Abstract

The heating of lidar-irradiated multilayer particles is analyzed theoretically and numerically by solution of the heat conduction equation. The internal intensity and temperature distributions are presented for particles composed of air, quartz, and carbon. It is shown that the heating times of such particles substantially depend on particle radii, layer position, and shell thickness. In particular, the decrease in thickness of the surface carbon layer can result in a reduction of the heating time of multilayer particles.

© 2002 Optical Society of America

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References

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  1. R. L. Armstrong, A. Zardecki, “Propagation of high energy laser beams through metallic aerosols,” Appl. Opt. 29, 1786–1792 (1990).
    [CrossRef] [PubMed]
  2. A. P. Prishivalko, L. G. Astafyeva, S. T. Leiko, “Heating and destruction of metallic particles exposed to intense laser radiation,” Appl. Opt. 35, 965–972 (1996).
    [CrossRef] [PubMed]
  3. L. G. Astafyeva, A. P. Prishivalko, “Heating of solid aerosol particles to intense optical radiation,” Int. J. Heat Mass Transfer 41, 489–499 (1998).
    [CrossRef]
  4. L. G. Astafyeva, A. P. Prishivalko, “Heating of aluminum particles with oxide covers by intense laser radiation,” Fiz. Khim. Obrab. Mater. N4, 18–27 (1993).
  5. L. G. Astafyeva, A. P. Prishivalko, “Heating of metallized particles by high-intensity laser radiation,” Inzh.-Fiz. Zh. 66, 340–344 (1994).
  6. L. G. Astafyeva, A. P. Prishivalko, “Heating of homogeneous and hollow particles of aluminum oxide by intense laser radiation,” Teplofiz. Vys. Temp. 32, 230–235 (1994).
  7. L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Disruption of hollow aluminum particles by intense laser radiation,” J. Opt. Soc. Am. B 14, 432–436 (1997).
    [CrossRef]
  8. L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Heating and destruction of hollow aluminum oxide particles by laser radiation,” Fiz. Khim. Obrab. Mater. N5, 27–32 (1997).
  9. W. Fett, Der Atmospharische Staub (Wissenschaften, Berlin, 1958).
  10. H. L. Green, W. R. Lane, Particulate Clouds: Dusts, Smokes and Mists (Van Nostrand, New York, 1964).
  11. G. A. D’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (A. Deepak, Hampton, Va., 1991).
  12. K. Ya. Kondrat’ev, N. I. Moskalenko, D. B. Posdnyakov, Atmospheric Aerosol (Gidrometeoizdat, Leningrad, 1983).
  13. K. Ya. Kondrat’ev, ed., Aerosol and Climate (Gidrometeoizdat, Leningrad, 1973).
  14. R. E. Krzhizhanovsky, Z. Yu. Shtern, Thermophysical Properties of Nonmetallic Materials (Oxides) (Energy, Leningrad, 1973).
  15. V. S. Chirkin, Thermophysical Properties of Materials of Nuclear Technics (Atomizdat, Moscow, 1968).
  16. L. V. Gurvich, I. V. Veits, V. A. Medvedev, eds., Handbook of Thermodynamic Properties of Individual Matter (Nauka, Moscow, 1979).

1998 (1)

L. G. Astafyeva, A. P. Prishivalko, “Heating of solid aerosol particles to intense optical radiation,” Int. J. Heat Mass Transfer 41, 489–499 (1998).
[CrossRef]

1997 (2)

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Heating and destruction of hollow aluminum oxide particles by laser radiation,” Fiz. Khim. Obrab. Mater. N5, 27–32 (1997).

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Disruption of hollow aluminum particles by intense laser radiation,” J. Opt. Soc. Am. B 14, 432–436 (1997).
[CrossRef]

1996 (1)

1994 (2)

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

L. G. Astafyeva, A. P. Prishivalko, “Heating of homogeneous and hollow particles of aluminum oxide by intense laser radiation,” Teplofiz. Vys. Temp. 32, 230–235 (1994).

1993 (1)

L. G. Astafyeva, A. P. Prishivalko, “Heating of aluminum particles with oxide covers by intense laser radiation,” Fiz. Khim. Obrab. Mater. N4, 18–27 (1993).

1990 (1)

Armstrong, R. L.

Astafyeva, L. G.

