Abstract

Milli-Joule, femtosecond laser pulses have been used to propel microbeads for the first time. The microbeads of three different materials (iron, glass, and polystyrene) are used, weighting from 0.84 mg to 1.4 mg with a diameter range of 0.7–1.1 mm. Experimental parameters such as focused beam spot diameter, pulse energy, and pulse width are carefully varied to investigate their respective influences on the specific ablative laser propulsion. It is found that both the momentum coupling efficiency and the overall energy conversion efficiency from light energy to kinetic energy are greater for shorter laser pulses. A typical value of the momentum coupling efficiency of 5.0 dyne/W for iron beads is obtained. It is also evident that for metallic and non-metallic microbeads the momentum coupling efficiency has different variation tendencies versus the focused beam spot diameter.

© 2004 Optical Society of America

1. Introduction

The concept of laser propulsion was first proposed by Arthur Kantrowitz of the Avco Everett Research Laboratory in 1972 [1]. Arthur Kantrowitz considered that focusing a beam of high power laser to a propellant could be a very attractive substitute of chemical propulsion systems. In the recent years, due to the development of laser technologies, laser propulsion has gained increasing attention of the propulsion research groups around the world. On one hand, ultra-high average power laser systems have emerged and found applications in laser propulsion. For example, In October 2000, Leik Myrabo of the Rensselaer Polytechnic Institute and other scientists from the United States Air Force and NASA used a 10-kW infrared pulsing laser at the White Sands Missile Range to successfully impulse an acorn-shaped craft with a diameter of 12.2 cm and a mass of 50 g to a height of 71 m [2]. On the other hand, the fast development of ultra-short pulse lasers makes ablative laser propulsion a very promising propulsion technique in the laser propulsion field [3]. In terms of specific impulse, energy conversion efficiency and mass-power ratios, ablative laser propulsion is superior to other laser propulsion schemes.

In this work, we have performed some experimental study of laser propulsion of microbeads using femtosecond laser pulses to explore the relations between the flying distance and the pulse duration, pulse energy, pulse spot diameter and the material of the microbeads. Our experimental results for microbeads of metallic and non-metallic materials indicate that the momentum coupling efficiency Cm is largely dependent on material and the pulse spot diameter; furthermore, for shorter laser pulses greater momentum coupling efficiency is obtained for iron beads.

2. Principle of ablative laser propulsion

In ablative laser propulsion, laser pulses of high power and short time duration are focused on the surface of a solid propellant, and the duration of the laser pulses is shorter than the formation time of the plasma, which is about 10-10 s. The short duration of the laser pulse makes the laser-induced plasma be temporally separated from the laser pulse itself, so that the interaction between the laser pulse and laser-induced plasma is negligible. The momentum transition in this process is thus dominated by the laser-induced plasma’s counterforce exerted on the surface of the solid propellant [3].

In a simplified picture, the following three steps of the process of ablative laser propulsion [4] may be described: first, light is absorbed by free electrons via inverse bremsstrahlung, (in those materials of few free electrons, the free electrons must first be generated through multi-photon ionization); secondly, the accelerated electrons ionize their neighboring atoms via impact ionization such that the electron density grows exponentially; and thirdly, the wave of energetic electrons propagates into the bulk of the target leaving the lattice behind electrostatically unbalanced, which eventually leads to the so-called Coulomb explosion. Therefore, as a result of absorption of the laser pulse energy at a solid target, supersonic ejection of highly ionized matter from the target surface occurs. Due to conservation of momentum, ablation exerts an impulse to the solid propellant in the direction opposite to the jetted material, thus propelling the laser-ablated object.

