FUSION SCIENCE CENTER FOR EXTREME STATES OF MATTER AND FAST IGNITION PHYSICS

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1 FUSION SCIENCE CENTER FOR EXTREME STATES OF MATTER AND FAST IGNITION PHYSICS University of Rochester, Ohio State University Massachusetts Institute of Technology Lawrence Livermore National Laboratory University of Texas at Austin University of Nevada at Reno General Atomics University of California at San Diego University of California at Los Angeles Institute for Laser Science Applications ANNUAL REPORT January 1- December 31,

2 Executive Summary The Fusion Science Center (FSC) for Extreme States of Matter and Fast Ignition (FI) Physics began operation in August 2004 under the sponsorship of the Department of Energy (DOE), the Laboraotry for Laser Energetics (LLE), the University of Rochester (UR) and the Institute for Laser Science Applications (ILSA) at Lawrence Livermore National Laboratory and the University of California. In FY05, LLE provided $150K through the New York State Energy Research and Development Authority (NYSERDA), ILSA contributed $42K, UR contributed with $138K of indirect-cost waivers, and the DOE provided $1.066M under cooperative agreement DE-FC03-ER The FSC involves ten institutions and ten principal investigators. The FSC is aimed at fostering a close collaboration among the Center investigators with the ultimate goal of successfully integrating compression and FI-heating experiments. A major goal of the Center is to bring together researchers from around the entire country and the international community to build a comprehensive understanding of the physics underlying the creation of extreme states of matter and fast ignition. Another major function of the Center is to stimulate academic involvement and student interest in the area of High Energy Density Physics. As part of its academic mission, the FSC organizes a summer school in High Energy Density Physics every two years. Progress in the FSC education mission The FSC held its first High Energy Density Summer School on August 6-13, 2005 at the Clark-Kerr campus of the University of California at Berkeley. The school, attended by 96 participants, included seniors, graduate students, post docs, and research scientists. Fourteen lecturers from the field of High Energy Density Physics gave presentations in laser-plasma interactions, laboratory astrophysics, equations of state, laser-wakefield particle accelerators, fast ignition, inertial confinement fusion, shock physics, Z-pinches, high-power lasers, and HEDP diagnostics. Essential to this summer school were student and participant posters, which were of excellent quality (several included in the proceedings to be found at the FSC web site and which accompanied each day s thematic focus. Daily poster sessions offered students a unique opportunity to discuss their work in detail, not only with the lecturers but with the many other students who were in attendance. As part of its educational mission, the FSC was a co-sponsor of the 2005 mini-conference on Fast Ignition that took place on October during the Division of Plasma Physics - American Physical Society meeting in Denver, CO. The FSC is also organizing the 2006 Fast Ignition Workshop on November 3-5 in Cambridge, MA that is attended by the international fast-ignition community. 2

3 Progress in Fast-Ignition research The FSC has promoted a close collaboration among several HEDP researchers (some supported by the Center and some by other sources) in the area of laser-plasma interactions, electron transport, hydrodynamics and target fabrication, with the main focus of these disciplines centered on Fast Ignition inertial confinement fusion. The FSC identified the following fundamentals areas critical to the success of Fast Ignition: [1] Fuel Assembly [2] Fast Electron Transport and Intense Laser-Plasma Interaction [3] Integrated Fast Ignition Simulations Progress in Fast-Ignition Fuel Assembly (Theory/Experiments). Fuel Assembly for Fast Ignition. A method to assemble thermonuclear fuel for fast ignition with high densities, high areal densities (ρr) and a small hot spot has been developed by the FSC [R. Betti and C. Zhou, Phys. Plasmas 12, (2005)]. It is found that massive cryogenic wetted-foam shells can be imploded with a low implosion velocity on a low adiabat using the relaxation-pulse technique. While the low velocity yields a small size hot spot, the low adiabat leads to large values of the density and areal density. Such slowly assembled massive targets have low in-flight aspect ratios (IFAR = 15-25), shaped adiabats, and large thicknesses. All these characteristics make these targets insensitive to the hydrodynamic instabilities during the acceleration phase. Due to their low velocity, their small hot spot is relatively cold and extremely dense reaching densities of a few hundreds g/cc. Because of its small size, the hot spot can be easily quenched by hydrodynamic mixing induced by the deceleration phase Rayleigh-Taylor instability. However, this circumstance, fatal for standard hot-spot ignition, is not a concern for Fast Ignition which relies on an externally-induced hot spot. It has been shown theoretically that a 750-kJ UV laser can assemble a ~650µm thick, 650µm inner radius, wetted-foam FI target with an implosion velocity of cm/s, adiabat of 0.7, yielding an areal density of 3g/cm 2 and a spatially averaged density of 400g/cc. Two dimensional simulations (J. Delettrez and R. Betti) of ignition with a 2 MeV, 12kJ, 20 µm electron beam have indicated that such a target produces a yield of 120MJ, a value of immediate relevance to fusion energy. A similar target scaled to 25kJ has been designed for future integrated experiment on the Omega-EP laser system. The target is a 130µmthick wetted-foam shell with a 300µm inner radius driven by a relaxation laser pulse to an implosion velocity of cm/s on an inner surface adiabat of 1. Such a target is predicted to reach areal densities of 0.8g/cm 2 and peak densities of 700g/cc. A set of plastic targets and pulse shapes have been designed to test the ability of slow, low-adiabat implosions to achieve high densities and large areal densities with a small hot spot. The capsules are 40µm-thick CH shells driven by 17-20kJ of UV laser energy with a relaxation laser-pulse characterized by a 80-ps picket followed by a 2.5-ns shaped mainpulse. A total of six capsules were imploded on January 11, 2006 (Stoeckl, Betti, 3

