OS2-6
静電浮遊炉を用いたレーザーアブレーション推力の計測および推力推定モデルの構築
Measurement of laser ablation thrust using anelectrostatic levitation furnace and development of athrust estimation model
國分ひなた 1, 森浩一 1, 石川毅彦 2, 小山千尋 2, 織田裕久 2,Hinata KOKUBU1, Koichi MORI1, Takehiko ISHIKAWA2, Chihiro KOYAMA2 and Hirohisa ODA2
大阪公立大学大学院 工学研究科 航空宇宙海洋系専攻，Osaka Metropolitan University Aerospace Engineering,JAXA，Japan Aerospace Exploration Agency.

121. Introduction
In recent years, space debris have been increasing in number and has become an obstacle to spacedevelopment. In particular, space debris of 1-10 cm in diameter cannot be observed from the ground and cantotally destroy a spacecraft by collision. Therefore, debris removal by deorbit using laser ablation is promising.
A scenario in which debris is deactivated and incinerated in the earth's atmosphere by irradiating it with alaser using a debris removal satellite has been proposed. In order to avoid debris splitting due to the use ofhigh-power laser, the use of low-power and high-density laser is being considered. However, this removal
method has not been realized. In order to achieve it, it is necessary to estimate the laser ablation thrust acting
on the actual debris. Previous experiment measured laser ablation thrust in a thermally isolated environment
using a ground-based electrostatic levitation reactor. However, this experiment had difficulties in levitatingaluminum, the main material of debris, and convection currents in the metallic droplets caused the heattransfer coefficient to be different from that in the space environment. Therefore, in this study, we used theelectrostatic levitation furnace (ELF) installed in the ISS to measure laser ablation thrust in the use of aluminumand in the space environment. In addition, a model for estimating the generated thrust from the viewpoint ofheat conduction was constructed in a previous study, but it is not in sufficient agreement with theexperimental results. Therefore, in this study, the heat conduction model was improved in parallel with thespace experiment, and the mechanism of thrust generation was reexamined in order to complete a model thatcan quantitatively explain the results of the above-mentioned ground experiment.

1 of 7

2.

Thrust Measurement Experiment2.1. Experimental method
In this experiment, an ELF installed in the ISS was used. Figure 1 shows a schematic diagram of the ISS-ELF.
The sample is floated stably in the chamber by adjusting the applied voltage to the top, bottom, left, and rightelectrodes by PD control based on a position sensor called IVS. The chamber is filled with Ar and the pressureis 2 atm. The experiment was divided into three stages: free drift experiments were conducted before, during,and after heating the sample. This experiment was filmed by a high-speed camera and a magnifying camera.
First, the metal sample is stably floated, and then the voltage applied to the sample is turned off to allow it
to free-drift. When the sample moves 2mm from the initial position, the applied voltage is turned on again toreturn the sample to its initial position. This operation is hereinafter referred to as FD. Next, the sample ismelted by four lasers mounted on the ELF. After confirming that the sample was floating stably after melting,the output of only one laser was reduced and FD was performed again. After that, all lasers were turned off,the sample was cooled, and FD was performed.

2.2. Analysis method
The forces acting on the sample are considered to be residual gravity, laser ablation thrust, and Coulomb
force due to the voltage between the electrodes. In the following, the physical quantities before, during, andafter heating are denoted by subscripts 1, 2, and 3. The control voltage is denoted by 𝑉, the offset voltage by
𝑉𝑟 , the microgravity acceleration by 𝐺𝜇 , the electric charge in the sample by 𝑄, and the distance between theelectrodes by 𝑑.
The equation of motion of the sample at FD before heating is expressed by the following
𝑚𝒙𝟏̈ = 𝑄1

𝑽𝒓+ 𝑚𝑮𝝁 .
𝒅(1)Next, the equation of motion of the sample in FD during heating is expressed by the following equation. Since
the laser continues to irradiate the sample during heating FD, the thrust due to the laser is added to theFigure 1. A schematic diagram of ISS-ELF

2 of 7equation (1).
𝑚𝒙𝟐̈ = 𝑄2

𝑽𝒓+ 𝑚𝑮𝝁 + 𝑭𝒍𝒂𝒔𝒆𝒓 .
𝒅(2)The equation of motion of a sample at FD after heating is expressed by the following
𝑚𝒙𝟑̈ = 𝑄3