3. Experimental setup

The experimental setup of ablative laser propulsion of microbeads is as shown in Fig. 1. In our experiments, a commercial femtosecond Ti: Sapphire laser system (Spitfire of Spectra Physics Inc.) is employed that provides sub-50 femtoseconds laser pulses around 780 nm with energy of up to 2 mJ at a repetition rate of 1 kHz. The system can also operate in a pulse-on-demand mode through computer interface. The actual pulse width may be increased up to 40 picoseconds by changing the effective grating separation inside the pulse compressor of the chirped-pulse amplification unit. During the experiments, the He-Ne laser beam for illumination is first aligned in collinear with the femtosecond laser beam. With the proper adjustment of the telescope, the He-Ne laser beam should be at a common focus with the fs laser beam after the focal lens B. The microbead sitting on a mini platform is then carefully brought into the focus of lens B while monitoring the surface reflection of the He-Ne laser from the bead using a CCD camera. The mini platform is attached to a bracket mounted on a high precision 3-D motorized translation stage.

Tables Icon

Table 1. Average size and weight of microbeads used in fs laser propulsion

 

Fig. 1. Experimental setup of femtosecond laser propulsion of microbead(s), h=152 mm.

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After the alignment has been completed, we fire a femtosecond laser pulse on the microbead to make it fly off the platform. By measuring the flying distance S along the horizontal direction and the falling distance h in the vertical direction of the microbead as a result of laser ablation, we are able to estimate some very important propulsion parameters, such as the momentum coupling efficiency Cm and the energy conversion efficiency η.

As shown in Table 1. microbeads made of three different materials are used in our femtosecond laser propulsion experiments. The beads are carefully screened and selected under a microscope to have a diameter as uniform as possible. The estimated variation in bead diameter is less than 3%. The average weight per bead is around 1.4 mg for iron beads, 1.1 mg for glass beads, and 0.84 mg for polystyrene beads. In addition, the experimental parameters of pulse width, pulse energy, three different focal lengths of lens B are employed to perform the experiments of ablative laser propulsion of the microbeads.

4. Experimental results and analyses

4.1 Effect of femtosecond laser beam size

We first investigate the effect of femtosecond laser beam size on ablative propulsion of microbeads. The laser pulse width and pulse energy are kept at 47 fs and 0.94 mJ in this case. Various beam diameters at the focus are achieved by using three different focal lenses (for lens B) with a focal length of 10, 15, and 30 cm respectively. The beam spot diameter(s) at focus are estimated by using the following formula:

d=2(λπw)fM2

where λ is the central wavelength of the femtosecond laser pulse, w is the radius of the laser beam at the entrance of lens B, f is the focal length of the lens used, and M2 is the beam quality factor. The experimental data obtained from this experiment are shown in Fig. 2.

 

Fig. 2. Flying distance S of a microbead as a function of laser beam spot size d for three different materials (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2=1.5).

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Fig. 3. Momentum coupling efficiency Cm as a function of laser beam spot diameter d obtained for microbeads made of three different materials (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2=1.5)

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From Fig. 3 we can find that the relation between Cm and d for iron beads is obviously different from that for polystyrene beads and glass beads. When d increases, Cm also increases for iron beads but decreases for both polystyrene and glass beads. This may be explained by their different matter structure. Iron as a metal has enough free electrons in normal state but for polystyrene and glass they almost have no free electrons in normal state. All the free electrons needed by ablative laser propulsion process for polystyrene and glass must be generated through multi-photon ionization first. When d increases, the laser pulse intensity I decreases quickly (because I∝1/d2). The drop of I thus goes against the generation of free electrons for polystyrene and glass. As a result of lack of free electrons, the absorption of laser energy will be low and so the momentum coupling efficiency Cm decreases as d increases for polystyrene and glass.

Furthermore, for d larger than 28.6 µm (the second data point), Cm of iron beads changes more slowly. This is because when d is comparatively large, the increase of d leads to a larger laser-induced plasma volume that is in favor of ablative laser propulsion, but the decrease of I is so great that it will counteract the contribution of the increase of the laser-induced plasma volume to laser propulsion. The values of Cm obtained from this experiment range from 3.7 dyne/W to 5.3 dyne/W, and it is expected that the value of Cm can be further increased through increasing the effective absorption of the laser pulse energy in the propellant material involved.

