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Aerosol protection of laser optics
by
Electrostatic Fields
(not manetic)
L. Bromberg
ARIES Meeting
Madison WI
April 23, 2002
Motivation
• Aerosols are created in chamber due to large heating flux on surface of
liquid, nucleation in the volume, ….
• Aerosols are charged, due to presence of plasma afterglow following
the pulse
• Electric fields can be used to remove aerosol
• Similar to electrostatic precipitators used commercially for
removing particulate matter from industrial flows
Structure of talk
• Charge state of aerosols exposed to plasma conditions
• Motion of charged aerosols under the presence of an electric field
• Implications to IFE laser optics
Aerosol clearing steps
Charging step
Clearing step
Aerosol charging
•
In the presence of a plasma, a particulate charge varies as
dq/dt = Ii+Ie
where
Ie = - p a2 e ve ne exp ( -e2 | Z | / e0 a Te)
Ii = p a2 e vi ni (1 + e2 | Z | / e0 a Ti)
•
Z is the average number of electronic charges in the particulate
• It is assumed that all radiation fields have decayed away
• Good for times > 1 microsecond
•
In the presence of irradiation:
• If Jph > e p a2 Y-1 ve ne , different sign sheath
Ie = - p a2 e ve ne (1 + e2 | Z | / e0 a Te)
Ii = p a2 e vi ni exp ( -e2 | Z | / e0 a Te)
Iph = jph e Y exp( -e2 | Z | / a Tph)
•
•
Much faster equilibration times, due to the lack of ion contribution to the charging
But at the large intensities, aerosols will not survive…
Average electronic charge number vs Te for several densities
35000
Number of electronic charges on aerosol
30000
ne = 5 1018 - 2 1019 m-3
ne : 5.e18 - 2.e19 /m3
25000
a = 10 mm
20000
15000
10000
5000
0
0
2
4
6
8
T e (eV)
10
12
14
16
Average electronic charge number vs aerosol size
9000
8000
Te = 5 eV
7000
Elementary charge number
Ti = 0.2 eV
6000
5000
4000
For electrostratic precipitators
(Q ~ d2)
3000
0.1 mm
3
1 mm
165
10 mm
16500
2000
1000
0
0.0E+00
2.0E-06
4.0E-06
6.0E-06
Aerosol diameter (m)
8.0E-06
1.0E-05
1.2E-05
Time evolution of aerosol charging
• Aerosol charge equilibrates very fast with background
• ~ several microseconds at densities of 1015 /m3
• Aerosol charge not very dependent on initial state
• Initial aerosol charge depends on radiation field and fast
electron/ion bombardment
• Aerosols are charged at higher rates than in ESP
Impact of
presence or absence of plasma
in front of the mirrors
•
If there is a plasma present in the space in front of the final optics mirrors
• Aerosols are charged negatively and move to the location of highest
potential
• In etching reactors (for the semiconductor industry), accumulation of
aerosols somewhere in between electrodes
• As long as there is a plasma and limited velocity of the gas, aerosols do
not deposit on the surface
• If vgas > 0.1 m/s, deposition could occur
• Deposition occurs by impaction (separation from flow due to
acceleration from changing flow direction), and by diffusion
•
If there is no plasma, it is possible to establish an electric field to remove the
charged aerosols.
SPATIAL AEROSOL
DISTRIBUTION IN
THE PRESENCE
OF PLASMA
Aerosol motion in the presence of an electric field
Absence of plasma
•
The motion of a particulate in a gas under the effect of an applied field is given
by:
v = Zp E
E is the applied electric field and Zp is the particulate mobility:
Zp = qp Cc / 3 p  a
where
qp is the particulate charge
Cc is the Cunningham correction factor
 is the gas viscosity
a is the particulate radius
Cc = 1 + Kn ( 1.25 + 0.40 exp( -1.1/ Kn ) )
Kn = 2 l / a,
l being the mean free path of the a gas molecule
For Xe at 1 Torr (STP), l = 2.62 x 10-5 m
Gas viscosity
• For Xenon,
• m ~ 44 mPa s at 600K
At 1000 K, m ~ 70 mPa s
viscosity (micro Pa s)
• Using the kinetic theory of transport gases (assuming hard sphere
collisions):
90
•  =  ( T / T0 ) 1/2
80
(independent of density!!!)
70
60
50
40
y = 0.3282x
0. 7649
30
20
10
0
0
500
Te m per atur e (K)
1000
1500
Aerosol velocity
10 kV/m, 1 Torr Xe, 5 eV
0.16
0.14
aerosol velocity (m/s)
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1.0E-07
1.0E-06
1.0E-05
Aerosol diameter (m)
1.0E-04
Electrostatic removal of aerosols
evaluation for laser optics
ESP
760
0.06
pressure (STP)
Electron temperature
Viscosity, Xe
Mean Free path
Torr
eV
Pa s
m
1
5
7.0E-05
2.6E-05
Aerosol diameter
Knudsen number
Cunningham factor
m
1.0E-06
52.4
87
1.0E-06
320
6.8E-06
10000
165
1.8E-07
100000
0.068
0.09
Elementary charges
Mobility
Applied electric field
m2/V s
V/m
Aerosol velocity
m/s
Aerosol clearing with electric fields
• Velocity of aerosols is sufficient for removal of aerosols in front of
mirrors
• ~ several cm/s
• Limited speed of flow in front of mirrors to prevent deposition of
aerosols by impaction (depositon due to change of velocity of the
fluid)
• Relatively large electric fields are required (100 V/cm)
• Capacitive field generation requires electrodes in chamber
• Mirror themselves could serve as an electrode
• Second electrode a short disctance (10 cm) away from mirrors