CO 2 laser–plume interaction in materials processing

K. R. Kim and D. F. Farson

Citation: Journal of Applied Physics 89, 681 (2001); doi: 10.1063/1.1329668

View online: http://dx.doi.org/10.1063/1.1329668
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 JOURNAL OF APPLIED PHYSICS VOLUME 89, NUMBER 1 1 JANUARY 2001

CO2 laser–plume interaction in materials processing

K. R. Kima) and D. F. Farsonb)
Department of IWSE, The Ohio State University, 1248 Arthur E. Adams Drive, Columbus, Ohio 43221
共Received 24 April 2000; accepted for publication 3 October 2000兲
In laser materials processing, localized evaporation caused by focused laser radiation forms a plume
of mixed vapor and ambient gas above the material surface. The beam is refracted and absorbed as
it traverses the plume, thus modifying its power density on the surface. In this work, plume–beam
interaction is studied using an axisymmetric, high-temperature gas-dynamic model of a plume
formed by vapor from an iron surface. The beam propagation in the plume is calculated from the
paraxial wave equation including absorption and refraction. The simulation results quantify the
effects of plasma plume properties on the beam radius and laser power density variations at the
material surface. It is shown that absorption and refraction in the plume have significant impacts on
the laser–material interaction. Absorption of the beam in the plume has much less direct effect on
the power density at the material surface than refraction does. However, absorption is essential for
the formation of the plume, without which there is no refraction. Helium gas is more efficient than
argon for reducing the beam refraction and absorption effects. Laser energy reflected from the
material surface has significant effects on the plume properties. © 2001 American Institute of
Physics. 关DOI: 10.1063/1.1329668兴

I. INTRODUCTION formed by Beck et al.,19 who calculated absorption and de-

focusing of a laser beam propagating through a laser-induced
In many laser materials processes, a continuous-wave plasma with assumed composition and temperature distribu-
共CW兲 laser beam is focused onto the material surface at an tions. Although the plume conditions were approximated in
energy density sufficient to cause localized heating and Beck’s work, there was evidence that both absorption and
evaporation. As a result, a plume of hot, ionized material refraction could have significant effects on the power density
vapor mixed with ambient gas forms above the surface. An at the work surface.
example of a process where plume formation is important is The present work extends previous results by incorporat-
CO2 laser welding.1 Experimental measurements2,3 show that ing laser beam propagation into a relatively complete physi-
the material vapor/ambient gas mixture that forms at irradi- cal model of the plume above a surface so that the dynamic
ances typical of welding is partially-ionized. However, interaction of the two can be studied in detail. The coupled
partially-ionized gases absorb infrared wavelength by the in- dynamic model of the plume and beam propagation is used
verse Bremsstralung mechanism4,5 and electron density gra- to calculate the dynamic beam radius and intensity changes
dients refract the beam so as to defocus it. Hence, the power on the material surface during CO2 laser–material interac-
and trajectory of the laser beam are modified as it traverses tion.
the plume and the laser power density impinging on the ma-
terial surface is decreased as the plume–beam interaction
effects become stronger.
The plume model described in this work builds on a rich
literature. Many articles, e.g., Refs. 6–9, and a book10 pro- II. LASER-PRODUCED PLASMA PLUME MODEL
vide examples of recent models of pulsed laser plumes 共im-
portant in physical vapor deposition兲, which are similar to The flow and mixing of the gas/vapor mixture in the
CW laser plumes in some respects. Laser energy absorption plume is modeled with compressible Navier–Stokes equa-
and scattering is sometimes considered in these analyses but tions. In an axisymmetric cylindrical coordinate system,
beam refraction is not. Other efforts that are somewhat re- these can be written as20
lated to the current work deal with modeling of phenomena
in laser weld keyholes.11–15 In examples of articles that do ⳵␳ s 1 ⳵ ⳵
consider plume–beam interaction, Lacroix et al.16 analyzed ⫹ 共 ␳ ru 兲 ⫹ 共 ␳ s u z 兲 ⫽0, 共1兲
⳵t r ⳵r s r ⳵z
scattering in Nd:YAG laser plumes. Models of CW laser
plumes that calculate beam propagation by ray-tracing are
discussed by Dowden et al.17 and Jeng and Keefer.18 A much ⳵ 1 ⳵ ⳵ ⳵p 1 ⳵
more accurate calculation of beam propagation was per- 共 ␳ur兲⫹ 共 ␳ ru r2 兲 ⫹ 共 ␳ u r u z 兲 ⫹ ⫺ 共 r ␶ rr 兲
⳵t r ⳵r ⳵z ⳵r r ⳵r

