Kaplan-Meier Survival Function for Diamond-turned Alumiplate Mirrors Introduction:  As apertures become larger, fluence limits tend to decrease due to the statistical nature of damage initiation.  Reliability, over many shots, is a critical issue for power plants and even NIF.  NIF-type transmissive optics tend to fail due to a statistical, sudden initiation and rapid growth pathways.  For GIMM’s, there appears to be both a statistical aspect, which leads to a rapid onset of damage (ROD), and a cumulative growth damage (CGD), which will eventually lead to failure.  For any optic there are two ways in which statistics are important. 1. The spatial and temporal variations in the laser beam 2. The distribution of susceptibility to damage of the mirror  As the distributions overlap more and more, the probability of ROD increases. Beam Statistics:  We examined the statistical behavior of perturbations in the laser intensity, in both space and time.  Equivalent position profiles (EPP) CCD C A B A+B=C GIMM Equivalent position beam path Six consecutive shots from the laser Local Fluence of Laser Beam Probability of Event ROD Laser Failure Zone Spatial Variations: Temporal Variations:  Standard deviation of intensity over many shots  Areas where the fluctuations are large, also tend to be areas with the most fluence  Statistical damage will depend on two temporal aspects of the laser. 1.The intensity fluctuations in the beam 2.The pointing stability of the laser Mirror Damage Susceptibility Statistics:  To collect data on a mirror's susceptibility to damage would require a very large testing program.  A heuristic explanation of important factors: 1.There are always defects in GIMM’s. 2.The instantaneous defect size determines the remaining lifetime. 3.Laser fluence determines the defect growth rate. 4.There is a critical size, where failure occurs. Laser-induced Damage Statistics:  We see a large variation in the lifetime of the mirrors.  The laser intensity variations play a role.  Damage susceptibility variations are probably more important.  A Kaplan-Meier survival function indicates the reliability and survivability of a mirror.  Failure times at higher fluence tend to be spread over a large range due to the statistical nature of the damage.  The lower fluence (10 J/cm 2 ) indicates that the failure is from CGD. Conclusion:  The laser profile is not an important factor for GIMM's.  For GIMM’s there are always defects, but their growth rate must be slow enough for the mirror to last. 1.Decreased initial defect size 2.Increased mechanical properties to reduce the growth rate  At lower fluence damage is less statistical and more cumulative. CCD Unfocused profiling beam path Compex Compex 201 beam profile A. A. Base-profile for EPP B. Difference between Base-profile & actual profile E.F. E. Base-profile for unfocused beam F. Difference between Base-profile & actual profile  To get 10 8 shots we need: B. Standard deviation of 25 shots Intensity Short axis poly-fit unfocused beam Intensity Long axis poly-fit unfocused beam Intensity Short axis poly-fit of EPP Long axis poly-fit of EPP Intensity 1.small initial defect size 2.slow enough growth rate Normalized Intensity Number of Pixels Profile Histogram C. Normalized Intensity Number of Pixels Subtracted Histogram D.  The underlying shape of the profile (base-profile) is the main contributor to the shape of the energy distribution in the beam. C.  The base-profile was subtracted from the raw profile, giving a more statistical (Rician like) profile.  We have more hotspots than a Rician distribution.  This is bad for the survivability of an optic if the goal is to have a high fluence base-profile. D. Different colors represent different fluences Examination of the Statistical Aspects of Laser-Induced Damage in Metal Mirrors K. Sequoia, M. S. Tillack, J. Pulsifer, R. Harrison University of California, San Diego