4 Theobald, Li, Zhou), and preliminary results will be presented at the January FSC meeting. Cone Target Experiments. Prior to the operation of the FSC, fuel assembly experiments using cone-in-shell targets with 70 degree opening angle cones were performed. Both x- ray radiography and charged particle spectroscopy were used to estimate the shell areal density to be ~60 mg/cm 2, approximately 80% of that predicted by symmetric 1-D simulations under similar drive conditions. Work during the recent period has extended this in three ways: (1) Performing fuel assembly experiments with 35 degree openingangle cones; (2) Using x-ray self-emission images to estimate the amount of the goldcone material mixed into the compressed core; (3) and obtaining streaked optical measurements of compression-induced shockwaves propagating through the cone material. Progress in Fast-Electron Transport and Intense LPI Benchmarking Experiment for 1-D Electron Transport. A test bed for one-dimensional fast electron transport has been designed and experiments are scheduled for January- February 2006 on the Beamlet laser facility at Sandia National Laboratory. The goal of these experiments (Beg, Stephens, Freeman) is to probe electron transport in a nearly 1-D geometry and to test hybrid code descriptions of electron transport at the high current levels characteristic of a FI experiment. An imaging Cu-K α diagnostic with ~10 µm resolution along with fluorescence spectrometry, optical interferometry and Faraday rotation is used to simultaneously measure hot electron propagation length, temperature, magnetic field and expansion rate along the length of a thin wire. This will be modeled with a hybrid code (hot electron particles in a fluid background). The targets necessary for these experiments have been developed over the last year, and are currently being constructed. Shot time has been provided by the Sandia s Z-Petawatt (ZPW) facility in February 06 for the initial experiments; January/February is available for installing the necessary diagnostics. Later in the year, when ZPW can deliver two energetic shortpulse beams, proton beam magnetic deflectometry will be added to look at the magnetic field deeper in the plasma. LSP simulations for an isolated 20-µm diameter wire target show that the energetic electrons have a maximum energy of 2 MeV with an average temperature of 0.15 MeV. Strong self-generated magnetic fields (10 s of MG) have been observed. The conversion efficiency (laser to total electron energy) is about 10%. LPI studies with different laser polarizations have also been performed. Preliminary results show that the circularly polarized laser generates more collimated electron beam than the linearly polarized laser, which potentially could increase the energy deposition efficiency. Electron Acceleration in Cones. A set of experiments to elucidate the electron acceleration in cones have been conducted (Ditmire, Cho, Kneip and Dyer) by irradiating micro-cone targets using the THOR laser at the University of Texas at Austin (delivering 800nm, 600mJ, 38fs, pulses focused to a 10µm diameter focal spot, yielding focused intensities greater than W/cm 2 ). The titanium K α emission from a Ti foil was measured using x-ray pinhole cameras and two crystal spectrometers. Hard x-rays were 4

5 also measured using a six-channel hard x-ray spectrometer with various cut-off filters. Additional diagnostics are scheduled for implementation in early 2006, including an electron spectrometer and an x-ray penumbral imaging camera. A pinhole camera was used to image the x-ray emission from flat, 25µm thick titanium foils. The emission was compared to pyramid targets backed with these same foils. The foils were shot with the laser being incident at an angle of 45º in p-polarization. Pyramid targets were shot along the pyramid axis of symmetry. The data show both an enhancement in overall signal as well as a sharper peak in the region of x-ray emission for the pyramid targets as compared to plain flat targets. During this last year, x-ray emission spectra have been examined to derive some information on hot electron temperature with various target configurations (flat, pyramid and wedge targets). Theory of Fast Electron Stopping. An electron stopping model has been developed and applied [C. K. Li and R.D. Petrasso, Phys. Rev. E, 73, , 2006] to investigate fast electron slowing down in the ultra dense plasmas characteristics of Fast Ignition. Fundamental to this model is the inextricable coupling between electron scattering and electron energy loss. To investigate the consequences of this model, many calculations have been carried out that involve semi-realistic FI scenarios, such as energy deposition profiles of 1 MeV electrons injected into a uniform 300 g/cc DT plasmas; for this case, the radii of the electron beam footprint varies from near zero to 20µm. From these results, the combined effects of beam size and scattering, as manifest in blooming and straggling, can be clearly discerned. The average penetration (measured in areal density) of 1 MeV electrons is calculated to be approximately 0.42 g/cm 2 with straggling excursions about the mean of approximately ±0.09 g/cm 2 and transverse blooming of 0.15 g/cm. 2 Progress in Integrated Fast-Ignition Simulations and Code Development Fully integrated PIC simulations [C. Ren et al, to be published in Phys. Plasmas, 2006] of fast electron generation and transport have been carried out for an isolated 50-µm diameter FI target showing a divergent hot electron source and no global merging of current filaments. PIC simulations have also been used to test the linear theory concerning the space charge effects on the current filament instability occurring in the underdense plasma surrounding the dense core of FI targets [M. Tzoufras, C. Ren, F. S. Tsung, W. B. Mori, R. A. Fonseca, L.O. Silva, to be published in Phys. Rev. Lett., 2006]. An extensive benchmarking effort has been undertaken by the FSC [A. Solodov and C. Ren] to compare the results of the implicit algorithms, in both particle mode and hybrid fluid mode, of LSP against the explicit PIC code OSIRIS. Two problems have been chosen for the benchmark: a plasma wake generated by an electron bunch and the electron beam filamentation in a plasma. When the time step and grid resolution in LSP are chosen to satisfy both the numerical and physics requirements, LSP agrees reasonably well with OSIRIS in these two simulations. The benchmark also gives a picture of what happens when the simulation parameters satisfy only the numerical requirements but not 5