a兲 ␶ ␪␪ ⳵
Electronic mail: kim.494@osu.edu ⫹ ⫺ 共 ␶ rz 兲 ⫽0, 共2兲
b兲
Electronic mail: Farson.4@osu.edu r ⳵z

0021-8979/2001/89(1)/681/8/$18.00 681 © 2001 American Institute of Physics

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 682 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson

⳵
⳵t
共 ␳uz兲⫹
1 ⳵
r ⳵r
⳵ ⳵p 1 ⳵
共 ␳ ru r u z 兲 ⫹ 共 ␳ u z2 兲 ⫹ ⫺
⳵z ⳵z r ⳵r
共 r ␶ rz 兲 I abs⫹␭ l 冉 冊
⳵T
⳵n l
⫽Q v v n , 共14兲

⳵ in which
⫺ 共 ␶ 兲 ⫹ ␳ g⫽0, 共3兲
⳵ z zz
⳵Et 1 ⳵
⫹
⳵ ⳵ ⳵
共 ru r E t 兲 ⫹ 共 u z E t 兲 ⫹ 共 pu r 兲 ⫹ 共 pu z 兲
v n⫽
p0
␳l
冑 M
2 ␲ RT v
exp
RT v冉
⫺⌬G lv
, 冊 共15兲
⳵t r ⳵r ⳵z ⳵r ⳵z
and
1 ⳵ ⳵ 1 ⳵
⫹
r ⳵r
共 rq r 兲 ⫹ 共 q z 兲 ⫺
⳵z r ⳵r
共 ru r ␶ rr ⫹ru z ␶ rz 兲
⌬G lv⫽⌬H lv 冉 Tv
T lv 冊
⫺1 . 共16兲
⳵ ur
⫺ 共 u ␶ ⫹u z ␶ zz 兲 ⫹ 共 ␶ ␪␪ 兲 ⫺
⳵ z r rz r 兺 ␣ I⫽0, 共4兲 Here, I abs is absorbed laser intensity, ␭ l is thermal conduc-
tivity of the liquid, n is the interface normal, Q v is the volu-
where metric heat of evaporation of iron, v n is interface velocity,

冋 册
T lv is the liquid–vapor equilibrium temperature of iron at
2 ⳵ur ⳵uz ur
␶ rr ⫽ ␮ 2 ⫺ ⫺ , 共5兲 ambient pressure p 0 , M is the molar mass of iron, R is the
3 ⳵r ⳵z r universal gas constant, T v is the liquid surface temperature,

冋 册
and ⌬H lv is the molar latent heat of evaporation. As de-
2 ur ⳵ur ⳵uz
␶ ␪␪ ⫽ ␮ ⫺ ⫺ , 共6兲 scribed below, the laser intensity on the material surface is
3 r ⳵r ⳵z calculated by modeling the propagation of a Gaussian laser
2
␶ zz ⫽ ␮ 2
3 冋
⳵uz ⳵ur ur
⳵z
⫺
⳵r
⫺
r
, 册 共7兲
beam through the plume. The liquid–solid phase change is
assumed to occur at the equilibrium melting temperature of
the iron and the boundary position is described by a Stefan

␶ rz ⫽ ␶ zr ⫽ ␮ 冉 ⳵ur ⳵uz
⫹ 冊 共8兲
condition

冉 冊 冉 冊
,
⳵z ⳵r ⳵T ⳵T
␭s ⫺␭ l ⫽Q l v nl , 共17兲
⳵T ⳵n s ⳵n l
q r ⫽⫺k , 共9兲
⳵r where ␭ s is thermal conductivity of the solid, Q l is the volu-
⳵T metric heat of melting of iron and v nl is the interface veloc-
q z ⫽⫺k , 共10兲 ity.
⳵z
In a thin 共several mean-free paths thick兲 region at the
dI liquid surface known as the Knudsen layer, the thermal mo-
⫽⫺ ␣ I, 共11兲 tion of the vapor particles evolves from a half-to a full-
dz
Maxwellian distribution.23 By kinetic analysis, and using a