L. G. Astafyeva, A. P. Prishivalko, “Heating of solid aerosol particles to intense optical radiation,” Int. J. Heat Mass Transfer 41, 489–499 (1998).
[CrossRef]

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Disruption of hollow aluminum particles by intense laser radiation,” J. Opt. Soc. Am. B 14, 432–436 (1997).
[CrossRef]

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Heating and destruction of hollow aluminum oxide particles by laser radiation,” Fiz. Khim. Obrab. Mater. N5, 27–32 (1997).

A. P. Prishivalko, L. G. Astafyeva, S. T. Leiko, “Heating and destruction of metallic particles exposed to intense laser radiation,” Appl. Opt. 35, 965–972 (1996).
[CrossRef] [PubMed]

L. G. Astafyeva, A. P. Prishivalko, “Heating of homogeneous and hollow particles of aluminum oxide by intense laser radiation,” Teplofiz. Vys. Temp. 32, 230–235 (1994).

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

L. G. Astafyeva, A. P. Prishivalko, “Heating of aluminum particles with oxide covers by intense laser radiation,” Fiz. Khim. Obrab. Mater. N4, 18–27 (1993).

Chirkin, V. S.

V. S. Chirkin, Thermophysical Properties of Materials of Nuclear Technics (Atomizdat, Moscow, 1968).

D’Almeida, G. A.

G. A. D’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (A. Deepak, Hampton, Va., 1991).

Fett, W.

W. Fett, Der Atmospharische Staub (Wissenschaften, Berlin, 1958).

Green, H. L.

H. L. Green, W. R. Lane, Particulate Clouds: Dusts, Smokes and Mists (Van Nostrand, New York, 1964).

Koepke, P.

G. A. D’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (A. Deepak, Hampton, Va., 1991).

Kondrat’ev, K. Ya.

K. Ya. Kondrat’ev, N. I. Moskalenko, D. B. Posdnyakov, Atmospheric Aerosol (Gidrometeoizdat, Leningrad, 1983).

Krzhizhanovsky, R. E.

R. E. Krzhizhanovsky, Z. Yu. Shtern, Thermophysical Properties of Nonmetallic Materials (Oxides) (Energy, Leningrad, 1973).

Lane, W. R.

H. L. Green, W. R. Lane, Particulate Clouds: Dusts, Smokes and Mists (Van Nostrand, New York, 1964).

Leiko, S. T.

Moskalenko, N. I.

K. Ya. Kondrat’ev, N. I. Moskalenko, D. B. Posdnyakov, Atmospheric Aerosol (Gidrometeoizdat, Leningrad, 1983).

Posdnyakov, D. B.

K. Ya. Kondrat’ev, N. I. Moskalenko, D. B. Posdnyakov, Atmospheric Aerosol (Gidrometeoizdat, Leningrad, 1983).

Prishivalko, A. P.

L. G. Astafyeva, A. P. Prishivalko, “Heating of solid aerosol particles to intense optical radiation,” Int. J. Heat Mass Transfer 41, 489–499 (1998).
[CrossRef]

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Disruption of hollow aluminum particles by intense laser radiation,” J. Opt. Soc. Am. B 14, 432–436 (1997).
[CrossRef]

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Heating and destruction of hollow aluminum oxide particles by laser radiation,” Fiz. Khim. Obrab. Mater. N5, 27–32 (1997).

A. P. Prishivalko, L. G. Astafyeva, S. T. Leiko, “Heating and destruction of metallic particles exposed to intense laser radiation,” Appl. Opt. 35, 965–972 (1996).
[CrossRef] [PubMed]

L. G. Astafyeva, A. P. Prishivalko, “Heating of homogeneous and hollow particles of aluminum oxide by intense laser radiation,” Teplofiz. Vys. Temp. 32, 230–235 (1994).

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

L. G. Astafyeva, A. P. Prishivalko, “Heating of aluminum particles with oxide covers by intense laser radiation,” Fiz. Khim. Obrab. Mater. N4, 18–27 (1993).

Shettle, E. P.

G. A. D’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (A. Deepak, Hampton, Va., 1991).

Shtern, Z. Yu.

R. E. Krzhizhanovsky, Z. Yu. Shtern, Thermophysical Properties of Nonmetallic Materials (Oxides) (Energy, Leningrad, 1973).

Zardecki, A.