6 the physics ones. In addition, the benchmark helps define a practical validity range on empirical simulation parameters such as the fluid electron streaming factor. The LSP collision model has been modified (A. Solodov) to include relativistic effects. The slowing-down of monoenergetic relativistic electron beams have been simulated and compared with the theoretical results. With the improved collision model, the LSP code is capable of reproducing the blooming, straggling and penetration predicted by the theory [C. K. Li and R.D. Petrasso, Phys. Rev. E, 73, , 2006]. The FSC has also supported code development for the PIC code OSIRIS at UCLA (Mori, Tonge and Tzoufras). Load-balancing has been added and an up to 4-fold speedup is realized in fast-ignition simulations with isolated targets. A quadratic-spline current deposition scheme has been added, which extends the grid size up to 12 Debye-length without significant numerical heating in 2D. An absorbing core is added to prevent fast electron recirculation in a limited-sized target. The ability to run explicit PIC codes with cells much larger than the Debye length makes the explicit codes much more competitive in FI simulations. Similarly, the UNR group (Sentoku and Cowan) has included a fully relativistic collision model in PICLS (the UNR PIC code). PICLS has been validated for the electron-ion energy transfer rate and the electron stopping power from the nonrelativistic to the ultra relativistic regime. The UNR group has succeeded in reducing the computational cost of explicit PIC calculations, and in extending the spatial cell size to the plasma skin depth, which is much larger than the Debye length of the dense plasma, while avoiding numerical heating. This reduces the computational cost of PIC calculations drastically. This has been demonstrated through a full-scale explicit simulation of a fast ignition integrated cone-experiment. Results from this simulation indicate that there are three heating processes involving hot electrons, fast ions and heat conduction from the extremely hot cone. The core heating in the FI experiment can be explained by a combination of these processes. Progress in innovative HEDP concepts. In addition to conventional Fast Ignition research, the FSC has sponsored activities in innovative HEDP concepts such as electromagnetic field measurements during laserplasma interaction and shock ignition of high density thermonuclear fuel. Shock Ignition. A novel method separating the assembly and ignition phases of thermonuclear fuel has been developed within the FSC (Betti and Zhou). In common with conventional fast ignition, massive cryogenic shells are first imploded with a low implosion velocity on a low adiabat [R. Betti and C. Zhou, Phys. Plasmas 12, (2005)]. The assembled fuel is then ignited from the central hot spot heated as a result of the collision of a spherically converging ignitor shock and the return shock. The ignitor shock can be driven by the same driver used in the assembly, and the resulting thermonuclear gain can be significantly larger than that of standard hot-spot ignition of the same driver energy. The high gains are caused by the low adiabats and large masses of the imploded shells. The National Ignition Facility or other laser driver with an energy 6

7 exceeding about 200kJ and power exceeding 300TW should be able to test the shockfast-ignition concept. One and two-dimensional simulations have been carried out (also in collaboration with J. Perkins of LLNL) to validate the shock ignition concept. Electromagnetic Field Measurements in HED Plasmas. Another area of investigation concerns the generation of magnetic and electric fields by the interaction of laser beams with matter, an example of HED Physics and Extreme states of matter and another goal of the FSC. A monoenergetic proton source, resulting from the implosion of a capsule with D 3 He fuel on OMEGA, has been used to sensitively probe these EM fields (R. Petrasso and C. Li). The fusion products include 14.7-MeV D 3 He protons and 3.0-MeV DD protons, both of which are then used to simultaneously probe time-dependent B and E fields resulting from laser-matter interactions. Such monoenergetic sources have distinct advantages over broad-band proton sources associated with intense-laser-beam experiments. To further explore these field generation processes, 2 full days of OMEGA shots have been scheduled for February and August, In addition, this type of backlighting with 14.7-MeV protons leads in a natural way to the radiographing of implosions, the aim of which would be to fully characterize the assembled mass and its ρr distribution. Such experiments at the OMEGA facility are being actively considered since, with 60 beams, both backlighting and implosions can occur simultaneously. 7

8 TABLE OF CONTENTS EXECUTIVE SUMMARY... 2 FSC MEMBERS AND COLLABORATORS... 9 REFEREED PUBLICATIONS INVITED TALKS AT CONFERENCES THE EDUCATION MISSION The Summer School in High Energy Density Physics Synopsis of the HEDP Summer School CODE DEVELOPMENT AND SIMULATION EFFORT OSIRIS code development PICLS code development LSP code development OSIRIS Fast-Ignition Simulations PICLS Fast-Ignition Simulations LSP benchmarking EFFORT IN FAST ELECTRON TRANSPORT Electron transport in wires and laser-plasma interfaces Electron acceleration in cones Fast electron stopping in HED plasmas EFFORT IN FUEL ASSEMBLY FOR FAST IGNITION Fuel assembly for Fast Ignition: theory and simulations Fuel assembly experiments with cone targets EFFORT IN INNOVATIVE HEDP CONCEPTS Shock ignition of thermonuclear fuel with high areal densities E and B fields generation by laser-plasma interaction