冉
E t ⫽ ␳ e⫹
u r2 ⫹u z2
2
冊 . 共12兲
common assumption that the Mach number of the vapor flow
on the downstream side of the layer approaches sonic speed,
the state of the vapor on the downstream side of the layer
In Eqs. 共1兲–共12兲, u r is the velocity in the r direction, u z is the 共the inlet to the gas-dynamic plume simulation兲 can be ex-
velocity in the z direction, ␳ is density, p is pressure, T is pressed in terms of the surface temperature of the liquid20
temperature, k is thermal conductivity, I is local laser inten-
sity including reflection from material melting surface, ␣ is T inlet⫽0.67T̄, 共18兲
laser absorption coefficient, ␮ is the viscosity, g is gravita-
tional constant, e is internal energy and subscript ‘‘s’’ refers ␳ inlet⫽0.31¯␳ , 共19兲
to individual species 共iron and helium or argon兲 as well as
P inlet⫽0.21P̄, 共20兲
the mixture.
Flow in the plume is induced by evaporation from the where subscript ‘‘inlet’’ denotes boundary conditions for the
material surface. To model evaporation, one must consider plume model, Eqs. 共1兲 to 共12兲, and the overbar refers to
heating of the surface 共liquid in this case兲 and substrate. As- properties of vapor in equilibrium with the liquid at tempera-
suming constant thermal properties for each phase, the heat ture T v .
conduction in the liquid and solid iron is written in axisym- The pressure of saturated vapor adjacent to the liquid
metric coordinates as surface can be approximated by
1 ⳵ T 1 ⳵ T ⳵ 2T ⳵ 2T
⫽ ⫹ ⫹
␣p ⳵t r ⳵r ⳵r2 ⳵z2
, 共13兲 冋
p̄ 共 T v 兲 ⫽ p 0 exp ⌬H lv
T v ⫺T lv
RT v T lv册. 共21兲

where ␣ p is thermal diffusivity of phase ‘‘p,’’ either liquid or A perfect gas relation,
solid. The evaporation phase change is represented with Ste-
fan and kinetic boundary equations21,22 ¯␳ 共 T v 兲 ⫽ p̄ 共 T v 兲 M /RT v , 共22兲
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 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson 683

can then be used to obtain the saturated vapor density. The

inlet flow velocity, V s,inlet is calculated as the theoretical
sound speed at the downstream side of the Knudsen layer,22

V v ,inlet⫽ 冑␥ P v ,inlet
␳ v ,inlet
⫽ 冑␥ R
T ,
M inlet
共23兲

where ␥ is the ratio of specific heats for the monatomic va-

por. Hence, the inlet flow velocity distribution depends on
the material surface temperature. The viscosities of indi-
vidual plume species ‘‘s’’ are obtained from a Chapman–
Enskog kinetic relation24
冑M s T
␩ s ⫽2.6693⫻10⫺1 , 共24兲
D ␴2 ,s
where ␩ s is viscosity, M s is atomic mass, T is temperature,
FIG. 1. Physical domain for plume simulation.
D ␴2 ,s is atomic collision diameter. Wilke’s formula24 is ap-
plied to calculate the viscosity of the plume mixture. The

冋 册
thermal conductivity of individual pure atomic species ‘‘s’’
are calculated from a Chapman–Enskog kinetic relation24 ␻ 3p
n⫽ 1⫺ , 共32兲
␻ 共 ␻ 2p ⫹ ␻ 2e 兲
1.9891⫻10⫺4 冑T/M s
k s⫽
D ␴2 ,s
,

