Download Chamber clearing

Chamber Clearing
by
Electrostatic Fields
L. Bromberg
ARIES Meeting
UCSD
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 = - 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
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
3000
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
Density and temperature evolution
(assumption)
1.E+15
8
9.E+14
7
Density
Te
Ti
Density (1/m3)
7.E+14
6.E+14
6
5
5.E+14
4
4.E+14
3
3.E+14
2
2.E+14
1.E+14
1
0.E+00
0
0
0.00001
0.00002
0.00003
time (s)
0.00004
0.00005
Temperature (eV)
8.E+14
Average electronic charge number vs time
Elementary charges in aerosol
100000
10000
1000
100
0
0.00001
0.00002
0.00003
time (s)
0.00004
0.00005
Time constant for evolution
(Z-Z final )/(dZ/dt)
1.0E-04
1.0E-05
1.0E-06
0
10
20
time ( ms)
30
40
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 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 0.1 Torr, l = 2.62 x 10-4 m
Gas viscosity
• For Xenon,
• m ~ 44 mPa s at 600K
At 2000 K, m ~ 110 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
g/cm s = 0.1 Pa s
Aerosol cleaning
pre ssure (STP)
Ele ctro n te mpera ture
Vi sco sity, Xe
Mean Free path
To rr
eV
Pa s
m
0.1
5
1.10E-04
2.62E-04
Ae rosol dia mete r
Knu dsen num ber
Cunn ingh am factor
m
3.00E-07
17 47
28 83
Ele mentary ch arges
Mobi lity
Ap plie d el ectric fiel d
V/m
2.54E+0 2
3.77E-04
1.00E+0 4
Aeros ol velocity
m/s
3.77E+0 0
Velocity of aerosols
10 kV/m, 0.1 Torr Xe, 5 eV
4.00
3.50
aerosol velocity (m/s)
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.0E+00
2.0E-06
4.0E-06
6.0E-06
Aerosol diameter (m)
8.0E-06
1.0E-05
1.2E-05
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.