Status of Modeling of Damage Effects on

1
Status of Modeling of Damage Effects on Final
Optics Mirror Performance T.K. Mau, M.S.
Tillack Center for Energy Research Fusion Energy
Division University of California, San
Diego High Average Power Laser Program
Workshop April 4-5, 2002 General Atomics, San
Diego
2
Background and Objectives

• GIMM (Grazing Incidence Metal Mirror) has
  been proposed as the final
• optical element that provides uniform
  illumination of the DT fusion targets
• by the driver laser beams to achieve a full
  target implosion.
• Threats to GIMMs such as X- and g-rays,
  neutrons, laser, charged particles and
• condensable target and chamber materials can
  cause damage to the mirror surface,
• resulting in increased laser absorption,
  reduced damage threshold, shorter lifetime,
• and reduced beam quality (mirror
  reflectivity, focusing, and illumination
  profile).
• The objectives of final optics modeling are
  threefold
• (1) Quantify mirror damage effects on
  mirror and beam performance.
• (2) Provide analysis of laser-target
  experimental results.
• (3) Provide design windows for the GIMM
  in an IFE power plant
• e.g., power density threshold,
  coating and material selection, etc.

3
Final Mirror is a Critical Component in a
Laser-Driven IFE Power Plant

• Typically there are 60 beamlines all focusing
  on the target at the center
• of the chamber. The incident angle is 80o
  from the GIMM surface normal.

(20 m)
(SOMBRERO values in red)
(30 m)
GIMM
Prometheus-L reactor building layout
4
Mirror Defects and Damage Types, and Approaches
to Assess their Effects on Beam Quality
v
v
( Ray tracing )
5
Ray Tracing Analysis of Gross Mirror Deformation
Limits
Target
Wall
Laser Beam

• The ZEMAX optical design
• software was used for the analysis.
• Gross deformation d gt l
• due to thermal or gravity load,
• or fabrication defect.
• Deformation d am2/2rc surface
  sag
• Analysis assumes that flat GIMM surface
  acquires a curvature (rc), and
• calculates resultant changes in beam spot
  sizes on the target, and intensity
• profiles as the deformation size is varied.
  
• Beam propagation between focusing mirror and
  target is modeled.
• Prometheus-L final optics system as a
  reference
• Wavelength l 248 nm (KrF)
• Focusing mirror focal length 30 m
• GIMM to target distance 20 m

Focusing Mirror
GIMM
6
Typical Output from a ZEMAX Run
Mirror Surface Sag rc 5x104 m
(mm)
Ray Trajectories
0.3m
Target
Focusing Mirror
GIMM
0ne million rays used q 80o
-0.3m
0.3m
2-D Illumination Profile
1-D Illumination Profiles
Y-scan
3mm
X-scan
y
-3mm
3mm
x
7
Mirror Curvature Causes Spot Size to Elongate
The isotropic surface curvature causes the rays
to diverge preferentially in the direction of
beam propagation.
8
Spot Size and Illumination Constraints Limit
Allowable Gross Mirror Deformation

• The dominant effect of gross deformation is
• enlargement (and elongation) of beam spot
  size,
• leading to intensity reduction and beam
  overlap.
• Secondary effect is non-uniform illumination
• DI / I 2 for d 0.46 mm
• Mirror surface sag limit for grazing incidence
  is
• d lt 0.2 mm, (for a mirror of 0.3 m
  radius)
• with the criteria DI / I lt 1, and
  Dasp / asp lt 10.

d 0 mm
d 0.46mm
Relative Illumination
d 0.92mm
2mm
d 0.92 mm
0mm
0.46mm
-2mm
y-scan
2mm
9
Kirchhoff Theory of Wave Scattering from Rough
Surfaces (d lt l)

• In the presence of a scatterer (mirror
  surface), total field is given by
• where is given by
• where S0 is surface of scatterer and G(r,r0)
  is the full-space Greens function.
• With appropriate approximationsOgilvy, the
  average scattered field is given as
• , where y0sc is field
  scattered from smooth surface, ?(kz) is the
• characteristic function of the rough
  surface, given by
• p(h) is the statistical height distribution,
  and kz is a characteristic wavenumber
• normal to the mean surface.
• Our interest is focused on the specularly
  reflected coherent intensity Icoh, which
• is the component that is aimed at the
  target.