and combined using Wilke’s formula. The specific heat of

共25兲
␻ p⫽ 冑 e 20 n e
␧ 0m e
, 共33兲

the partially-ionized mixture is calculated as detailed in a n 2e

previous article.25 ␣ ⫽3.3⫻10⫺39 3/2 . 共34兲
Te
Ionization is calculated from the Saha equation coupled with
a perfect gas equation of state, both written for single ion- In the above equations, k opt is the optical wave number, ␭ is
ization as25 the laser wavelength, n̂ is complex index of refraction, ␻ is
CO2 laser frequency, ␻ p is plasma frequency, ␻ e is electron
n s⫹ n e
ns
⫽
2Z z⫹ 共 2 ␲ m e k B T 兲 3/2
Zs h3
exp ⫺ 冉
eV I,s
k BT
, 冊 共26兲 collision frequency 共please refer to the literature17,19 for de-
tails兲, e 0 is the elementary charge, n e is electron number
density, ⑀ 0 is the permittivity of vacuum, m e is the electron
where n s , n s⫹ , and n e are, respectively, the particle densities
mass, and c is the speed of light. The expression for the
of species ‘‘s,’’ ions of ‘‘s’’ and electrons, Z s is the partition
electron–ion inverse Bremstrahlung absorption coefficient
function of ‘‘s,’’ m e is electronic mass, k B is the Boltzmann
for CO2 laser radiation, ␣, assumes partial ionization.1
constant, h is the Planck constant, and V I,s is the ionization
Electron-neutral absorption is negligible.5 For a Gaussian
potential of ‘‘s.’’ This equation is coupled with an ideal gas
beam characterized by beam quality parameter M 2 , the com-
equation of state and charge balance equation to solve for the
plex amplitude is
various particle densities.25 In this equation 共and all others兲,
all particles are assumed to all be at the same temperature.
When the electric field E(r,z) of a propagating axisym- U 共 r,z 兲 ⫽ 冉 1
R共 z 兲
⫺i
M 2␭
␲W 共z兲
2 exp ⫺
ikr 2
冊 冉
2R 共 z 兲
r2
exp ⫺ 2
W 共z兲
. 冊 冉 冊
metric laser beam is written as 共35兲
E 共 r,z 兲 ⫽U 共 r,z 兲 exp共 ⫺ikz 兲 , 共27兲 where R(z) is wave front radius of curvature and W(z) is
beam radius. The beam is distorted in is passage through the
it can be shown26 that the complex scalar amplitude U(r,z)
plume and has nonspherical wave fronts. Consequently, its
satisfies the paraxial wave equation
effective radius at a given axial distance is calculated by
⳵ U 共 r,z 兲
⳵z
⫽⫺
i ⳵2
2k ⳵ r 2⫹ 冋
1 ⳵
r ⳵r
⫹k opt
2
共 n̂ 2 ⫺1 兲 U 共 r,z 兲 . 册 共28兲
integrating the complex amplitude to find the radius W(z)
that contains 86% of the total power,

In Eqs. 共27兲 and 共28兲, 兰 w0 兩 U 共 r,z 兲 兩 2 dr

⫽0.86.
兰 ⬁0 兩 U 共 r,z 兲 兩 2 dr
2␲
k opt⫽ , 共29兲 The axisymmetric boundary conditions for the plume
␭
simulation are illustrated in Fig. 1. All physical and flow
␭ properties at the plume simulation inlet are updated at each
n̂⫽n⫹i ␣, 共30兲
4␲ time step and vary in response to beam absorption at the
material surface. The physical domain size along the
c z-direction can be changed as a result of the transient behav-
␭⫽2 ␲ , 共31兲
n␻ ior of the plume vapor under certain conditions. Boundary
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 684 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson

FIG. 2. Velocity 共m s⫺1兲 and temperature 共K兲 profiles at 10⫺9 s. Inlet maxi-
mum velocity is 826 m s⫺1.
FIG. 3. Steady-state maximum surface temperature as a function of ab-
sorbed laser intensity.