9 THE FUSION SCIENCE CENTER MEMBERS, COLLABORATORS, ADVISORS and ADMINISTRATORS Members -Faculty and Research Scientists F. Beg (UCSD) PI R. Betti (UR-LLE) Director D. Correll (LLNL) T. Cowan (UNR) PI T. Ditmire (UT) PI R. Freeman (OSU) PI M. Key (LLNL) PI C. Li (MIT) D. Meyerhofer (UR-LLE) Deputy Director W. Mori (UCLA) PI R. Petrasso (MIT) PI C. Ren (UR-LLE) F. Seguin (MIT) Y. Sentoku (UNR) PI R. Stephens (GA) PI Members - Post docs K. Anderson (UR- starting 06) E. Baronova (UCSD) O. Gotchev (UR) F. He (UCSD) P. Nelson (UR-starting 06) J. Pasley (GA) A. Solodov (UR) J. Tonge (UCLA) Member s- Graduate Students D. Casey (MIT) C. Chen (MIT) G. Dyer (UT) B. Ick Cho (UT) S. Kneip (UT) E. Shipton (UCSD) M.Tzoufras (UCLA) C. Zhou (UR) Administrators M. Kyle (UR-LLE) J. Morris (UR) Collaborators - Research Scientists J. Delettrez (UR-LLE) J. Knauer (UR-LLE) J. Myatt (UR-LLE) C. Sangster (UR-LLE) C. Stoeckl (UR-LLE) W. Theobald (UR-LLE) M. Wei (UCSD) Collaborators - Graduate Students P. Brijesh (UR) B. Bucher (UCSD) S. Chen (UCSD) N. Jang (UR) T. Ma (UCSD) M. Storm (UR) External Advisors J. Kilkenny (GA) M. Porkolab (MIT) J. Sheffield (U. Tennessee) M. Tabak (LLNL) R. Town (LLNL) Member is a Researcher (student, post doc or scientist) partially or fully supported by the FSC, or a Principal Investigator. Collaborators are not currently supported by the FSC.

10 REFEREED PUBLICATIONS (published or accepted for publication) High-density and High-ρR Fuel Assembly for Fast-Ignition Inertial Confinement Fusion R. Betti and C. Zhou, Phys. Plasmas 12, , Low-Adiabat Implosions for Fast-Ignition Inertial Confinement Fusion R. Betti and C. Zhou, to be published in the proceeding of The 4 th Inertial Fusion Science and Applications (IFSA), Biarritz, France, Global Simulation for Laser-driven MeV Electrons in 50µm-diameter Fast Ignition Targets C. Ren, M. Tzoufras, J. W. Tonge, F. S. Tsung, W. B. Mori, M. Fiori, R. A. Fonseca, L.O. Silva, J. C. Adam, and A. Heron, to be published in Phys. Plasmas, Space-charge Effects in the Current-filamentation/Weibel instability M. Tzoufras, C. Ren, F. S. Tsung, J. W. Tonge, W. B. Mori, to be published in Phys. Rev. Lett., 2006 Full Scale Explicit PIC Simulation of a Fast Ignition Experiment, Y. Sentoku, A. Kemp, and T. E. Cowan, to be published in the proceeding of The 4 th Inertial Fusion Science and Applications (IFSA), Biarritz, France, Stopping, Straggling, and Blooming of Directed Energetic Electrons in Hydrogenic and Arbitrary-Z Plasmas C. K. Li and R.D. Petrasso, Phys. Rev. E, 73, , Energy Deposition of MeV Electrons in Compressed Targets of Fast-Ignition Inertial Confinement Fusion C. K. Li and R.D. Petrasso, to be published in Physics of Plasmas, Electron Transport in Dense Plasmas R. R. Freeman et at, to be published in the proceeding of The 4 th Inertial Fusion Science and Applications (IFSA), Biarritz, France,

11 INVITED PRESENTATIONS AT CONFERENCES Global Simulations for Laser Driven MeV Electrons in Fast Ignition C. Ren, M. Tzoufras, J. Tonge, F.S. Tsung, W.B. Mori, S. Amorini, R.A. Fonseca, L.O. Silva, J.C. Adam, A. Heron The 8th International Workshop on Fast Ignition of Fusion Targets June 29 - July 1, 2005, Tarragona, Spain. Global Simulations for Laser Driven MeV Electrons in Fast Ignition C.Ren, M.Tzoufras, J. Tonge, F.S.Tsung, W.B.Mori, S.Amorini, R.A.Fonseca, L.O.Silva, J.C.Adam, A.Heron APS-DPP meeting, October 24-28, 2005, Denver, CO. Stopping, Straggling and Blooming of Directed Energetic Electrons in Hydrogenic Plasmas C. K. Li and R. Petrasso APS-DPP meeting, October 24-28, 2005, Denver, CO. Low-Adiabat Implosions for Fast-Ignition Inertial Confinement Fusion R. Betti and C.Zhou The 4 th International Conference in Inertial Fusion Science and Applications (IFSA), Biarritz, France, September 4-9, 2005 Electron Transport in Dense Plasmas R.R. Freeman et al. The 4 th International Conference in Inertial Fusion Science and Applications (IFSA), Biarritz, France, September 4-9,

