Fiz. J. (1)

L. G. Astafieva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh. Fiz. J. 66, 340–344 (1994).

J. Appl. Mech. Theoret. Physics (1)

A. V. Burmistrov, “About role of bubble during interaction of high intense flux of energy with medium,” J. Appl. Mech. Theoret. Physics 3, 35–44 (1979).

J. Appl. Phys. (2)

D. E. Poulain, D. R. Alexander, J. P. Barton, S. A. Schaub, J. Zhang, “Interaction of intense ultraviolet laser radiation with solid aerosol,” J. Appl. Phys. 67, 2283–2288 (1990).
[CrossRef]

H. G. Dreehsen, C. Hartwich, J. H. Schaefer, J. Uhlen-busch, “Measurement of optical constants of Al above the melting point at λ = 10.6 μm,” J. Appl. Phys. 56, 238–240 (1984).
[CrossRef]

J. Vacuum Sci. Technol. (1)

G. B. Shinn, F. Steigerwald, H. Stiegler, R. Sauertbrey, F. K. Tittel, W. L. Wilson, “Excimer laser photoablation of silicon,” J. Vacuum Sci. Technol. 4, 1273–1277 (1986).
[CrossRef]

Metallofizika (1)

L. G. Astafieva, A. P. Prishivalko, “Heating of solid aluminium particles by intense laser radiation with λ = 0.53 μm,” Metallofizika 13, 122–126 (1991).

Teplofiz. Vys. Temp. (1)

L. G. Astafieva, A. P. Prishivalko, S. T. Leiko, “Heating of aluminum particles by radiation,” Teplofiz. Vys. Temp. 30, 579–583 (1992).

Other (5)

E. M. Lifshitch, L. P. Pitaevski, Physical Kinetics (Nauka, Moscow, 1979).

S. Anisimov, Ya. Imas, G. Romanov, Yu. Khodyko, Action of High Power Radiation on Metals (Nauka, Moscow, 1970).

V. A. Besprozvanyich, V. A. Ermakov, A. A. Razdobreev, “The explosion of metallic particles in the field of laser radiation,” in The Combustion of Heterogeneous and Gaseous Systems, Proceedings of the Eighth All-Union Symposium on Combustion and Explosion (Ob’yedineny Institut Chimicheskoy Fiziki AN SSSR, Chernogolovka, USSR, 1986), pp. 58–62.

A. V. Baranov, I. L. Klukach, S.A. Ubogov, “Laser heating of small metallic particles in inert gas,” in Interaction of Radiation with Material, A. Yglov, ed. (Kuibyishev Gosuniversitet, Kuibyishev, Russia, 1988), pp. 106–115.

J. E. Hatch, ed., Aluminium Properties and Physical Metallo-conduct Handbook (Metalurgiya, Moscow, 1989).

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Figures (11)

Fig. 1
Fig. 1

Distribution of absorbed energy for λ = 10.6 μm along the particle diameter parallel to the propagation direction of the incident laser beam (curves from left to right) at initial temperature, T = 293 K; melting temperature, T = 933 K; and above the melting point. R = 20 μm. In the figure the radius of the particle is normalized to 1, i.e., r ¯ = r / R .

Fig. 2
Fig. 2

Temperature distribution along the particle diameter parallel to the incident laser beam at times t = 30, 44, and 60 μs. λ = 10.6 μm. R = 20 μm, and I = 106 W/cm2.

Fig. 3
Fig. 3

Temperature distribution along the particle diameter parallel to the incident laser beam at times t = 5.0, 5.4, 6.3, and 8.2 μs. λ = 10.6 μm, R = 20 μm, and I = 107 W/cm2.

Fig. 4
Fig. 4

Temperature distribution along the particle diameter parallel to the incident laser beam at times t = 1.68, 1.72, 2.08 μs. λ = 10.6 μm, R = 20 μm, and I = 5 × 107 W/cm2.

Fig. 5
Fig. 5

Temperature distribution for the moment of destruction along the particle diameters definedby angles θ = 0°, 20°, 30°, and 40°. λ = 10.6 μm, R = 20 μm, I = 107 W/cm2, and t = 8.2 μs.

Fig. 6
Fig. 6

Contours of the constant values of temperature (in degrees Kelvin) depending on r and θ. λ = 10.6 μm, R = 20 μm, I = 106 W/cm2, and t = 60 μs.

Fig. 7
Fig. 7

Contours of the constant values of temperature (in degrees Kelvin) depending on r and θ. λ = 10.6 μm, R = 20 μm, I = 107 W/cm2, and t = 8.2 μs.

Fig. 8
Fig. 8

Contours of the constant values of temperature (in degrees Kelvin) depending on r and θ. λ = 10.6 μm, R = 20 μm, I = 5 × 107 W/cm2, and t = 2.08.

Fig. 9
Fig. 9

Energy-loss rate at ( r ¯ , θ ) = ( 1 . 0 , 0 . 0 ) through each surface term in Eq. (4) with time R = 20 μm. I = 106 W/cm2. a, vaporization; b, shrinkage; c, convection; d, heat exchange.

Fig. 10
Fig. 10

Energy-loss rate at ( r ¯ , θ ) = ( 1 . 0 , 0 . 0 ) through each surface term in Eq. (4) with time. R = 20 μm, and I = 107 W/cm2 a, vaporization; b, shrinkage; c, convection.

Fig. 11
Fig. 11

Energy-loss rate at ( r ¯ , θ ) = ( 1 . 0 , 0 . 0 ) through each shrinkage (b) surface term in Eq. (4) with time. R = 20 μm, and I = 108 W/cm2 a, vaporization; b, shrinkage; c, convection.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

c ( T ) ρ ( T ) T ( r , θ , t ) t = 1 r 2 r [ λ 1 ( T ) r 2 T r ] + 1 r 2  sin θ ∂θ           × [ λ 1 ( T ) sin θ  T ∂θ ] + Q ( r , θ , t , T ) ,
Q = I B ( 4 π n χ / m s λ ) ,
B = ( E r E r * + E θ E θ * + E φ E φ * ) E 0 2 .
λ 1 ( T ) T ( R , θ , t ) r = α [ T ( R , θ , t ) T s ] + R t ρ           × [ L + c ( T T ) + ν ¯ 2 2 ]           + σε λ T 4 ,
T ( 0 , θ , t ) < , 0 θ π , t > 0 ,
T ∂θ θ = 0 = T ∂θ θ = π = 0 ,
α = β P ( 2 π M k T ) 1 / 2 ( c ν + 1 2 k ) .
R t = c s ( 3 4 π ) 1 / 3 exp ( L M / R s T ) ,
n = ( 1 . 5 × 10 5 ) T 1 . 5 ,
χ = ( 3 . 9 × 10 4 ) T 1 . 125 .

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