conditions at the outlet are calculated by extrapolation. To

include shielding gas effects, uniform axisymmetric flow of taken as M 2 ⫽5. U(r,z) is calculated where the beam exits
helium or argon gas 共5–10 m/sec兲 is imposed at the side the lens and is propagated to the top of the simulation do-
boundary. It is assumed that the beam absorption into the main by matrix optics.26 After each material/plume simula-
molten iron is 13%.27 tion time step, this initial U(r,z) is propagated backwards
To correspond to CW 共rather than pulsed兲 laser interac- through the plume simulation domain by explicit integration
tion, established initial plume velocity and temperature field of Eq. 共28兲. The maximum distance step size for stability
are assumed. The initial plasma plume 共which is very small was determined by trial and error.
relative to its developed size兲 is assumed to be elliptical and The plume/beam/material simulation outlined above is
having Gaussian temperature and velocity distributions. The computationally intensive. For practicality, the material
temperature and flow fields shown in Fig. 2 at 10⫺9 s are simulation is run separately from the plume/beam simula-
little changed from the initial conditions. tion. Steady-state results are summarized in a curve–fit rela-
Effects at the plume–material boundary are expected to tionship between maximum intensity at the material surface
play an important role in the laser interaction and were the and resulting maximum surface temperature 共Fig. 3兲. From
subject of parametric studies using the model. Since absorp- these surface temperature relations, updated inlet conditions
tion at the flat material surface is low, reflected energy will for the plume/beam simulation are calculated at each time
be high. Incorporation of the reflection into the beam propa- step using Eqs. 共18兲 to 共20兲 and Eq. 共23兲. By comparison
gation presents simulation complications28 and depends criti- with the material simulation results, the inlet speed distribu-
cally on the macroscopic and microscopic geometry of the tion is well-approximated by a cosine relationship, illustrated
liquid surface. In the simulations described below, reflection in Fig. 1. This computational approach eliminates the dy-
is approximated by increasing the power in the incident namic response of the material simulation. For Gaussian heat
beam by 50%, an experimental value reported in Ref. 2. input to a liquid iron surface, the dynamics of the maximum
Detailed analysis and accurate modeling of reflection phe- temperature can be approximated22 by a time constant of
nomena is planned for future work. It is noted that emission 10⫺3 s. This is so slow compared to the plume dynamics that
and absorption of electrons from the material may affect the eliminating its effect was necessary for computational feasi-
absorption coefficient of the vapor near surface. Tix et al.13 bility. The effects of this assumption on the results are noted
carried out analyses of these effects in the laser weld key- in the discussion below.
hole, assuming a nonflowing, highly-ionized plasma. Incor-
poration of these phenomena is also planned for future work.
III. NUMERICAL MODELING STUDY RESULTS
The explicit MacCormack scheme is used to calculate
velocity, density, and temperature profiles in the plume. The Plots of simulation results at ‘‘nominal’’ conditions 共3
optimal time step is calculated as the minimum of the Von kW power, 0.1 mm spot radius, 9⫻1010 W m⫺2 surface in-
Neumann and Courant–Friedrichs–Levy 共CFL兲 stability tensity, helium shielding兲 are shown in Figs. 4 and 5. Begin-
conditions. The shield gas and iron vapor mixing is com- ning from the initial conditions, the vapor plasma continu-
puted using strong coupling of the single-species continuity ously expands as a result of the beam absorption. At 10⫺5 s
equations at each time step.20 The continuity equations are after the start, Fig. 5 shows that the maximum temperature in
combined with the Navier–Stokes equations and computed the core of the plume reaches 8100 K. The plume height is
at the same time step. about 2 mm, the maximum pressure is 36 atm and the maxi-
Boundary conditions for the beam propagation calcula- mum flow velocity is approximately 900 m s⫺1. The pressure
tion correspond to a collimated 2 cm diameter CO2 laser indicates that the plume is still evolving since it is sur-
beam focused by a 12 cm lens. The laser beam quality is rounded by a boundary at 1 atm. At longer simulation times,
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 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson 685

FIG. 6. Velocity 共m s⫺1兲 and temperature 共K兲 profiles at 5⫻10⫺6 s, argon

FIG. 4. Velocity 共m s⫺1兲 and temperature 共K兲 profiles at 5⫻10⫺6 s, helium shielding gas.
shielding gas.