12 THE FUSION SCIENCE CENTER EDUCATION MISSION The Summer School in High Energy Density Physics August 7-13, 2005 Clark-Kerr Campus, UC Berkeley Lecturers and subjects covered R. Betti UR, Inertial Confinement Fusion R. Collins LLNL, Equation of State C. Deeney SNL, HEDP with Z-pinches P. Drake- UM, Introduction to HEDP E. Esarey LBNL, Plasma Accelerators R. Freeman OSU, Fast Electron Transport M. Knudson SNL, Shock Waves W. Kruer, UC Davis, Laser-Plasma Interaction D. Meyerhofer UR HEDP Diagnostics W. Mori UCLA, Large-scale PIC Simulations C. Ren UR PIC Method D. Ryutov LLNL, Laboratory Astrophysics M. Tabak LLNL, Fast Ignition B. White SLAC, Intense Lasers The Clark-Kerr Campus UC Berkeley hosted the FSC HEDP Summer School 96 attendees 50 financial aid packages from the FSC 55 graduate students 5 undergraduates 23 post docs 13 research scientists Sponsors Fusion Science Center Institute for Laser Science Applications 12

13 SYNOPSIS OF THE 2005 FSC HEDP SUMMER SCHOOL The Fusion Science Center Summer School occurred at the Clark Kerr Campus at the University of Berkeley, California, 7-12 August 2005, and national and international participants, of which there were 96, included seniors, graduate students, and post docs and research scientists. A wide range of lectures, given by some of the world s foremost authorities, focused on the fundamentals of high-energy density physics. Essential to this summer school were student and participant posters, which were of excellent quality, and which accompanied each day s thematic focus. The poster session offered students a unique opportunity to discuss in detail their work not only with world authorities in an informal and congenial setting but with the many other students who were in attendance, challenging each to think more deeply, or perhaps along different lines, about their own research. The topics covered on Monday s first day of lectures were an Introduction to High-Energy Density Physics, by Professor Paul Drake of the University of Michigan; Shocks, by Dr. Marcus Knudson of Sandia National Laboratory (SNL); and the High- Energy Density Physics of Z Pinches, by Dr. Christopher Deeney of SNL. Common to these set of lectures, and those of the following days as well, was the truly remarkable set of diverse circumstances --- from astrophysics to geophysics to laboratory physics in which high-energy density phenomena, that for which the energy density exceeds erg/cc, occur. Monday concluded by several outstanding student posters on X-pinches and wire array Z-pinches. Tuesday s lectures included Laser-plasma interactions, by Dr. William Kruer of Lawrence Livermore National Laboratory (LLNL); an Overview of High-Intensity Short Pulse Lasers, by Dr. Bill White of Stanford Linear Accelerator Center; and Astrophysical High-Energy Density Physics, by Dr. Dmitri Ryutov of LLNL. As in the other lectures, the focus was a mixture of fundamentals, needed for illuminating the basic concepts, as well as the exciting new frontiers emerging in high-energy density physics. The day concluded by a set of fine student posters on Laser-Plasma Interactions and on Plasma Diagnostics. Wednesday s lectures centered on Inertial Confinement Fusion (ICF), by Professor Riccardo Betti of the University of Rochester (UR); and on Full Scale Comparisons between Simulations and Experiments, by Professor Warren Mori of UCLA. One of the grand challenges of high-energy-density physics is the achievement of fusion ignition through ICF and, ultimately, of fusion energy. To that end, and using physically motivated considerations, Professor Betti analytically derived the basic equations necessary to understand the framework for implosion dynamics and for achieving ignition. From a contrasting point of view, Dr. Mori discussed the large computational requirements and methods that are required to simulate many of the experiments in high-energy-density physics, including that of fast ignition which is computationally one of the most difficult problems. In addition to another excellent student poster session, Wednesday s activities included tours of the National Ignition 13

14 Facility and of the Lawrence Berkeley Laboratory. The day concluded by a panel discussion of job opportunities in high-energy-density physics. This forum, comprised of leaders in the field, gave students the opportunity, through questions and dialog, to investigate different career options. Thursday s lectures were on Fast Ignition, by Dr. Max Tabak of LLNL; on Relativistic Electron Transport, by Professor Richard Freeman of Ohio State University; on Equations of State, by Dr. Gilbert Collins of LLNL; and on Plasma Based Accelerators, by Dr. Eric Esary of LBNL. The emphasis of these lectures was on the methods by which highly energetic particles are generated, both theoretically and experimentally; how these energetic particles are envisioned to be used in both the Fast Ignition scenario and in compact accelerators; and, finally, the equations-of-state needed to characterize highly compressed igniting matter as well as matter in the interior of giant planets and brown dwarfs, to name but two. Thursday s activities concluded with excellent student posters on, and lively discussions about, ICF, Fast Ignition, and astrophysics. Friday s lectures were on Particle-in-Cell Simulations, by Professor Chuang Ren of UR; and Diagnostics Required for High-Energy Density Physics, by Professor David Meyerhofer of UR. As was discussed, and the basic principles illuminated, particle-in-cell computational methods are one of the central means by which simulation is used to replicate actual experiments; and the diverse and complex set of diagnostics of HED Physics, as was elaborated, are the essential ingredients through which we ultimately learn about, and extend our understanding of, this exciting and challenging area of physics. Friday s session also saw the awards of outstanding student posters to eight students. The cash prizes were given to Patrizio Antici of LULI - Ecole Polytechnique (experimental) and Michael Tzoufras of University of California, Los Angeles (simulations). Making this selection most difficult was the fact that the entire set of student posters were of high quality and the Fusion Science Centers congratulates all students for their outstanding efforts. 14