The main elements of polystyrene are carbon and hydrogen, and the main elements of glass are oxygen and silicon. From the results shown in Fig. 3 we can see that for larger d the heavier element Fe has a greater value of Cm. When d decreases, however, such a pattern no longer exists. The relation between the energy conversion efficiency η (defined as the ratio of the kinetic energy of the microbead to the single pulse energy) and the laser pulse spot diameter is shown in Fig. 4. From the data given in this figure we notice that, for d less than 28.6 µm, larger energy conversion efficiency exists for the microbeads of lighter elements.

4.2 Effect of femtosecond laser pulse energy

In order to further investigate the influence of laser parameters on the propulsion of microbeads, we have also tried to repeat the propulsion experiments with different pulse energies for iron beads. The corresponding experimental data for single pulse energy of 0.94, 1.12, and 1.42 mJ are shown in Fig. 5 and Fig. 6. In this case the focal length of lens B is fixed at 10 cm and the duration of the laser pulse is 47 fs. As it is expected, when the single pulse energy E increases the flying distance increases, but interestingly Cm reaches maximum at the point of E=1.12 mJ, and it drops to a lower value at E=1.42 mJ. That implies the increase of the initial velocity of iron beads is not proportional to the increase of the pulse energy. Therefore, it appears that optimal incident pulse energy exists for Cm. In sharp contrast, for energy conversion coefficient η, the same rule does not apply. Variation of η versus pulse energy is shown in Fig. 7. It is clearly seen that as E increases η increases monotonically.

 

Fig. 4. Energy conversion efficiency η as a function of laser beam spot diameter d for three different types of microbeads (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2=1.5)

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Fig. 5. Flying distance S as a function of single pulse energy E for iron beads (The laser pulse duration is 47 fs and the focal length of lens B is 10 cm.)

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Fig. 6. Momentum coupling efficiency Cm as a function of single pulse energy E for iron beads (The laser pulse duration is 47 fs and the focal length of lens B is 10 cm.)

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Fig. 7. Energy conversion efficiency η as a function of single pulse energy E for iron beads (The pulse duration is 47 fs and the focal length of lens B is 10 cm.)

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4.3 Effect of femtosecond laser pulse duration

The experimental data of laser propulsion for iron beads taken for different laser pulse durations are shown in Fig. 8 and Fig. 9. In this case, the single pulse energy is maintained at 1.20 mJ and the focal length of lens B is 10 cm.

From Fig. 9, we can see that when laser pulse duration Δt increases, the momentum coupling efficiency Cm for iron beads decreases. Such a phenomenon may be explained by using Eqs. (2), (3), and (7) given in Section 5 of this text. When the pulse width decreases, the electron temperature at the end of laser pulse heating Te0 increases [see Ea. (3)]. Consequently, the velocity of the plasma expansion increases [Eqs. (2), (7)]. Thus, the momentum of the laser-induced plasma increases and due to the momentum conservation law, the initial momentum of the microbead increases. So shorter laser pulses lead to higher plasmas expansion velocity, namely, higher specific impulse and higher momentum coupling efficiency.

Variation of the energy conversion efficiency as a function of pulse width is plotted in Fig. 10. It can be seen, from the data points shown in Fig. 10, that much lower conversion rate from light energy to kinetic energy are obtained for longer laser pulses.

