Optics and Photonics Journal, 2013, 3, 11-14
doi:10.4236/opj.2013.32B003 Published Online June 2013 (http://www.scirp.org/journal/opj)
Numerical Simulation on Laser Propulsion Capability of
Polymer Target
Nanlei Li, Jifei Ye, Weijing Z hou
State Key Laboratory of Laser Propulsion and Application, Academy of Equipment, Huairou, Beijing, China
Received 2013
ABSTRACT
A computational model of laser ablated polymer was established. Set the ablation criterion based on threshold energy.
Put forward the polymer ablation criterion in the numerical model. It established the energy distribution equation to
describe the laser ablation process. When the ablation products ejected, the target gained recoil impulse from ejection
process. Get the ejection energy and the recoil momentum of target based on momentum conservation law. The numer-
ical analysis model can reflect the propulsion capability of different polymer propellant, revealed the law of propulsion
parameters in laser ablation process.
Keywords: Laser Propulsion; Laser Ablatio n; Polymer Target
1. Introduction
Laser propulsion as a new concept propulsion technology,
it is given more and more extensive concern by the main
astronautic powers. As one of the practical application
achievements, laser ablation micro thruster is one of th e-
focus[1,2]. With its hig h specific impulse, wide dynamic
range o f i mpuls e, s mal l mi nimu m i mp u lse bit, lo w power
and easy to realized the lightweight and digital control
etc, laser ablation micro thruster has wide application
prospects on high-precision task of satellite attitude ad-
justment, orbit maintain and networking formation con-
trol. Ba sed on these applications, the generation of micro
thrust using a middle or low intensity laser ablation was
studied. The principle of laser ablation micro thruster is
that using small portable laser ablated target can generate
micro thrust. Due to low thermal conduction, low abla-
tion threshold, polymer material was easily ablated to
generate thrust[3,4]. Based on the summary of domestic
and international laser micro propulsion development,
this paper studied the polymer propulsion properties
thro ugh establishing the theoretical calculation model.
Simulated the micro-thruster working vacuum envi-
ronment, a computational model of low intensity laser
ablated polymer was established. Put forward the poly-
mer ablation criterion based on the experimental pheno-
mena. The polymer doesn’t have fixed fusion point, so
building the ablation criterion based on threshold energy,
whic h has obs erve d in many e xpe ri ments o f re fere nce. In
the numerical model, the target ablation phenomenon
happens when inner deposited energy achieves the thre-
shold value. Along with inner deposited energy increas-
ing, ablation phenomenon continually happened and ab-
lation depth rose. It established the energy distrib ution
model to describe the ablation process of temperature
rise, phase change and the influence of chemical exo-
thermic process. When ablation phenomenon happened
the ablation products would ejected, and the target gained
recoil impulse from ejection process. Based on the con-
servation law, assumed that in the ablation process the
laser deposited energy consume in such aspects: fusion
and vaporization process, target inner energy which
made temperature rose, the exothermic energy in chemi-
cal reaction, product ejection energy. According to ener-
gy distribution equations we can get the ejection energy,
and then get the recoil momentum of target based on
momentum conservation law. Propulsion capability of
laser ablated polymer was studied through the numerical
analyse model. The generation law of impulse, thrust,
impulse coupling coefficient, specific impulse, ejection
velocity and ablation efficiency was calculated. And it
analyzed the propulsion capability of different polymer
targets.
The conclusions showed that, the numerical analysed
model can reflect the propulsion capability of different
polymer propellant, revealed the law of propulsion pa-
rameters in laser ablation process. The results for propel-
lant selection, micro-thruster design and improve ment of
propulsion performance are valuable.
2. Numerical Modeling

N. L. LI ET AL.
12
Laser ablated a target can caused micro-thrust, the direc-
tion is showed in Figure 1. Based on the physical
process of interaction between laser and polymer materi-
al, a numerical model was set up to simulate the ablation
thru s t and moment um coupli ng coefficient.
2.1. Thermal Conduction Equation
The first equation for interaction between laser and po-
lymer is thermal conduction energy conservation equa-
tions for column symmetric case.
1( )()
i
T TT
CK rq
trrrz z
ρ
∂∂ ∂∂∂

= ++

∂∂ ∂∂∂

(1)
where ρ, C and K are the target density, specific heat and
thermal conductivity, qi is target inner deposited power
whe n laser is heating.
2
02
(1)exp(), 0
0,
i
r
I Rzrb
qbrb
αα
−− −≤≤