experimental temperature measurements presumably corre-

the plume shown in Fig. 5 continued to grow vertically and spond to lower core pressures than the transient simulated
eventually detached from the material surface before dissi- simulation conditions.
pating. Experimental measurements of plume flow fields at con-
It is interesting to compare these results to experimental ditions comparable to those used in this simulation are not
measurements and previous simulation results. The most rel- available in the literature. In a prior simulation, Aden et al.6
evant experimental temperature plume measurements are solved the Euler equations, steady heat-flow equation, and
from laser welding experiments, although the fact that the the kinetic equation to calculate the gas dynamic properties
material surface develops a keyhole makes the conditions at the edge of the Knudsen layer. They calculated the veloc-
significantly different from the flat surface assumed in the ity of the metal vapor and the displaced ambient air for an
simulation. When CO2 laser welding iron plates at 1⫻1010 absorbed laser intensity of 1010 W m⫺2. At an intensity of
⬃5⫻1010 W m⫺2 power density under helium shielding gas, 1011 W m⫺2, the plume core pressure increased up to 60 atm
Poueyo et al.29 measured averaged plasma temperatures of at a simulation time of 2⫻10⫺5 s. The inlet velocity, maxi-
5200–6800 K using spectroscopy. Sokolowski30 reported an mum velocity, and maximum pressure in Figs. 4 and 5 are
average CO2 laser weld plume temperature of 7500 K under comparable with those found in the Aden’s model. A pulsed
a power density of 4⫻1010 W/m2. He used helium as a laser plume model was described by Nielsen.31 At a focused
shielding gas. Poueyo et al.29 again measured temperatures irradiance of 1011 W m⫺2 共approximately that of the current
of 6300–6900 K using 1–15 kW laser power with helium simulation兲, he obtained core pressures of 115 atm after 2
shielding gas. In the present simulation, the maximum ␮s. This is significantly higher than the maximum pressure
plasma plume temperature at 10⫺5 seconds and 3 kW of in Fig. 5, but the initial conditions did not assume an estab-
laser power with helium shielding gas is 8100 K. Thus, the lished flow field so the overall character of the flow was
temperatures predicted by the axisymmetric simulations cor- quite different.
respond reasonably well to experimental results, although the The shielding gas is recognized as a very important pa-
rameter in laser materials processing, where helium and ar-
gon are both popular options. The plume conditions resulting
from laser material interaction under argon shielding gas are
presented in Fig. 6. The maximum 共11 000 K兲 and average
plume temperatures for argon shielding are higher than those
predicted for helium shielding. This result corresponds well
to experimental measurements made during welding at com-
parable powers, where maximum plume temperatures from
9000 共Ref. 3兲 to 13 000 共Ref. 32兲 have been reported.
The predicted variation of the index of refraction and the
absorption coefficient within the plume are shown in Fig. 7
for helium shielding gas. The index of refraction decreases
from 1.0 in the unionized gas/vapor outside the plume to
0.995 at its core. The absorption coefficient increases from 0
to 42 m⫺1. Since electron density directly determines its
value through Eq. 共34兲, the absorption coefficients reflect
FIG. 5. Pressure contours 共atm兲 and temperatures 共K兲 at 10⫺5 s, helium electron density, which reaches a maximum value of the or-
shielding gas. Maximum temperature at center of plume is 8100 K. der 1023 m⫺3 in the center of the plume. The results for argon
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 686 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson

FIG. 7. Real part of index of refraction and absorption coefficients 共m⫺1兲 at

5⫻10⫺6 s, helium shielding gas.