Appl. Opt. (2)

Fiz. Khim. Obrab. Mater. (2)

L. G. Astafyeva, A. P. Prishivalko, “Heating of aluminum particles with oxide covers by intense laser radiation,” Fiz. Khim. Obrab. Mater. N4, 18–27 (1993).

L. G. Astafyeva, A. P. Prishivalko, S. T. Leiko, “Heating and destruction of hollow aluminum oxide particles by laser radiation,” Fiz. Khim. Obrab. Mater. N5, 27–32 (1997).

Int. J. Heat Mass Transfer (1)

L. G. Astafyeva, A. P. Prishivalko, “Heating of solid aerosol particles to intense optical radiation,” Int. J. Heat Mass Transfer 41, 489–499 (1998).
[CrossRef]

Inzh.-Fiz. Zh. (1)

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

J. Opt. Soc. Am. B (1)

Teplofiz. Vys. Temp. (1)

L. G. Astafyeva, A. P. Prishivalko, “Heating of homogeneous and hollow particles of aluminum oxide by intense laser radiation,” Teplofiz. Vys. Temp. 32, 230–235 (1994).

Other (8)

W. Fett, Der Atmospharische Staub (Wissenschaften, Berlin, 1958).

H. L. Green, W. R. Lane, Particulate Clouds: Dusts, Smokes and Mists (Van Nostrand, New York, 1964).

G. A. D’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (A. Deepak, Hampton, Va., 1991).

K. Ya. Kondrat’ev, N. I. Moskalenko, D. B. Posdnyakov, Atmospheric Aerosol (Gidrometeoizdat, Leningrad, 1983).

K. Ya. Kondrat’ev, ed., Aerosol and Climate (Gidrometeoizdat, Leningrad, 1973).

R. E. Krzhizhanovsky, Z. Yu. Shtern, Thermophysical Properties of Nonmetallic Materials (Oxides) (Energy, Leningrad, 1973).

V. S. Chirkin, Thermophysical Properties of Materials of Nuclear Technics (Atomizdat, Moscow, 1968).

L. V. Gurvich, I. V. Veits, V. A. Medvedev, eds., Handbook of Thermodynamic Properties of Individual Matter (Nauka, Moscow, 1979).

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Figures (6)

Fig. 1
Fig. 1

Intensity distribution inside a two-layer air–quartz sphere: V air/V 3 = 1/3, V quartz/V 3 = 2/3, R 3 = 5 µm, λ = 1.06 µm. The arrow shows the propagation direction of the incident lidar beam.

Fig. 2
Fig. 2

Intensity distribution inside a three-layer air–carbon–quartz sphere: V air/V 3 = V carbon/V 3 = V quartz/V 3 = 1/3, R 3 = 5 µm, λ = 1.06 µm. The arrow shows the propagation direction of the incident lidar beam.

Fig. 3
Fig. 3

Temperature distribution inside a two-layer air–quartz sphere: V air/V 3 = 1/3, V quartz/V 3 = 2/3, R 3 = 5 µm, λ = 1.06 µm. The irradiance is 106 W/cm2. The arrow shows the propagation direction of the incident lidar beam.

Fig. 4
Fig. 4

Temperature distribution inside a three-layer air–carbon–quartz sphere: V air/V 3 = V carbon/V 3 = V quartz/V 3 = 1/3, R 3 = 5 µm, λ = 1.06 µm. The irradiance is 106 W/cm2.

Fig. 5
Fig. 5

Heating time of the air–quartz–carbon spheres up to a maximum temperature of T max = 400 K inside the particle as a function of outer particle radius V air/V 3 = 1/3. The variation effect of the carbon fraction is illustrated: curve 1, V carbon/V 3 = 2/3, V quartz/V 3 = 0; curve 2, V carbon/V 3 = 1/3, V quartz/V 3 = 1/3; curve 3, V carbon/V 3 = 0.25, V quartz/V 3 = 0.42; curve 4, V carbon/V 3 = 0.20, V quartz/V 3 = 0.47; curve 5, V carbon/V 3 = 0.15, V quartz/V 3 = 0.52. The irradiance with λ = 1.06 µm is 106 W/cm2.

Fig. 6
Fig. 6

Same as Fig. 5 but for air–carbon–quartz spheres. The variation effect of the quartz fraction is illustrated: curve 1, V quartz/V 3 = 2/3, V carbon/V 3 = 0; curve 2, V quartz/V 3 = 1/3, V carbon/V 3 = 1/3.