𝑽𝒓+ 𝑚𝑮𝝁 .
𝒅(3)Here, the offset voltage is sufficiently small compared to the control voltage, and the microgravity is alsosufficiently smaller than the Coulomb force due to the control voltage, so these forces can be considerednegligible. Therefore, the equation of motion of a sample in stable suspension before heating can betransformed as follow:
𝑚𝒙𝟏̈ = 𝑄1𝑽.
𝒅(4)In the same way, the equation of motion of a sample in stable suspension after heating can be transformed asfollow:
𝑚𝒙𝟑̈ = 𝑄3𝑽.
𝒅(5)Since the sample position is known from the IVS position detection data, the above equation can be used tocalculate the charge on the sample before and after heating. With the charge known, the offset voltage andresidual gravity can be calculated using equations (1) and (3). Finally, the laser ablation thrust is calculatedusing equation (2).
The energy conservation law of FD during heating is expressed as follow:
1𝑉𝑟 𝑋
2𝑚𝑣𝑓𝑖𝑛= 𝐹𝑙𝑎𝑠𝑒𝑟 𝑋 + 𝑄2 () + 𝑚𝐺𝜇 𝑋,2𝑑(6)where 𝑋 is displacement and 𝑣𝑓𝑖𝑛 is velocity of the sample at the end of FD. The charge 𝑄2 and laser
ablation thrust were obtained by solving equations (2) and (6) in series.

2.3. Experimental results
As an example of the experimental results, Figure 2 shows the IVS position detection and its fitting results.
The IVS data were rounded to the first decimal place 1), and the fitting was done as a quadratic function. After
fitting in this way, the obtained function was used to calculate the generated thrust using the analytical method
described in the previous section. The results of the thrust calculation are shown in Figure 3 and 4. Figure 3
shows that when the Al sample was irradiated with a laser power density of 4.6-5.6 [kW/cm2], a thrust of 15 –30 [nN] was generated. Figure 4 shows that when the Ti sample was irradiated with a laser power density of
18 to 20 [kW/cm2], a thrust of 70 - 85 [nN] was generated. These results indicate that a thrust force is generated
by the laser. It was also found that the laser power density was not dependent on the laser power density.

3 of 7

(a) x-direction(b) y-direction(c) z-direction

Figure 2. Example of position change in FD during heating

Figure 3. Laser thrust generated on the sample

Figure 4. Laser thrust generated on the sample

4 of 7

3.

Thrust Estimation Model

3.1.

Thermal conductivity model

In this study, with the aim of completing a model that quantitatively explains the laser ablation thrust usinga ground electrostatic levitation reactor, the thermal conduction model3) constructed in the previous study wasimproved. The conceptual diagram is shown in Figure 5 and the procedure is as follows.
Ⅰ) The temperature increases locally due to heat input on the laser-irradiated surface.
Ⅱ) Inside the sample, heat is transferred based on a temperature gradient.
Ⅲ) The sample evaporates on the surface in response to temperature.
Ⅳ) Thrust is generated by the reaction of the impulse of the evaporated mass.
In step Ⅱ, the heat transfer is calculated by the following diffusion equation for heat conduction
𝜕𝑇𝜕2𝑇 𝜕2𝑇
𝜕2𝑇= α ( 2++),𝜕𝑡𝜕𝑥𝜕𝑦 2𝜕𝑧 2(7)where 𝑇 is temperature and α is thermal diffusivity. In addition, the following Neumann boundary
conditions were defined from Fourier's law for the cells at the outer edges of the sample.
λ𝑇𝑖,𝑗,𝑘 − 𝑇𝑖−1,𝑗,𝑘4= − 𝜀𝜎 ( 𝑇𝑖−1,𝑗,𝑘− 𝑇∞4 ) − 𝐽𝐿,∆𝑡(8)where λ is thermal conductivity, 𝜀 is emissivity, 𝜎 is Stefan-Boltzmann constant, 𝐽 is evaporation massand 𝐿 is latent heat. In step Ⅲ, the amount of evaporation is calculated by the Herz-Knudsen formula shownbelow.
𝐽 = α𝑃𝑊 √𝑚,2𝑘𝐵 𝑇𝑊(9)where 𝑃𝑊 is surface pressure, 𝑚 is molecular mass, 𝑘𝐵 is Boltzmann constant and 𝑇𝑊 is surface
temperature. In step Ⅳ, the thermal velocity of the evaporating mass obtained in equation (9) was calculated
from the temperature, and the impulse was obtained by multiplying it by the mass. The computational grid isconsidered to be a cubic lattice with 3-dimensional Cartesian coordinates. Furthermore, since the presence orabsence of sample rotation during the experiment is unknown, constant velocity rotation around an axis
perpendicular to the laser irradiation axis was considered as a simplified rotation model.