10
Reflected Beam Intensity can be Degraded by
Microscopic Mirror Surface Roughness (s lt l)

• For cumulative laser-induced and
  thermomechanical damages, we may
• assume Gaussian surface statistics with rms
  height s, giving rise to
• ?(kz) exp-kz2s2/2 .
• - Grazing incidence is less affected by
  surface roughness.
• - To avoid loss of laser beam intensity,
  s / l lt 0.01.

Isc
Iinc
1.0 0.8 0.6 0.4 0.2 0
q2
q1
q1 80o
Intensity Degradation
70o
Io reflected intensity from smooth
surface Id scattered incoherent intensity g
(4p s cosq1/l)2
60o
At q1 80o, s/l 0.1, degradation, e-g 0.97.
0 0.1 0.2 0.3
0.4 0.5
s / l
11
Specularly Reflected Field is Independent of
Surface Correlation Lengths

• Phase difference between two rays scattered
  from different points
• (x1, h1) and (x2, h2) is given by
• Df k (h1-h2)(cosq1cosq2)
  (x2-x1)(sinq1-sinq2)
• where q1 is the incident angle, and q2 is
  an angle of reflection.
• For specular scattering (q1 q2), Df
  2k (h1-h2) cos q1
• Thus, around the specular direction, the
  relative phases of waves scattered from
• different points on the surface depend only
  on the height difference, Dh, between
• these points, but not on the point
  separations, Dx.
• Correlations along the surface do not
  affect scattering around the specular
• direction, in which the coherent field is
  most strongly reflected.
• Thus, only the characteristic function ?(k)
  needs to be specified to evaluate
• the coherent field.

12
Analytic Form of the Scattered Intensities

• Along the plane of incidence, the coherent
  scattered field is
• where the rough surface is assumed
  rectangular -X x X, -Y y Y,
• g k2 s2 (cosq1 cosq2)2, A sinq1 -
  sinq2 , and R is the reflection coefficient.
• The factor sin(kAX)/kAX2 is due to
  diffraction from the surface edge, and
• as long as kX gtgt 1, the specular lobe is
  very narrow around q2 q1.
• Assuming a Gaussian surface correlation
  function C(R) exp(-R2/lc2),
• the diffuse scattered field for slightly
  rough surfaces is given by
• where F F(q1, q2, R).
• ltIdgt is a strong function of the surface
  correlation length lc .

13
Summary of Results and Conclusions

• A number of techniques have been used to
  assess the mirror surface
• damage limits on GIMM and driver beam
  performance, depending on
• the characteristics and size of the damage.
• Gross deformation d gtgt l
• - Ray tracing approach
• - For a simple gross surface deformation
  shape,
• d lt 0.2 mm
• (1) for a 30-cm radius mirror, l 248
  nm
• (2) uniform beam illumination DI/I lt 1 at
  the target
• (2) fixed spot size Dasp/asp lt
  10.
• Microscopic deformation d lt l
• - Kirchhoff theory
• - Surface roughness s/l lt 0.01 for lt 1
  illumination reduction
• - Specularly reflected field is
  independent of surface correlations

14
On-Going and Future Work

• Kirchhoff theory will be extended to evaluate
  beam wavefront distortion
• from reflection off a damaged mirror at
  grazing incidence, for various
• types of microscopic surface deformation
  (Gaussian, spatially anisotropic,
• multiple scale lengths) and for measured
  data.
• The effect of self-shadowing and multiple
  reflections will be investigated.
• Quantify effect of gross and macroscopic
  surface damage on mirror and
• beam performance using the ray tracing
  technique, among others. The
• surface damage characteristics should be
  consistent with the damage
• source.
• The effects of local contaminants in the form
  of aerosol, dust
• and other debris on mirror reflective
  properties will be examined.