Chamber Clearingby

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 = - 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 16

Te (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-05

Aerosol diameter (m)

Elementary charge number

Te = 5 eV

Ti = 0.2 eV

Density and temperature evolution (assumption)

0.E+00

1.E+14

2.E+14

3.E+14

4.E+14

5.E+14

6.E+14

7.E+14

8.E+14

9.E+14

1.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)

Density

Te

Ti

Average electronic charge number vs time

100

1000

10000

100000

0 0.00001 0.00002 0.00003 0.00004 0.00005

time (s)

Elementary charges in aerosol

Time constant for evolution

1.0E-06

1.0E-05

1.0E-04

0 10 20 30 40

time ( )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 / a, being the mean free path of the a gas molecule For Xe at 0.1 Torr, = 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

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-05

Aerosol 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.