Development of Radiation Hydrodynamic code STAR for EUV plasmas Atsushi Sunahara suna@ile.osaka-u.ac.jp Institute for Laser Technology 2013 International Workshop on EUV and Soft x-ray Sources University College Dublin November 3-7 2013
Introduction EUV conversion efficiency consists of three factors. EUV 1) Conversion efficiency (CE) 1) 13.5nm wavelength with 2% bandwidth X-ray = laser absorption fraction conversion fraction EUV spectral efficiency absorbed laser energy input laser energy x-ray emission energy inputed energy into plasma EUV emission energy x-ray emission energy In order to get high EUV CE, we have to maximize the product of three factors. Especially, we pay attention to the laser absorption fraction.
Laser absorption fraction CO2 Laser :10 10 W/cm 2, pulse duration:110ns, spot diameter:200μm Φ (cm) electron density electron temperature EUV emission BMP êlí ÉvÉçÉOÉâÉÄ BMP êlí ÉvÉçÉOÉâÉÄ BMP êlí ÉvÉçÉOÉâÉÄ (cm) (cm) (cm) critical density ncr ne Te ~ constant in space low absorption 1/e ncr density scale length Density scale length keeps 25 μm in time due to the lateral flow from the laser spot.
Double pulse irradiation was proposed to atcheive Efficient, High Power EUV light Double pulse irradiation scheme delay Sn droplet X100KHz pre-pulse λl=arbitrary main-pulse λl=10.6um minimum mass target pre-formed plasma EUV emission Dynamics of tin droplet is key issue for achieving high CE.
One fluid two temperature model of plasma fluid continuity equation momentum equation pdv work ion conduction ion energy equation Fluid pdv work ion-electron T relaxation e conduction electron energy equation Laser heating term Laser multi-group diffusion approximation Radiation heating term Radiation EOS dependent Atomic physics calc. dependent
Te Log10(Te (ev)) Sn EOS Log10(P) dyn/cm 2 pressure L-V region Density Log10(ρ (g/cm 3 ))
Position (μm) Sn Sphere 100μm Φ wavelength: 1.06μm intensity : 5X10 10 W/cm 2 (cm -3 ) 10 22 Ion Density STAR1D 10 20 laser peak timing (10ns) 10 18 10 16 300 10 14 250 200 150 10 12 10 (ev) 0 0.5 1.0 1.5 2.0 Temperature (cm) 100 50 0 1.0-50 -100 0 5 10 15 20 Time (ns) 0.1 0 0.5 1.0 1.5 2.0 (cm)
Temperature Temperature Sn EOS Sphere (r0=100μm) 100ns (cm -3 ) (cm -3 ) 10 23 5 10 23 500ns 0.7 10 22 10 21 Ion Density 4 10 22 10 21 0.6 0.5 10 20 10 19 10 18 10 17 10 16 3 2 L=75μm 1 0 0 200 400 600 800 1000 (μm) 10 20 10 19 10 18 10 17 Liquid-gas mix L=250μm 0.4 0.3 0.2 0.1 10 16 0.0 0 500 1000 1500 2000 2500 (μm) Expanding region can enter in the liquid-vapor mix phase.
STAR2D 2D cylindrical simulation (cm) Microsoft Video 1 êlí ÉvÉçÉOÉâÉÄ 20μmΦ Sn Droplet Laser 1.06μm 1x10 11 W/cm 2 (cm) axis symmetry
Pressure dyn/cm 2 BMP êlí ÉvÉçÉOÉâÉÄ (cm) axis symmetry
Pressure dyn/cm 2 BMP êlí ÉvÉçÉOÉâÉÄ (cm) axis symmetry
Density g/cm 3 BMP êlí ÉvÉçÉOÉâÉÄ (cm) axis symmetry
Temperature ev BMP êlí ÉvÉçÉOÉâÉÄ (cm) axis symmetry
electron density (cm -3 ) (cm) BMP êlí ÉvÉçÉOÉâÉÄ (cm) axis symmetry
1E10W/cm 2 @3.0ns (16) spot diam. =100μm Pressure 1E10W/cm 2 @4.2ns (22) spot diam. =100μm Pressure 1E10W/cm 2 Spot=100μm 1E10W/cm 2 @5.8ns (30) spot diam. =100μm Pressure 8.0 8.0 8.0 1E10W/cm 2 @6.8ns (35) spot diam. =100μm Pressure 1E10W/cm 2 @8.6ns (44) spot diam. =100μm Pressure 1E10W/cm 2 @10ns (51) spot diam. =100μm Pressure 8.0 8.0 8.0 7.0
Summary & Conclusion We simulated the tin droplet irradiated by the 1.06μm nano-second laser. pre-formed plasma Most expanding region is in the liquid-vapor region Increase of the scale length Droplet Sn Dynamics of over-dense region Laser Liquid-vapor region is very important for the dynamics of tin droplet irradiated by the pre-pulse.