Transcript ppt - Fusion Energy Research Program

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
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.
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
Mirror Defects and Damage Types, and
Approaches to Assess their Effects on Beam Quality
Dimensional Defects
Gross deformations, >
Compositional Defects
Surface morphology ,  <
Gross surface
contamin ation
Local contamin ation
CONCERNS
•
•
•
•
Fabrication quality
Neutron swelling
Thermal swelling
Gravity loads
• Laser-induced
damage
• Thermomechani cal
damage
• Transmutations
• Bulk redeposition
• Aerosol, dust &
debris
MODELLING TOOLS
Optical design software √ Scattering by rough
( Ray tracing )
surfaces (Kirchhoff)
√
Fresnel mul ti-l ayer
solver
Scattering by particles
Ray Tracing Analysis of Gross Mirror Deformation Limits
Target
• The ZEMAX optical design
software was used for the analysis.
• Gross deformation:  > 
due to thermal or gravity load,
or fabrication defect.
Deformation:  = am2/2rc [ surface sag ]
Wall
Laser
Beam
GIMM
• 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  = 248 nm (KrF)
Focusing mirror focal length = 30 m
GIMM to target distance = 20 m
Mirror radius am = 0.3 m
Grazing incidence angle = 80o
Target radius = 3 mm
Beam spot size asp = 0.64 mm
Focusing
Mirror
Typical Output from a ZEMAX Run
Mirror Surface Sag
Ray Trajectories
+0.3m
(mm)
rc = 5x104 m
Target
Focusing
Mirror
GIMM
0ne million rays used; q = 80o
2-D Illumination Profile
-0.3m
+0.3m
1-D Illumination Profiles
Y-scan
+3mm
X-scan
y
-3mm
x
+3mm
Mirror Curvature Causes Spot Size to Elongate
The isotropic surface curvature causes the rays to diverge preferentially
in the direction of beam propagation.
Beam Spot Size [a,b] (mm)
0.9
GIMM Radius = 0.3 m
GIMM-to-Target Distance = 20 m
Nominal Spot Size = 0.64 mm
0.85
0.8
b
0.75
0.7
a
0.65
0.6
0
0.2
0.4
0.6
Mirror Surface Sag (m)
0.8
1
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.
 = 0 m
• Secondary effect is non-uniform illumination:
DI / I ~ 2% for  = 0.46 m
• Mirror surface sag limit for grazing incidence is :
 < 0.2 m,
 = 0.46m
(for a mirror of 0.3 m radius)
with the criteria: DI / I < 1%, and Dasp / asp < 10%.
Relative Illumination
=
0.92m
+2mm
0m
 = 0.92 m
0.46m
y-scan
-2mm
+2mm
Kirchhoff Theory of Wave Scattering from Rough Surfaces ( < )
• In the presence of a scatterer (mirror surface), total field is given by
y(r )  yinc (r )  ysc(r )
where y sc (r ) is given by
y sc (r ) 

S0

G( r , r )
y( r ) 
0
0 dS
 y( r )
 G( r , r0 )
0
0

n
n

0
0
where S0 is surface of scatterer and G(r,r0) is the full-space Green’s function.
• With appropriate approximations[Ogilvy], the average scattered field is given as
sc is field scattered from smooth surface, (k ) is the
,
where
y
ysc  (k z )y sc
0
z
0
characteristic function of the rough surface, given by
(s) 


p(h )e
ish dh

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. I
 y sc y sc   e g
coh
o
Reflected Beam Intensity can be Degraded
by Microscopic Mirror Surface Roughness (s < )
• 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 /  < 0.01.
Isc
Iinc
1.0
q1
q2
0.8
q1 = 80o
0.6
Isc
70o
0.4
0.2
0
0.1
g

Id
Io : reflected intensity from
smooth surface
Id : scattered incoherent intensity
g : (4p s cosq1/)2
60o
0
 I 0e
0.2
s/
0.3
0.4
0.5
At q1 = 80o, s/ = 0.1,
degradation, e-g = 0.97.
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)(cosq1+cosq2) + (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.
Analytic Form of the Scattered Intensities
•
Along the plane of incidence, the coherent scattered field is
p2 r2
kAX 
coh
I

(XY)2 exp(g)[cos q2 (1  R)  cos q1(1  R)]2 
 sin kAX  2
k2
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)/kAX]2 is due to diffraction from the surface edge, and
as long as kX >> 1, the specular lobe is very narrow around q2 = q1.
•
Assuming a Gaussian surface correlation function : C(R) = exp(-R2/c2),
the diffuse scattered field for slightly rough surfaces is given by:
Id 
k 2F2 2c
pr 2
  k2 A22 
c
g exp(g)(XY)exp
4


where F = F(q1, q2, R).
<Id> is a strong function of the surface correlation length c .
• The total scattered field intensity is:
<I> = Icoh + <Id>
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:  >> 
- Ray tracing approach
- For a simple gross surface deformation shape,
 < 0.2 m
(1) for a 30-cm radius mirror,  = 248 nm
(2) uniform beam illumination DI/I < 1% at the target
(2) fixed spot size Dasp/asp < 10%.
• Microscopic deformation:  < 
- Kirchhoff theory
- Surface roughness s/ < 0.01 for < 1% illumination reduction
- Specularly reflected field is independent of surface correlations
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.