Figure 5. Conceptual diagram of heat transfer model
5 of 7

3.2.

Simulation results and Future vision

The results of numerical simulation under the experimental conditions shown in the Table 1 are shown in
the figure 6. Here, 𝑇𝑚 is the temperature at boiling point. The emissivity and absorptivity wereexperimentally determined to be close to the experimental and simulated results, since they were unknown
for the liquid metal. Overlapping of the graphs was based on laser power output. The figure 6 shows thatsufficient agreement was obtained for the temperature. However, the thrust was about 100 times larger thanthe experimental value, as shown in the figure 6. Furthermore, while a part of the experimental thrust appears
to be in a steady state, the simulation results show no such behavior. These results indicate that while the heattransfer model for estimating temperature can be considered complete, the model for calculating thrust is notadequate. Therefore, the method of generating thrust is currently being reexamined from the viewpoint ofexternal gas analysis, leaving the heat conduction model intact.
Table 1.

Simulation conditions

SampleZrSpecific heat

436 J/(kg・K)

Emissivity

0.13

Absorption rate

0.17

Density6782－0.27𝑇 kg/m3

Thermal conductivity

94.61+0.0441(𝑇 − 𝑇𝑚 ) W/(m・K)

Vapor pressure

1011.812−30295/𝑇 Pa(a) Comparison of temperature(b) Comparison of thrust

Figure 6. Comparison of experimental and simulation results

6 of 7

Acknowledgement
I would like to thank the researchers at JAXA's Ishikawa Laboratory for allowing us to use their electrostatic
levitation furnace as an experimental device, for their advice and cooperation on experimental methods, andfor giving us the opportunity to conduct on-orbit experiments on the ISS. I would like to take this opportunity
to express our deepest gratitude.

References
1)

2)
3)
4)
5)
6)
7)

Takehiko ISHIKAWA, Chihiro KOYAMA, Haruka TAMARU, Hideki SARUWATARI, Masato OHSHIO and Yasuhiro
NAKAMURA, Status of the Electrostatic Levitation Furnace in the ISS –Evaluation of Sample Position Control-,International Journal of Microgravity Science and Application, 2018, Volume 35, 2, 35025.
Naoki, MINAGAWA, Measurement of thrust generated by low-power CW laser irradiation of metallic droplets in anelectrostatic levitation furnace, master’s thesis for Osaka Metropolitan University, 2023.
Tomoya AKITA, Experiments on thrust measurement by CW laser ablation using an electrostatic levitation furnace anddevelopment of a thrust generation model, master’s thesis for Nagoya University, 2022.
Yuri B. Zudin, Non-equilibrium Evaporation and Condensation Processes, 3rd Ed, pp.17-24.
Paul-Francois Paradis and Won-Kyu Rhim. Thermophysical properties of zirconium at high temperature．𝐽𝑜𝑢𝑟𝑛𝑎𝑙 𝑜𝑓𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 𝑅𝑒𝑠𝑒𝑎𝑟𝑐ℎ，Vol. 14, No.9, pp.3713-3719, 1999.
Aaron J. Rulison and Won-Kyu Rhim ． Constantpressure specific heat to hemispherical total emissivity ratio forundercooled liquid nickel, Zirconium, and Silicon. 𝑀𝑒𝑡𝑎𝑙𝑙𝑢𝑟𝑎𝑔𝑖𝑐𝑎𝑙 𝑎𝑛𝑑 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 𝑇𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛𝑠 𝐵, Vol. 26, 1995.
Bonnell, D. W. , Treverton, J. A. , Valerga, A. J. , Margrave, J. L. The emissivities of liquid metals at their fusion temperature.
1972.
© 2024 by the authors. Submitted for possible open access publication under theterms and conditions of the Creative Commons Attribution (CC BY) license(http://creativecommons.org/li censes/by/4.0/).

7 of 7