Simulating Mono-energetic Proton Radiographs of Inertial Confinement Fusion Experiments using Geant4 Monte Carlo Particle Transport Toolkit M. Manuel, F. H. Séguin, C. K. Li, D. T. Casey, J. R. Rygg, J. A. Frenje, R. D. Petrasso MIT PSFC R. Betti, O. Gotchev, J. Knauer, F. Marshall, D. D. Meyerhofer, V. A. Smalyuk, UR-LLE 2007 HEDP Summer School UCSD San Diego, CA July. 30 th - Aug. 3 rd, 2007

Abstract Proton radiography has been used to image Inertial Confinement Fusion (ICF) capsules during their implosions as well as to quantitatively measure magnetic fields generated by laser-plasma interaction at the OMEGA laser facility. An imploded, D 3 He-filled capsule provides mono-energetic, ~15- MeV protons for radiographing another capsule. We are developing simulated models of these experiments using the Geant4 Monte Carlo Particle Transport Toolkit (G4). Of particular interest are the limitations on spatial resolution caused by scattering effects. Experimental and simulated results will be presented for different experiments and models. This work was performed in part at the LLE National Laser User’s Facility (NLUF), and was supported in part by US DOE (Grant No. DE-FG03-03SF22691), LLNL (subcontract Grant No. B504974), LLE (subcontract Grant No G) and FSC at University of Rochester.

Proton Radiography is a powerful diagnostic tool for ICF  Proton radiography is being used to study B & E fields and mass distributions in a range of ICF experiments (laser-plasma interactions, ICF implosions, magnetic reconnection, etc. )  The information content of radiography images is affected by imaging system parameters, such as source size, and by the slowing and scattering of the protons in the imaged sample  We need to know what the information content is and what applications are practical, so we are using Geant4 as a simulation tool to analyze experiments Radiograph of a plasma bubble 2.4 ns after the laser pulse began.

Protons interact in several ways with fields and matter; each affects the information content of images 1. Protons Lose Energy while Traversing Matter This can be good: If we know the initial proton energy, an energy- sensitive detector tells us how much energy was lost along a proton trajectory and we can use that information to infer ∫ρdl. 2. Protons Scatter while Traversing Matter This is usually bad: Scatter limits image spatial resolution 3. Proton Trajectories are Affected by Electric and Magnetic Fields This is good: Measurements of beamlet displacements allow us to study field strengths.

Mono-energetic protons are created by a D 3 He filled backlighter implosion capsule Laser drive ~ 10 kJ in a 1-ns pulse T i ~ 12 keV D + D  T (1.01 MeV)+ p (3.02 MeV, Y ~ 1  10 9 ) D + 3He   (3.6 MeV) + p (14.7 MeV,Y ~ 2  10 9 ) Burn duration ~ 150 ps Burn region size (FWHM) ~ 45  m D+ 3 He gas Glass Shell ~ 2.3  m ~ 420  m

Measuring scattering effects of beamlets as they pass through a scattering target foil Drive Lasers Backlighter Capsule Metal Mesh Al Filter Scattering Foil Proton beamlets are created by different mesh hole frequencies Examine scattering of beamlets through different types of materials; CH, Au, Be, Ta, etc. With G4 we can turn off and on the scattering effects to compare images with and without scattering

G4 simulation of proton beamlets scattering through a 25- μm mylar foil Not all particle tracks are shown. Sources are isotropic, but the simulation samples only those particles whose direction is toward the image target.

Simulated proton radiographs of beamlets through a 25- μm mylar foil with and with out scattering effects Radiograph simulated with out scattering.Radiograph simulated with scattering. Both radiographs were created with identical parameters, μm Ni mesh, yield of 1.7*10 8 protons, 1/e radius of 27 μm, 15- MeV average energy with 8.7-keV T ion. The difference in these two images is evident; implying that for a 25 μm mylar foil, scattering is qualitatively strong (next slide will show a more quantitative analysis). The reason the image with out scattering still seems blurry, is due to the statistics of the number of particles used, if a larger number of particles was used the perfectly square beamlets would be apparent. 5 cm

By turning off scattering, we can see how the amplitude modulation changes By removing scattering from the simulation we have increased the amplitude modulation by ~60%.

Imaging an ICF implosion capsule with a D 3 He filled backlighter capsule Drive Lasers The amount of scattering and down shift is dependent on areal density of the capsule 2-D images of imploded capsules show strong particle-field interactions Temporal evolution of ρL can be evaluated by imaging at different times Mono-energetic Protons

G4 simulation of a proton radiograph experiment of an unimploded ICF capsule Not all particle tracks are shown. Sources are isotropic, but the simulation samples only those particles whose direction is toward the image target.

Simulated radiographs of number density and average energy for an unimploded ICF capsule Capsule Parameters: 19.3 µm CH shell 15-atm H 2 fill pressure 435 µm outer radius 0.9 cm source to capsule distance Num. density image of proton radiograph. Dark = Higher Fluency 8.4 cm Ave. energy image of proton radiograph. Dark = Higher Energy 8.4 cm ρL calculation still to be done

Experimental proton radiographs from shot of an unimploded ICF capsule Ave. diam. image of proton radiograph. Dark = Lower Diameter Num. dens. image of proton radiograph. Dark = Higher Fluency Unknown void ring outside of capsule shell. Perhaps small residual charge? (to be simulated) The background has lower diameters (higher energies) than inside the capsule, showing the energy loss due to the capsule ρL calculation still to be done

Measuring electromagnetic fields In laser induced plasmas by ionizing a CH foil Drive Lasers Backlighter Capsule Mesh Foil Al Filter Interaction Beam CH Foil Laser Induced Plasma Region Beamlet deflections are a function of proton energy and field strength Temporal evolution of B-Fields from laser induced plasmas are made by imaging at different times Using multiple laser beams, overlapping plasma bubbles are created involving complex magnetic fields

Image of a LASNEX simulated plasma bubble from a single laser incident on a 5 μm CH foil B E Incoming Proton Beamlets Simulated B field from laser-plasma interaction (LASNEX) Experiments still to be simulated using simulated magnetic fields from LASNEX.

Future Work  Advancement of Geant4 Simulation Electromagnetic fields Addition of plasma stopping power physics  Scattering parameterization Determine the modulation transfer function (MTF) for different materials Determine resolution limits for proton radiography in ICF experiments

Summary Proton radiography is an exciting new imaging technology for use in various ICF experiments. However, the usefulness of these images is limited by scattering affects due to the material the protons are traveling through. Geant4 has already been used to simulate simple geometries, and proven the usefulness it possesses to investigate the scattering of charged particles through materials. Through the use of Geant4, we will be able to simulate complex experimental setups and scenarios; including complex shapes, fields, and environments (plasmas). By correctly simulating these systems, we will be able to quantify the amount of scattering possible and resolution limits for proton radiography in ICF experiments.