15 CODE DEVELOPMENT AND SIMULATION OSIRIS Code Development W. Mori (UCLA), C. Ren (UR), J. Tonge (UCLA), M. Tzoufras (UCLA) In the past year we have made major improvements in OSIRIS aimed at integrated simulations of fast ignition plasmas. These improvements increase the efficiency of the simulations as well as improve the simulation model. Improvements include static and dynamic load balancing, quadratic spline interpolation, and an absorbing core. Static Load Balancing improves the efficiency of simulations by evening the load on processors in a multiprocessor cluster. In standard Domain Decomposition the simulation grid is split into domains with an equal number of grids in each domain. Each processor is responsible for the computation in one of the domains. With static load balancing the domains are set up to equalize the expected load on the processors. This is more efficient when the simulation particles are not initially uniformly distributed on the simulation grid and the distribution of particles by domain does not greatly change during the simulation. This has provided a 4-fold speedup in fast-ignition simulations with isolated targets. Dynamic load balancing will lead to another 50 to 100 % speed up. A Quadratic Spline current deposition and field interpolation scheme together with current smoothing suppresses numerical grid heating in PIC codes. This allows increased grid size, measured in Debye lengths, without numerical heating. If we assume Weibel type instabilities are the dominant mechanism for particle scattering (which is most likely true outside of the Fast Ignition target core and outside of the cone) then we must resolve the skin depth but not the Debye length in our simulations. Using the Quadratic Spline we have extended the grid size up to at least 12 Debye lengths without significant numerical heating over the time scale of a simulation (Figure 1). This allows us to use realistic electron temperatures in simulations. We have also mocked up the dense core of the target with an absorbing core. This absorber just slows particles within the core as a function of particle energy. This prevents fast electron recirculation in a limited-sized target, and provides current termination in approximately the correct location. In addition we have included a diagnostic of the particle energy flux spectrum into the core. 15

16 Quadratic Spline Current Deposition and Field Interpolation in OSIRIS Improves Energy Conservation Allowing Lower Temperature and Higher Density Simulations. Quadratic Spline 100 n c 1.3 kev electrons Quadratic Spline 40n c 1.3 kev electrons Quadratic Spline 40 n c 7.6 kev electrons Area Weighting 40n c 7.6 kev electrons Figure 1: Comparison of energy conservation for 2.5 dimensional periodic simulation of plasmas with fast ignition core parameters. Area weighting and quadratic spline current deposition are shown. Even at 100 critical density, with 1.3Kev electrons, quadratic spline shows only a few percent energy growth over approximately 500 femto-seconds. Note: The laser is off and the plasma is uniform in these simulations. PICLS Code Development Y. Sentoku and T. Cowan (UNR) The UNR PICLS code has been integrated with an accurate collision model that has been validated for the electron-ion energy transfer rate and the electron stopping power from the non-relativistic to the ultra relativistic regime. In the past year, we have integrated a fully relativistic collision model in PICLS and test the performance of a high order current deposition scheme. Performance of a high order current deposition scheme. We ran a test simulation to check the system energy conservation by changing the numerical resolution. The target plasma has a density of about 4x10 22 cm -3 with an initial electron temperature of 10 ev. Ions are initially at rest. In order to resolve the plasma Debye length, a standard PIC calculation requires a 1000 grids/µm resolution. When a simulation was performed with a lower resolution of 400 grids/µm, the numerical heating became significant and we observed an unphysical increase of the electron temperature. On the other hand, with a third order interpolation scheme in the current deposition and in the field interpolation, only 25 grids/µm meshes are sufficient to guarantee adequate energy conservation. By avoiding resolving the Debye length, we can extend the computational cell size and 16

17 significantly reduce the computational cost. For 2D simulations, it is about a 4-fold improvement. Since, in fast ignition, the relevant scale length is the plasma skin depth (for the Weibel, filamentation and other instabilities), we can extend the mesh size beyond the cold electron Debye length without neglecting the dominant plasma phenomena. Binary collision model. In order to simulate fast ignition scenarios, including processes like the laser-plasma interaction, hot electron transport and fast ion transport, a particlein-cell code needs to accurately describe particle energy transfer through collisions. The underlying collision model used in PICLS is the one by Takizuka and Abe [J. Comput. Phys. 25, 205 (1977)] where particles are scattered by the binary collision process and accurately conserve energy and momentum. Starting from the weakly relativistic version of this model [Sentoku, J. Phys. Soc. Jpn 67, 4084 (1998)], we had extended its applicability from the non-relativistic regime to the ultra-relativistic regime. The basic algorithm has also been improved to treat a collision between different weighted particles. Below, the results of two test simulations are described showing the accuracy of the model for fast ignition relevant plasmas. The first test is concerned with the rate of energy transfer from hot electrons to cold ions. All electrons have the same initial energy but move in randomly distributed direction (a shell distribution in momentum space). Taking into account that the shell distribution has a (π/2) 1/2 faster rate than a Maxwellian distribution, we have calculated the analytical exchange rate [Lifshitz and Pitaevskii, Physics Kinetics, Chap. 4], d(1 E i / E e ) dt = 1 E i E e 8πZ 2 e 4 nl Mm e c 3 (γ 1). (1) The corresponding test simulation is carried out with the following parameters; density 10 5 n c, ion mass M =1000, varying initial electron energy from 2 kev to 10 MeV. A constant Coulomb logarithm L=5 is used for simplicity, and the field calculation was omitted. Results are summarized in Fig. 2 showing that the simulation accurately reproduces the theoretical prediction (1). This confirms that integrating microscopic collision by means of a Monte Carlo method provides the same results as using macroscopic quantity such as the average density/energy. 17