Equations (34)

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

ciTiρiTiTit=1r2rKiTir2Tir+1r2 sin θθ×KiTisin θ Tiθ+Qir, θ, Ti, t.
QiTi=IBi4πniχi/λ,
Bi=|Eri|2+|Eθi|2E0-2.
Er1=E0 cos ϕk12r2l=1 ll+1ψlk1rψlk1R1 Cl1Qlθsin θ,
Eθ1=E0 cos ϕk1rl=1ψlk1rψlk1R1×Cl1Dlk1rSlθ+iBl1Qlθ.
Er2,3=E0 cos ϕk2,32r2l=1 ll+1ψlk2,3rψlk2,3R2,3 Cl2,3+ξlk2,3rξk2,3R2,3 C˜l2,3Qlθsin θ,
Eθ2,3=E0 cos ϕk2,3rl=1ψlk2,3rψlk2,3R2,3 Cl2,3Dlk2,3r+ξlk2,3rξlk2,3R2,3 C˜l2,3Glk2,3rSlθ+iψlk2,3rψlk2,3R2,3 Bl2,3+ξlk2,3rξlk2,3R2,3 B˜l2,3Qlθ.
Bl1=il2l+1ll+1m1ms1ψlk2R2ξlk2R1× 1ψlk3R3ξlk3R21ξlksR31Δ1,
Cl1=il2l+1ll+11ψlk2R2ξlk2R1×1ψlk3R3ξlk3R21ξlkR31Δ2,
Bl2=-il-1m2ms2l+1ll+11ψlk3R3ξlk3R21ξlkR3A2Δ1,
B˜l2=il-1m2ms2l+1ll+1ψlk2R1ψlk2R21ψlk3R3ξlk3R2×1ξlkR3A1Δ1,
Cl2=-il-12l+1ll+11ψlk3R3ξlk3R21ξlkR3Ã2Δ2,
C˜l2=il-12l+1ll+1ψlk2R1ψlk2R21ψlk3R3ξlk3R2×1ξlkR3Ã1Δ2,
Bl3=il2l+1ll+1m3ms1ξlkR3×ψlk2R1ψlk2R2ξlk2R2ξlk2R1 A1H2-A2L21Δ1,
B˜l3=il2l+1ll+1m3msψlk3R2ψlk3R31ξlkR3×A2H1-ψlk2R1ψlk2R2ξlk2R2ξlk2R1 A1L11Δ1,
Cl3=il2l+1ll+11ξlkR3×ψlk2R1ψlk2R2ξlk2R2ξlk2R1 Ã1H˜2-Ã2L˜21Δ2,
C˜l3=il2l+1ll+1ψlk3R3ψlk3R31ξlkR3×Ã2H˜1-ψlk2R1ψlk2R2ξlk2R2ξlk2R1 Ã1L˜11Δ2,
Δ1=A1ψlk2R1ψlk2R2ξlk2R2ξlk2R1×ψlk3R2ψlk3R3ξlk3R3ξlk3R2 F2L1-F1H2+A2F1L2-ψlk3R2ψlk3R3ξlk3R3ξlk3R2 F2H1,
Δ2=Ã1ψlk2R1ψlk2R2ξlk2R2ξlk2R1×ψlk3R2ψlk3R3ξlk3R3ξlk3R2 F˜2L˜1-F˜1H˜2+Ã2F˜1L˜2-ψlk3R2ψlk3R3ξlk3R3ξlk3R2 F˜2H˜1,
A1=Dlk2R1-m12Dlk1R1,
A2=Glk2R1-m12Dlk1R1,
L1=Dlk3R2-m23Glk2R2,
L2=Glk3R2-m23Dlk2R2,
H1=Dlk3R2-m23Dlk2R2,
H2=Glk3R2-m23Glk2R2,
F1=GlksR3-m3sDlk3R3,
F2=GlksR3-m3sGlk3R3.
|T10, θ, t|<, 0θπ, t>0,
T1R1, θ, t=T2R1, θ, t,
T2R2, θ, t=T3R2, θ, t,
K1T1R1, θ, tr=K2T2R1, θ, tr,
K2T2R2, θ, tr=K3T3R2, θ, tr,
-K3T3R3, θ, tr=σελT4,
TiRiθθ=0=TiRiθθ=π=0, i=1, 2, 3,

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