Chamber Clearingby
Electrostatic Fields
L. Bromberg
ARIES MeetingUCSD
January 10, 2002
Motivation
• Aerosols are created in chamber due to large heating flux on surface of liquid
• 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 chamber clearing
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 = - a2 e ve ne exp ( -e2 | Z | / 0 a Te)
Ii = a2 e vi ni (1 + e2 | Z | / 0 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
Average electronic charge number vs Te for several densities
0
5000
10000
15000
20000
25000
30000
35000
0 2 4 6 8 10 12 14 16Te (eV)
Number of electronic charges on aerosol
ne : 5.e18 - 2.e19 /m3ne = 5 1018 - 2 1019 m-3
a = 10 m
Average electronic charge number vs aerosol size
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.0E+00 2.0E-06 4.0E-06 6.0E-06 8.0E-06 1.0E-05 1.2E-05Aerosol diameter (m)
Elementary charge number
Te = 5 eV
Ti = 0.2 eV
Density and temperature evolution (assumption)
0.E+001.E+142.E+143.E+144.E+145.E+146.E+147.E+148.E+149.E+141.E+15
0 0.00001 0.00002 0.00003 0.00004 0.00005
time (s)
Density (1/m3)
0
1
2
3
4
5
6
7
8
Temperature (eV)
DensityTeTi
Average electronic charge number vs time
100
1000
10000
100000
0 0.00001 0.00002 0.00003 0.00004 0.00005time (s)
Elementary charges in aerosol
Time constant for evolution
1.0E-06
1.0E-05
1.0E-04
0 10 20 30 40time (s)
(Z-Z
final
)/(dZ/dt)
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
Aerosol motion in the presence of an electric field
• 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 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 0.1 Torr, l = 2.62 x 10-4 m
Gas viscosity
• Using the kinetic theory of transport gases (assuming hard sphere collisions):
• = ( T / T0 ) 1/2
(independent of density!!!)
• For Xenon, • ~ 44 Pa s at 600K
At 2000 K, ~ 110 Pa s
y = 0.3282x0.7649
0102030405060708090
0 500 1000 1500Temperature (K)
viscosity (micro Pa s)
g/cm s = 0.1 Pa s
Aerosol cleaning
pressure (STP) Torr 0.1Electron temperature eV 5Viscosity, Xe Pa s 1.10E-04Mean Free path m 2.62E-04
Aerosol diameter m 3.00E-07Knudsen number 1747Cunningham factor 2883
Elementary charges 2.54E+02Mobility 3.77E-04Applied electric field V/m 1.00E+04
Aerosol velocity m/s 3.77E+00
Velocity of aerosols10 kV/m, 0.1 Torr Xe, 5 eV
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0.0E+00 2.0E-06 4.0E-06 6.0E-06 8.0E-06 1.0E-05 1.2E-05Aerosol diameter (m)
aerosol velocity (m/s)
Aerosol clearing with electric fields
• Velocity of aerosols is small, compared with the chamber size• ~ several m/s
• For a rep-rate of 10 Hz, the maximum distance that the aerosols will be able to move is 1 m!
• Relatively large electric fields are required (100 V/cm)• Difficult to generate inductively• Capacitive field generation requires electrodes in chamber
• Can the liquid wall itself be used as electrodes?
• Could be used to prevent aerosols from depositing in optics.
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