 

Fig 8. Flying distance S as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

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Fig 9. Momentum coupling efficiency Cm as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

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Fig 10. Energy conversion efficiency η as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

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5. Discussions and conclusions

Theoretically, the interaction between a femtosecond laser pulse and a metal target may be divided into two stages. The first stage happens before the end of the laser pulse heating. The isothermal expansion model [5] may be used to describe the hydromechanical behavior of the laser-induced plasma during this first stage. The velocity of the laser-induced plasma expansion can be estimated by [6]:

v=Cs=(γZ0Te0Mi)12

where Cs is the ion sound speed, γ=Cp/Cv (for ideal gases, γ=5/3). Z 0 stands for the average ion charge number, Mi is the ion mass. Te0 is the electron temperature at the end of the laser pulse heating in energy unit. Te0 can be determined by [6]:

Te0=CtE49Δt29

With Ct representing a material dependent constant, E the single pulse energy of the incident laser, and Δt the laser pulse duration, Ct is independent of both E and Δt.

Because the femtosecond laser pulse duration of interest to us is so short, the isothermal expansion of the laser-induced plasma is negligible within the time frame of the laser pulse itself. At the end of the laser pulse heating, the volume of the laser-induced plasma can be approximated as

V010πd2Ls4

where d is the laser pulse spot diameter, Ls is the skin depth of the solid-density plasma, the coefficient 10 is a fitting parameter we choose in order to make the ablative depth closer to the theoretical value [7]. From the standard plasma theory we know that [8]

Ls=Cωpe
ωpe=(nee2meε0)12

where ωpe is the electron frequency of the laser-induced plasma, ne is the electron number density, me is the electron mass, and e is the electron charge.

The second stage of laser ablation happens after the end of the laser pulse heating. This stage may be described by an adiabatic expansion model [915]. The free expansion velocity of the laser-induced plasma can be estimated by

v=3Cs

With the above formula, we may use our experimental results to determine an analytic relation between Te0 and the intensity of the incident laser pulse I for iron. The data used to fit the analytic curve obtained from our experiments are shown in Table 2, in which the intensity values for laser pulses are derived from the measured results of pulse energy, pulse width and the spot diameter whereas those of electron temperature are calculated from the flying distance S of iron beads based on the hydromechanical model described above.

Tables Icon

Table 2. Estimated electron temperature in iron for different laser pulse intensities

From the first four group data points given in Table 2, the following simplified empirical relation between the electron temperature Te0 and the pulse intensity I can be obtained

Te0I1.8405

where Te0 is in the unit of keV, and I in 1016W/cm2. Fig. 11 shows the plots of both the fitting curve from Eq. (8) and the first five data points given in Table 2. We can see that a sudden increase of Te0 occurs around I=1.64×1016 W/cm2.

 

Fig 11. Fitting curve of the electron temperature at the end of laser pulse heating (Te0 in keV.) versus the incident laser pulse intensity (I in 1016W/cm2)

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In conclusion, we have conducted, to our knowledge, the first experimental study of laser propulsion of microbeads with milli-Joule femtosecond laser pulses. The momentum coupling efficiency we have achieved with femtosecond laser pulses can be over 5 dyne/W; our experimental results also indicate that either light absorptive or non-absorptive target may be used as propellant in the regime of ablative laser propulsion; for shorter femtosecond pulses, the overall energy conversion efficiency from light energy to kinetic energy is greater. While our observations are made at rather lower pulse energy level and the microbeads being propelled only measure a diameter of ~1 mm, the main results provide us with some useful insight into the characteristics of femtosecond laser ablative propulsion, and are likely applicable to the situation of light propulsion of larger object with higher laser pulse energy.

According to our experimental results a microbead weighing 1 mg may attain an initial velocity of several cm/s under the strike of a milli-Joule femtosecond laser pulse. If we use linear scaling and provided that we can build a kJ femtosecond pulse laser in future, we can then use this laser to make a 1 kg object attain a velocity of 10 km/s within less than 20 minutes, which will easily overcome the gravitation of the earth. However, one may well question the correctness of such an oversimplified linear scaling. It is believed that a great many works remain to be done in this regard. Future studies include the search for optimal laser pulse duration, optimal incident laser pulse intensity and optimal propellant material for ablative laser propulsion, and multi-pulse propulsion.