FIG. 9. Beam radius changes for argon and helium shielding gases at 5
shielding are shown in Fig. 8. Because of the higher plume ⫻10⫺6 s.
temperatures, the index of refraction is somewhat smaller in
the center while the maximum absorption coefficient is argon shielding gas. The plume simulation was run with zero
larger than for helium. The beam radius variation with ver- absorption and zero refraction assumptions to determine their
tical distance for the two different shielding gases is pre- relative effects on surface power density. The top curve in
sented in Fig. 9. The radius increase is more pronounced for Fig. 11 shows the results of the zero absorption trial. In this
the argon plume, due to its larger index of refraction gradi- case, there was no energy to maintain the plume so it quickly
ent. The beam radius changes on the material surface are dissipated from its initial condition and the intensity at the
quantified in Fig. 10, at simulation times up to 5⫻10⫺6 s. surface corresponded to the fully-focused 3 kW beam. The
The beam radius for the helium shield case is about 15% flow field of the dissipated plume at 5⫻10⫺6 s is shown in
larger than the unrefracted case and remains fairly steady Fig. 12. When absorption was included in the plume simula-
over the time interval. The beam radius for argon shielding tion but refraction was not, the plume was fully formed 共with
increased rapidly by about 20% then steadily grew to 33% properties essentially identical to those shown in Fig. 4兲, but
and was still increasing at the end of the simulation time. the beam intensity at the material surface was only reduced
The zero refraction, zero absorption, and zero reflection by 3%. Thus, the significant power density decreases pre-
cases are discussed in more detail below. dicted by the lower two curves in Fig. 11 are mostly due to
The beam irradiance changes on the material surface for refraction. This result is also illustrated in Fig. 13, which
helium and argon shielding are shown in Fig. 11. These shows that the combined effects of absorption and refraction
curves correspond very closely to the focal spot radius 共lower curve兲 decrease the temperature of the vapor entering
changes in Fig. 10, indicating that power density on the ma- the plume from the Knudsen layer much more than absorp-
terial surface is decreased more by defocusing than by ab- tion alone.
sorption. Over the simulation time, the beam intensity de-
creased by 26% for helium shielding gas and by 46% for

FIG. 8. Real part of the index of refraction and absorption coefficients 共m⫺1兲 FIG. 10. Beam radius changes at the material surface for various plume
at 5⫻10⫺6 s, argon shielding gas. interaction conditions and shielding gases.
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 J. Appl. Phys., Vol. 89, No. 1, 1 January 2001 K. R. Kim and D. F. Farson 687

FIG. 13. Variation of maximum temperature of vapor at the plume simula-

tion inlet.
FIG. 11. Time variation of beam irradiance adjacent the material surface for
various plume interaction and ambient atmosphere conditions.
2⫻1011. Two unmodeled effects would tend to stabilize the
plume. One is increased absorption coefficient in the near-
As mentioned in the previous section, reflections from surface vapor due to electrons or particulates emitted from
the material surface, which is assumed to be flat in this study, the material. Another is distortion of the surface due to mo-
are expected to significantly influence the plume. All of the tion and evaporation of the melt. It is noted that the fast
simulation results shown above include a 50% reflection as- surface temperature response inherent in the simulation ap-
sumption. The significance of reflection was investigated by proach will tend to stabilize the simulated plumes since de-
running the simulation without considering it. The simula- creased surface power density due to plume development
tion predicted that the plume was dissipated somewhat more results in lower vapor flow rates.
rapidly than the nominal case. This is observed in the focus
spot radius variation curve in Fig. 10 labeled ‘‘zero reflec-
IV. CONCLUSIONS
tion.’’ The predicted radius is initially the same as for the
nominal case, but decreases toward the unrefracted radius as An axisymmetric model of the plasma plume formed by
the plume dissipates. a CO2 laser beam impinging on a flat iron surface has been
The stability of the plume is also of practical interest. As described. The following conclusions are drawn from the
mentioned above, the simulated plumes are not stable at the simulation results.
nominal conditions used in this work. Experimental 共1兲 The CO2 laser beam is significantly defocused as it
evidence33 confirms this behavior for plumes above flat sur- propagates through the plasma plume.
faces. However, the simulated plumes in the present work 共2兲 Refraction of the propagating CO2 laser beam in the
appear to dissipate at lower nominal power density than ex- plasma plume has a much larger direct effect on the beam
perimental ones. At nominal conditions (9⫻1010 W m⫺2), power density at the material surface than absorption does.
the simulation predicts plume instability whereas experimen- However, without absorption, the plume quickly dissipates.
tally, such behavior was only observed above a threshold of Thus, indirectly, the plume absorption also has a large im-
pact on power density at the material surface.
共3兲 Less beam refraction and absorption are observed for
helium shielding gas than argon.
共4兲 Surface power density changes that calculated as the
plume evolves have nontrivial effects on the properties of the
metal vapor entering the plume.
共5兲 At the nominal simulation conditions, the plume is
not stable but dissipates within 10⫺4 s.
共6兲 Laser energy reflected from the material surface has
significant effects on plume properties and stability.

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