18 Figure 2: Energy transfer rate between electrons and ions of mass M at density n. The line is calculated from Eq. (1). The solid circles are simulation results with constant weighted particles. The open circle indicates the result with weighted particles. The second test is concerned with the fast electron stopping in dense plasmas. The fast electron stopping power is calculated in hydrogen plasma with a mass density of 12.5 g/cm 3, and temperature of 5 kev. Both electron-electron and electron-ion collisions are included. We simulated 100 particles and computed the average stopping power for a fast electron energy varying from 10 kev to 1 GeV. Figure 3 shows a comparison between the computed stopping power with the stopping power from NIST database. The simulation results were also compared with the results of Fokker-Plank simulations [Private communication with Johzaki, ILE Osaka], and found to be in a very good agreement. Since the wave interaction increases the stopping power in plasmas by about 20% as mentioned by Deutsch [Deutsch et al., PRL, 1996], this effect will be automatically included in our collisional PIC simulations. Figure 3: The stopping power of the fast electron in hydrogen plasma with a mass density 12.5 g/cm 3, and electron temperature 5 kev. 18

19 LSP Code Development A. Solodov and J. Myatt (UR) Correct description of fast electron collisional transport is crucial in simulations of Fast Ignition scenarios. The LSP code was developed originally for use within the ion beam fusion community with a non-relativistic collisional package. Only very recently, an update by MRC became available (November 2005) to account for the relativistic effects in an approximate fashion. We performed a detailed analysis of the LSP collisional package devoting particular attention to both the physical model used and its implementation in the code. We found that the relativistic corrections introduced by MRC were not adequate. We have made significant changes to the collisional model to account for the relativistic effects. Then, we have carried out detailed simulations of relativistic electron slowing down, straggling and blooming, and compared them with the theory. We found an excellent agreement between the slowing-down theory of Li- Petrasso and our corrected version of LSP. The non-relativistic LSP collisional model is similar to the one described in Ref. [1]. The intra-species collisions are modeled through isotropic particle scattering in the center-ofmass frame off its own distribution (for particle species) and through inclusion of a pressure gradient force term in the equation of motion (for fluid species). The interspecies collisional model is based on the calculation of the time advance for the two first moments of the distribution function: mean momentum and temperature. Particle species are then elastically scattered in the reference frame of the scattering species and random components of their velocities are adjusted to account for the temperature change. For fluid species, a frictional force between the species is added directly in the equation of motion. We verified that this model is correctly implemented in the code except for the value of Coulomb logarithm. The classical value of the Coulomb logarithm should be replaced by its quantum value for large relative velocities of scattering particles. This is a simple modification which we have implemented in the code. We also found that the relativistic effects required additional modifications. We calculated relativistically correct expressions for particle momentum and temperature changes and implemented them in the code. The fluid collisional model is left nonrelativistic. To test the collisional model we simulated stopping of electrons in different energy ranges in plasmas relevant to Fast Ignition and standard ICF targets. In Fig. 1, the results for 1 MeV electron stopping in DT plasma with density 300 g/cm -3 (n e = cm -3 ) and temperature 5 kev are shown. The beam of fast electrons was simulated in a particle mode, while the background plasma is treated as a fluid. In figure 1 (a) and (b), the beam electrons are shown in the plane (xy), where x is the initial beam direction and y is one of the transversal coordinates (the simulation is three-dimensional), at the initial moment of time and at the time when the electrons are stopped. Figure 1 (c) shows the dependence of the mean electron energy on the mean coordinate (solid line) and beam straggling (dashed lines) and blooming (dashed-dotted line). One can compare the simulation results with predictions of the analytical model by Li and Petrasso [2]. Figure 2 shows the same quantities as Fig. 1 (c) obtained analytically. The agreement is excellent (in the analytical expression the initial length and width of the beam were taken close to zero). In the nearest future we plan to perform additional tests checking the energy deposition by fast electrons into the plasma. 19

20 We expect it, however, to be correct due to general momentum and energy conservation relevant to the collisional model used in the code. a. P. W. Rambo and R. J. Procassini, Phys. Plasmas 2, 3130 (1995). b. C. K. Li and R. D. Petrasso, Phys. Rev. E 70, (2004), in this reference the logarithmic term in Eq. (11) for the stopping power should be corrected: ( ( γ 1) / 2h) 2 ln mc. Fig. 1. Simulation of 1 MeV-electron stopping in plasma (parameters are given in the text). (a) Initial distribution of electrons in the beam; (b) Distribution of electrons after they are stopped in the plasma; (c) Dependence of the mean electron energy on the mean coordinate x (solid line), electron beam straggling 2 1/ 2 x ± (dashed lines) and blooming ( x x ) 2 1/ 2 y (dash-dotted line). (a) (b) (c) Fig. 2. Dependence of the mean electron energy on the mean coordinate (solid line), electron beam straggling (dashed lines) and blooming (dash-dotted line) obtained using the theory of Ref. [2]. Parameters of the beam and plasma are the same as in the simulation of Fig. 1, except for the initial beam length and width close to zero. 20