Acknowledgments

This work has been supported by Ministry of Science and Technology of China under the Grant No. 2002CCA01700, and by the National Natural Science Foundation of China under Grant No.60378007.

References and links

1. A. Kantrowitz, “Propulsion to orbit by ground-based lasers,” Astronautics & Aeronautics (A/A) 10, 74–76 (1972).

2. D. Darling, “The encyclopedia of astrobiology, astronomy, and spaceflight,” http://www.daviddarling.info/encyclopedia/L/laserprop.html.

3. A. V. Pakhomov and D. A. Gregory, “Ablative laser propulsion: an old concept revisited,” AIAA Journal 38, 725–727 (2000). [CrossRef]  

4. A. V. Pakhomov and D. A. Gregory, “Ablative laser propulsion: an advanced concept for space transportation,” Young Faculty Research Proceedings, the University of Alabama in Huntsville, 63–72 (2000).

5. O. L. Landen, D. G. Stearns, and E. M. Campbell, “Measurement of the expansion of picosecond laser-produced plasmas using resonance absorption profile spectroscopy,” Phys. Rev. Lett. 63, 1475–1478 (1989). [CrossRef]   [PubMed]  

6. Y. Cang, W. Wang, and J. Zhang, “Research of the dynamic process of the interaction between ultra-short laser pulse and solid-density plasma,” Acta Physica Sinica 50, 1742–1746 (2001) (in Chinese)

7. Y. H. Yan and M. L. Zhong, High Power Laser Process and Application (Tianjin Science and Technology Press, Tianjin, 1994) (in Chinese).

8. J. L. Xu and S. X. Jin, Plasma physics (Nuclear Energy Press, Beijing, 1981) (in Chinese).

9. G. J. Pert, “Model calculations of XUV gain in rapidly expanding cylindrical plasmas,” J. Phys. B: At. Mol. Phys. 9, 3301–3315 (1976). [CrossRef]  

10. G. J. Pert, “Model calculations of XUV gain in rapidly expanding cylindrical plasmas II,” J. Phys. B: At. Mol. Phys. 12, 2067–2079 (1979). [CrossRef]  

11. G. J. Pert, “Model calculations of extreme-ultraviolet gain in rapidly expanding cylindrical carbon plasmas,” J. Opt. Soc. Am. B 4, 602–608 (1987). [CrossRef]  

12. G. J. Pert and S. A. Ramsden, “Population inversion in plasmas produced by picosecond laser pulses,” Opt. Commun. 11, 270–273 (1974). [CrossRef]  

13. W. J. Fader, “Hydrodynamic model of a spherical plasma produced by Q-spoiled laser irradiation of a solid particle,” Phys. Fluids 11, 2200–2208 (1968). [CrossRef]  

14. A. V. Farnsworth, “Power-driven and adiabatic expansions into vacuum,” Phys. Fluids 23, 1496–1500 (1980). [CrossRef]  

15. M. A. Treu, J. R. Albritton, and E. A. Williams, “Fast ion production by suprathermal electrons in laser fusion plasmas,” Phys. Fluids 24, 1885–1893 (1981). [CrossRef]  

