1. Aerosol protection of laser optics by Electrostatic Fields (not manetic) L. Bromberg ARIES Meeting Madison WI April 23, 2002

2. 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

3. 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

4. Aerosol clearing steps Charging stepClearing step

5. Aerosol charging In the presence of a plasma, a particulate charge varies as dq/dt = I i +I e where I e = -  a 2 e v e n e exp ( -e 2 | Z | /  0 a T e ) I i =  a 2 e v i n i (1 + e 2 | Z | /  0 a T i ) 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 J ph > e  a 2 Y -1 v e n e, different sign sheath I e = -  a 2 e v e n e (1 + e 2 | Z | /  0 a T e ) I i =  a 2 e v i n i exp ( -e 2 | Z | /  0 a T e ) I ph = j ph e Y exp( -e 2 | Z | / a T ph ) Much faster equilibration times, due to the lack of ion contribution to the charging But at the large intensities, aerosols will not survive…

6. Average electronic charge number vs T e for several densities n e = 5 10 18 - 2 10 19 m -3 a = 10  m

7. Average electronic charge number vs aerosol size Te = 5 eV Ti = 0.2 eV For electrostratic precipitators (Q ~ d 2 ) 0.1  m 3 1  m 165 10  m 16500

8. Time evolution of aerosol charging Aerosol charge equilibrates very fast with background ~ several microseconds at densities of 10 15 /m 3 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

9. 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 v gas > 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.

10. SPATIAL AEROSOL DISTRIBUTION IN THE PRESENCE OF PLASMA

11. 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 = Z p E E is the applied electric field and Z p is the particulate mobility: Z p = q p C c / 3   a where q p is the particulate charge C c is the Cunningham correction factor  is the gas viscosity a is the particulate radius C c = 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 1 Torr (STP), = 2.62 x 10 -5 m

12. Gas viscosity Using the kinetic theory of transport gases (assuming hard sphere collisions):  =   ( T / T 0 ) 1/2 (independent of density!!!) For Xenon,  ~ 44  Pa s at 600K At 1000 K,  ~ 70  Pa s

13. Aerosol velocity

14. Electrostatic removal of aerosols evaluation for laser optics

15. 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