=
>

(2)
where I0 and b are laser power and radius, R is target
reflectivit y, α is laser absorption coefficient in tar get.
2.2. Ablation Threshold Energy
Summarizing laser ablated polymers experiment results,
the ablation process is described by the following equa-
tion[5,6]
1
( )ln()
t
F
dF F
α
=
(3)
where F and Ft are laser fluence and ablation threshold
fluence; d(F) is the ablation rate; α is the laser absorption
coefficient. In the process of laser ablation, The polymer
don’t have fixed fusion point, so in this paper we build
the ablation criterion based on threshold energy, which
has observed i n the experiment. In our numerical model,
the target ablation phenomenon happens when inner de-
posited energy achieve the threshold value. Along with
inner deposited energy increasing, ablation phenomenon
continually happened and ablation depth rose. According
to Eq.(3), the ablation threshold energy is
th t
exp( )EF z αα =
(4)
Laser
Target
Products
Ejection
Thrust
Direction
Figure 1. Sketch of laser ablated polymer target.
After laser ir rad iation la st t ime t, the t ar ge t i nner d epo-
sited energy is
0(1 )exp() i
E IRzt αα =−−
(5)
When inner deposited energy is larger than ablation
threshold ener gy, the ablation phenomenon happened, so
the ablation criterion is
i th
EE≥
(6)
2.3. Energy Distribution Equation
When Eq.(6) achieves, it means the ablation phenomeno n
happened, and the ablation products would ejected, the
target gained recoil impulse from ejection process. Based
on the co nservation law, we assume that in the ablation
process the laser deposited energy consume in such as-
pects: fusion and vaporization process, target inner ener-
gy which made temperature rose, the exothermic energy
in chemical reaction, product ejection energy. the distri-
bution equation of energy Ei is
0
[( )]
ifv caej
Ehh h CT TE ρ =+−+− +
(7)
where hf,hv and hc are fusion heat, vaporiza tio n heat and
exothermic energy; Ta and T0 are ablation temperature
and initial temperature; Eej is ejection energy. According
to all above equations we can get the ejection energy Eej,
so the mome n tum Pej is
2
eja ej
P mE=
(8)
where ma is ablation mas s. Based on mo mentum conser-
vation law, Pej is equal to the recoil momentum P of tar-
get.
2.4. Simulation Setting
Considering the symmet ry configuration of laser and tar-
get, planar symmetric column coordinate is used in si-
mulation model. In actual ablation process, the ablated
products would eject form target and dissipated , so i n the
simulation model we set a ablation moving boundary, see
Figure 2.
In this paper, chose PVC (Poly vinylchloride), POM
(Polyoxymethylene), GAP (Glycidylacide polymer) as
targets in computation example, the parameters[7,8] of
pol ymer in Table 1. It analyzed the propulsion capability
of d iffere nt polymer s .
3. Numerical Results and Analysis
3.1. Momentum Coupling Coefficient
Figure 2 shows the relation of momentum coupling
coeffici entwith laser power. When ablation begin, the
momentum coupling coefficient increased rapidly and
reach the peak then fall slowly, the reason is plasma
screening e ffect weakened reaction of laser and target.

N. L. LI ET AL.
13
The exother mic polymer GAP has the maxim al momen-
tum coupling coefficient48dyn/W, because released
chemical energy in the ablation process, but PVC and
POM don’t have additional energy in ablation.
3.2. Specific Imp uls e
Figure 3 shows the relation of specific impulse with la-
ser power. When ablation begins, the exothermic poly-
mer GAPreleased chemical energy in the ablation
progress so has the maximalspecific impulse200s. The
PVC and POMincreased slowly, the stab iliz ation are
120s and 50s.
3.3. Compare with Experiment
The Figure 4 shows the comparison between experiment
and numerical model. According to literature description,
using our numerical model to calculate the experiment
results, lines represent experiment data and dots
represent simulation result s [9,10]. The simulation re sults
are basically accord with the experiment data. But there
is a little differe nt, the simulat ion results are le ss than the
experiment data in short laser pulse width. The reason
maybe in short width the m echanismis more complex,
and the model can’t simulatevery well.
020 40 60 80100
0
10
20
30
40
50
Cm (dyn/W )
I
0
(GW/m
2
)
PVC POM GAP
Figure 2. Moment um coupling coeff icient of polymers .
Table 1. Parameters of p olymer target.
PVC POM GAP
Densityρ Kg/m3 1439 1410 1290
Thermal conductivityK W/ (m K) 0.15 0.36 0.40
Specific heatC J/( kg K) 1700 1450 1800
ReflectivityR 0.2 0.2 0.2
Absorptioncoefficientα 1/m 1.7×105 1.0×105 2.0×104
Vaporization heathv J/kg 2.8×105 5.0×105 1.9×106
Chemical heathc J/kg 0 0 3.0×106
Ablation thresholdFt J/m2 9.0×103 1.0×104 3.1×104
02040 60 80100
0
20
40
60
80
100
120
140
160
180
200
220
240
I
sp
(s)
I
0
(GW/m
2
)
PVC POM GAP
Figure 3. Specific impulse of poly mers .
10
0
10
1
10
2
10
0
10
1
10
2
10
3
10
4
C
m
(dyn/W ), P (n Ns ), I
sp
(s)
t (ms)
simulation: C
m
I
sp
P
experiment: C
m
I
sp
P
Figure 4. Comp a r e simulation with exper ime nt.
4. Conclusions
Numerical model of laser ablated polymer was founded
to analyzed the propulsion capability of PVC, POM,
GAP. The results show that, the exothermic polymer
GAP has great propulsion capability because released
chemical energy in the laser ablation process. Its max-
imalmomentum coupling coefficient and specific impulse
are 48 dyn/W and 200s, more than PVC and POM. Po-
lymer GAP is an excellent propellant in laser ablation
propulsion.
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