References

  • View by:
  • |

  1. A. Kantrowitz, �??Propulsion to orbit by ground-based lasers,�?? Astronautics & Aeronautics (A/A) 10, 74-76 (1972).
  2. D. Darling, �??The encyclopedia of astrobiology, astronomy, and spaceflight,�?? <a href="http://www.daviddarling.info/encyclopedia/L/laserprop.html">http://www.daviddarling.info/encyclopedia/L/laserprop.html</a>.
  3. A. V. Pakhomov, and D. A. Gregory, �??Ablative laser propulsion: an old concept revisited,�?? AIAA Journal 38, 725-727 (2000).
    [CrossRef]
  4. A. V. Pakhomov, and D. A. Gregory, �??Ablative laser propulsion: an advanced concept for space transportation,�?? Young Faculty Research Proceedings, the University of Alabama in Huntsville, 63-72 (2000).
  5. O. L. Landen, D. G. Stearns, and E. M. Campbell, �??Measurement of the expansion of picosecond laser-produced plasmas using resonance absorption profile spectroscopy,�?? Phys. Rev. Lett. 63, 1475-1478 (1989).
    [CrossRef] [PubMed]
  6. Y. Cang, W. Wang, and J. Zhang, �??Research of the dynamic process of the interaction between ultra-short laser pulse and solid-density plasma,�?? Acta Physica Sinica 50, 1742-1746 (2001) (in Chinese)
  7. Y. H. Yan, and M. L. Zhong, High Power Laser Process and Application (Tianjin Science and Technology Press, Tianjin, 1994) (in Chinese).
  8. J. L. Xu, and S. X. Jin, Plasma physics (Nuclear Energy Press, Beijing, 1981) (in Chinese).
  9. G. J. Pert, �??Model calculations of XUV gain in rapidly expanding cylindrical plasmas,�?? J. Phys. B: At. Mol. Phys. 9, 3301-3315 (1976).
    [CrossRef]
  10. G. J. Pert, �??Model calculations of XUV gain in rapidly expanding cylindrical plasmas II,�?? J. Phys. B: At. Mol. Phys. 12, 2067-2079 (1979).
    [CrossRef]
  11. G. J. Pert, �??Model calculations of extreme-ultraviolet gain in rapidly expanding cylindrical carbon plasmas,�?? J. Opt. Soc. Am. B 4, 602-608 (1987).
    [CrossRef]
  12. G. J. Pert, and S. A. Ramsden, �??Population inversion in plasmas produced by picosecond laser pulses,�?? Opt. Commun. 11, 270-273 (1974).
    [CrossRef]
  13. W. J. Fader, �??Hydrodynamic model of a spherical plasma produced by Q-spoiled laser irradiation of a solid particle,�?? Phys. Fluids 11, 2200-2208 (1968).
    [CrossRef]
  14. A. V. Farnsworth, �??Power-driven and adiabatic expansions into vacuum,�?? Phys. Fluids 23, 1496-1500 (1980).
    [CrossRef]
  15. M. A. Treu, J. R. Albritton, and E. A. Williams, �??Fast ion production by suprathermal electrons in laser fusion plasmas,�?? Phys. Fluids 24, 1885-1893 (1981).
    [CrossRef]

AIAA J.

A. V. Pakhomov, and D. A. Gregory, �??Ablative laser propulsion: an old concept revisited,�?? AIAA Journal 38, 725-727 (2000).
[CrossRef]

Astronautics & Aeronautics

A. Kantrowitz, �??Propulsion to orbit by ground-based lasers,�?? Astronautics & Aeronautics (A/A) 10, 74-76 (1972).

J Phys. B: At. Mol. Phys.

G. J. Pert, �??Model calculations of XUV gain in rapidly expanding cylindrical plasmas II,�?? J. Phys. B: At. Mol. Phys. 12, 2067-2079 (1979).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B: At. Mol. Phys.

G. J. Pert, �??Model calculations of XUV gain in rapidly expanding cylindrical plasmas,�?? J. Phys. B: At. Mol. Phys. 9, 3301-3315 (1976).
[CrossRef]

Opt. Commun.

G. J. Pert, and S. A. Ramsden, �??Population inversion in plasmas produced by picosecond laser pulses,�?? Opt. Commun. 11, 270-273 (1974).
[CrossRef]

Phys. Fluids

W. J. Fader, �??Hydrodynamic model of a spherical plasma produced by Q-spoiled laser irradiation of a solid particle,�?? Phys. Fluids 11, 2200-2208 (1968).
[CrossRef]

A. V. Farnsworth, �??Power-driven and adiabatic expansions into vacuum,�?? Phys. Fluids 23, 1496-1500 (1980).
[CrossRef]

M. A. Treu, J. R. Albritton, and E. A. Williams, �??Fast ion production by suprathermal electrons in laser fusion plasmas,�?? Phys. Fluids 24, 1885-1893 (1981).
[CrossRef]

Phys. Rev. Lett.