21 OSIRIS Fast-Ignition Simulations W. Mori (UCLA), C. Ren (UR), J. Tonge (UCLA), M. Tzoufras (UCLA) In the past year we have been running simulations based on those performed in the C. Ren et. al PRL (V93, n18) using an improved current-deposition scheme that allows lower temperature and increased density simulations. There are no changes in the power flux into the core region due to reduction in the initial electron temperature but there are changes in power flux spectrum into the target core with increased density. In the higher density s imulations (Fig.1) more of the power delivered to the core are from low velocity electrons, which should be more collisional. The addition of a resistive core (Fig. 2) reduces the recirculation of electrons but it also induces spontaneously generated Magnetic fields (Weibel). This results from current termination and return currents from the core. Although these effects are expected, they are probably enhanced by the lack of dielectric properties associated with higher densities, and the drag also effects flows induced by charge build up, increasing relaxation time. Effect of Electron Temperature and Density on Energy Flux into Core (5µm from center). Figure 1: The higher density simulation shows more of the power delivered to core is from low energy electrons. Total power into the core is similar for all simulations (note: comparison is good for first 400fs, since electrons refluxed from boundary after that time are included). Note: Simulations run with quadratic spline current deposition and field interpolation and no resistive core. 21

22 Resistive Core Simulation Increase drag on particles within 5 µm from center of target. Magnetic field produced by filamentation after 993 fs. Charge density of electrons after 993 fs. Figure 2: The resistive core causes a build up of electrons in the core and a return current to be generated from the core. This complicates the filamentation structures and reduces power delivered to the core. Although this effect is probably exaggerated by the implementation of the resistive core it represents a real effect as electrons are captured at the core. 22

23 PICLS Fast-Ignition Simulations Y. Sentoku and T. Cowan (UNR) Using PICLS1d, we have simulated the ILE fast ignition experiment [Kodama et al., Nature, 2002]. Using the experimental parameters, the intensity of the heating pulse has been set at 3.6x10 19 W/cm 2 and its duration at 500 fs. The cone tip is modeled as a slab plasma with 500 n c. The core density is 8000 n c, corresponding to 30 g/cc for DT plasma. This is the first explicit PIC simulation with a plasma density varying by 4 order of magnitude up to 8000 n c. The initial plasma is shown in Fig. 1(a). We used 500 electrons/ions in a cell with a 3rd order interpolation current deposition scheme to suppress numerical heating. The simulation resolves the plasma skin depth up to 1000 n c. We found that three heating processes on different time scales contribute to the core heating; the first one is the collisional heating by hot electrons, that occurs in less than a picosecond (laser pulse duration). The second process is triggered by fast ions gaining a few percent of the absorbed energy. The fast ions hit the core after ~ 1ps and deposit energy in the core. The third process is the heat conduction from the extremely heated cone tip, that is expected to occur over a picosecond time scale. In the simulation, the mean-core-ion-energy is 800 ev after 1.65 ps. The total laser absorption is 25 % and the laser coupling to the core is estimated at about 14 %. The other important result is that the beam-plasma instability, driven by the fast electron flow, develops in the coronal plasma, while it is fully suppressed by collisions in the high density region with n > 100 n c. Figure 2(a) shows the fast electron flow traveling through the coronal plasma. Strong turbulence can be observed in the low density region (Fig. 2(a )), where the fast electrons are mixed to the plasma electrons, leading to strong heating of the coronal plasma. Figure 2(b) also shows the electrons longitudinal momentum as a function of the electron density at the particle initial position. Notice the strong heating below 200 n c, but not around the core region. This suggests that the anomalous process is not important at the high densities in the core region, and the core heating is explained by collision between the hot electrons and the core electrons. Figure 1: (a) initial density profile. (b) energy density profile at 1.15 ps. 23

24 Figure 2: (a)&(a ) the electron phase plot, x-px at 165 fs. (b) the electron longitudinal momentum as versus its initial density at 500 fs. The colors indicate the initial density. LSP Benchmarking A. Solodov (UR), C. Ren (UR), J. Myatt (UR) The hybrid Particle-in-Cell (PIC) code LSP [1] was developed by Mission Research Corporation (MRC), for numerical simulations of particle beam transport in matter and plasmas. LSP had many applications within the heavy ion fusion community [1,2]. Since only a few attempts have been made to use LSP in the study of Fast Ignition [3], in the past year, we have carried out detailed benchmarking of LSP with other codes in relation to fast electron dynamics in plasmas. The benchmarking included the codes LSP and OSIRIS [4]. Two problems were chosen: the Weibel instability of a relativistic electron beam and the excitation of a plasma wake field by an electron bunch. While, in general, a good agreement between LSP and OSIRIS simulations was found, some details of the electron beam-plasma evolution differed. We found limits of applicability of the LSP implicit hybrid simulations and we studied the effects when these requirements are not met. Important features of LSP are its implicit scheme and the option to use a particle or fluid description of the different species. (On the contrary, OSIRIS is a fully explicit particle code.) Although we tested different combinations of particle and fluid descriptions, particle simulations are advantageous at relatively low plasma densities and high temperatures, when the plasma is only weakly collisional. Instead, fluid simulations are beneficial at higher densities and low temperatures, when plasma is strongly collisional. However, even in a strongly collisional plasmas, kinetic effects become important when a hot electron population coexists with a thermal one thus requiring a hybrid, both kinetic and fluid, description for electrons. Including an implicit algorithm can greatly relax the limitations on time step, particularly, the need to resolve the plasma frequency. At the same time, all the important high-frequency interactions should be resolved thus imposing additional constraints on the time step. 24

25 In our simulations of the Weibel instability we considered a plasma with electron density of cm -3, with 10 % of electrons representing a mono-energetic beam with dimensionless momentum p / mc = γβ = 2. 8 and other electrons providing a compensating return current. Two-dimensional simulations were performed, in the plane (xy) perpendicular to the beam direction, with no dependence on the third coordinate (the problem of R. