Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 1 Nuclear Stockpile Stewardship and Bayesian Image Analysis (DARHT and the BIE) (U) By James L. Carroll Jan 2011 LA-UR

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Abstract Since the end of nuclear testing, the reliability of our nation’s nuclear weapon stockpile has been performed using sub-critical hydrodynamic testing. These tests involve some pretty “extreme” radiography. We will be discussing the challenges and solutions to these problems provided by DARHT (the world’s premiere hydrodynamic testing facility) and the BIE or Bayesian Inference Engine (a powerful radiography analysis software tool). We will discuss the application of Bayesian image analysis techniques to this important and difficult problem. (U) Slide 2

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Talk Outline Stockpile Stewardship DARHT Bayesian Image Analysis BIE Slide 3

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Nuclear Weapons 101 Nuclear weapons are comprised of Primary Secondary Radiation Case Delivery Packaging Slide 4 Primary Pit: Sub-critical fissile mass surrounded by HE. Implosion creates super critical mass. Chain reaction energy and radiation “initiate” the secondary.

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Testing Nuclear Weapons: Atmospheric Testing July 16, 1945 (Trinity) – 1963 (Limited Test Ban Treaty) Slide 5 Underground Testing 1963 (Limited Test Ban Treaty) – 1992 (last critical US nuclear test)

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Sub-Critical Nuclear Testing Radiographic images from sub-critical testing help ensure the credibility of our enduring nuclear weapon stockpile. Evaluating effects of aging on materials Fine tuning computer modeling of weapon performance and behavior. Evaluating re-manufactured components. Certification of existing weapon systems in stockpile. Slide 6

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D What is Hydrodynamic Testing? High Explosives (HE) driven experiments to study nuclear weapon primary implosions. Radiographs of chosen instants during dynamic conditions. Metals and other materials flow like liquids under high temperatures and pressures produced by HE. Slide 7 Static Cylinder Set-upStatic Cylinder shotStatic Cylinder Radiograph

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D The challenge of imaging the pit: Spot size Motion blur Scatter Dose Noise Poisson events Camera Cosmic rays Tilt/Cone Effects Slide 8

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Challenges Spot size: Slide 9

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Challenges Motion blur: Slide 10

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Challenges Scatter: Slide 11

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Challenges: Dose Slide 12

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Challenges Dose Slide 13 Graded collimator

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Noise Slide 14

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Tilt Effects Slide 15

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Cone Effects Slide 16

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 17 England: Moguls United States: FXR United States: PHERMEX Russia: BIM-M France: AIRIX

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 18 DARHT: Phase 2: “Second Axis” Phase 1: “First Axis” Lab Space and Control Rooms Firing Point Optics and Detector Bunker

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D DARHT Two linear induction accelerators at right angles produce extremely powerful and tight electron beams Metal target stops electrons and makes x-rays with a very small spot size Scintillator converts x-rays to visible light Light is captured by specialized cameras Axis 2 can be “pulsed” to produce four separate “dynamic” images Slide 19

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D DARHT Accelerator Principles of Operation The DARHT accelerators use pulsed power sources to produce and accelerate a single electron beam pulse. DARHT Axis 2 chops the beam into 4 pulses just before the target. The two machines use different pulse power technology Slide 20 DARHT Axis 1 Accelerator 60-ns, 2-kA, 19.8-MeV electron beam for single pulse radiography. Linear Induction Accelerator with ferrite cores and Blumlein pulsed power. The injector uses a capacitor bank and a Blumlein at 4-MV. Cold velvet cathode. Single 60 ns pulse. Operation began in July DARHT Axis 2 Accelerator 2-ms, 2-kA, 18.4-MeV electron beam for 4-pulse radiography. Linear Induction Accelerator with wound Metglass cores and Pulse Forming Networks (PFNs). The Injector uses a MARX bank with 88 type E PFN stages at 3.2 MV. Thermionic cathode. 4 micropulses - variable pulse width. Operations began in 2008.

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Inside DARHT Slide 21

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D DARHT image resolution: Slide 22

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D “Bayesian” Image Analysis Slide 23

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D THE FTO Slide 24

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data True radiographic physics ? True density (unknown) Inverse approach (approximate physics) Transmission (experimental)

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data True radiographic physics ? True density (unknown) Inverse approach (approximate physics) Transmission (experimental) How do we extract density from this transmission?

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) How do we extract density from this transmission?

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data We develop a parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated)

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data We develop a parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) Model parameters are varied so that the simulated radiograph matches the experiment

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D What does any of this have to do with Bayes Law? Slide 30

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data We develop a parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) Model parameters are varied so that the simulated radiograph matches the experiment p(m|r) h(m)

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Bayesian Analysis Slide 32

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Assumptions Where n is some independent, additive noise. If n is Gaussian then: Slide 33

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Plug that in: If I assume a uniform prior then: Slide 34

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D A forward modeling approach is currently used in analysis of (single-time) radiographic data We develop a parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) Model parameters are varied so that the simulated radiograph matches the experiment p(m|r) h(m)

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D The Solution Building h(m) Optimizing parameters m Slide 36

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Using the Prior Computer vision is notoriously under constrained. Penalty terms on the function to be optimized can often overcome this problem. These terms can be seen as ill-posed priors GGMRF Slide 37

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Example, approximating scatter Slide 38

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D BIE A programming language to express h(m) Graphical Reactive Interactive Slide 39

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 40

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 41

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Future Work: Slide 42

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D The forward-modeling framework makes possible a global optimization procedure t2t1t3t4 Prior knowledge provides additional constraints at each time SOLUTION: Evaluated Density DATA: Transmission (experiment) Data constrain solution at each time Now, physics-based constraints on the evolution of the time-series data will also constrain the (global) solution t2t1t3t4

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D These physics-based constraints will maximize information extracted from each dataset Concept: Can we learn something about the solution at time 3 (blue) from the data at surrounding times? Approach: use physics to constrain solution at each time based upon time- series of data. WHEN WILL THIS APPROACH HAVE GREATEST VALUE? When certain conditions are met: 1) Must have the time between measurements (  t) on the order of a relevant time scale of the flow; and 2) Must have non-perfect data (due to noise, background levels, etc). time t1t1 t2t2 t3t3 t4t4 t5t5 Consider an evolving interface: Data must be correlated in time! Perfect data would be the only required constraint… (Noisier data means the global optimization adds more value).

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Statistical Improvements Hypothesis testing. Uncertainty estimation. Slide 45

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 46

Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA U N C L A S S I F I E D Slide 47