O. L. Landen, D. G. Stearns, and E. M. Campbell, �??Measurement of the expansion of picosecond laser-produced plasmas using resonance absorption profile spectroscopy,�?? Phys. Rev. Lett. 63, 1475-1478 (1989).
[CrossRef] [PubMed]

Physica Sinica

Y. Cang, W. Wang, and J. Zhang, �??Research of the dynamic process of the interaction between ultra-short laser pulse and solid-density plasma,�?? Acta Physica Sinica 50, 1742-1746 (2001) (in Chinese)

Other

Y. H. Yan, and M. L. Zhong, High Power Laser Process and Application (Tianjin Science and Technology Press, Tianjin, 1994) (in Chinese).

J. L. Xu, and S. X. Jin, Plasma physics (Nuclear Energy Press, Beijing, 1981) (in Chinese).

D. Darling, �??The encyclopedia of astrobiology, astronomy, and spaceflight,�?? <a href="http://www.daviddarling.info/encyclopedia/L/laserprop.html">http://www.daviddarling.info/encyclopedia/L/laserprop.html</a>.

A. V. Pakhomov, and D. A. Gregory, �??Ablative laser propulsion: an advanced concept for space transportation,�?? Young Faculty Research Proceedings, the University of Alabama in Huntsville, 63-72 (2000).

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Figures (11)

Fig. 1.
Fig. 1.

Experimental setup of femtosecond laser propulsion of microbead(s), h=152 mm.

Fig. 2.
Fig. 2.

Flying distance S of a microbead as a function of laser beam spot size d for three different materials (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2 =1.5).

Fig. 3.
Fig. 3.

Momentum coupling efficiency Cm as a function of laser beam spot diameter d obtained for microbeads made of three different materials (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2 =1.5)

Fig. 4.
Fig. 4.

Energy conversion efficiency η as a function of laser beam spot diameter d for three different types of microbeads (The single pulse energy is 0.94 mJ and the pulse duration is 47 fs, M2 =1.5)

Fig. 5.
Fig. 5.

Flying distance S as a function of single pulse energy E for iron beads (The laser pulse duration is 47 fs and the focal length of lens B is 10 cm.)

Fig. 6.
Fig. 6.

Momentum coupling efficiency Cm as a function of single pulse energy E for iron beads (The laser pulse duration is 47 fs and the focal length of lens B is 10 cm.)

Fig. 7.
Fig. 7.

Energy conversion efficiency η as a function of single pulse energy E for iron beads (The pulse duration is 47 fs and the focal length of lens B is 10 cm.)

Fig 8.
Fig 8.

Flying distance S as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

Fig 9.
Fig 9.

Momentum coupling efficiency Cm as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

Fig 10.
Fig 10.

Energy conversion efficiency η as a function of laser pulse duration Δt for iron beads (The single pulse energy is 1.20 mJ and the focal length of lens B is 10 cm.)

Fig 11.
Fig 11.

Fitting curve of the electron temperature at the end of laser pulse heating (Te0 in keV.) versus the incident laser pulse intensity (I in 1016W/cm2)

Tables (2)

Tables Icon

Table 1. Average size and weight of microbeads used in fs laser propulsion

Tables Icon

Table 2. Estimated electron temperature in iron for different laser pulse intensities

Equations (8)

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

d = 2 ( λ π w ) f M 2
v = Cs = ( γ Z 0 T e 0 M i ) 1 2
T e 0 = C t E 4 9 Δ t 2 9
V 0 10 π d 2 L s 4
L s = C ω pe
ω pe = ( n e e 2 m e ε 0 ) 1 2
v = 3 Cs
T e 0 I 1.8405

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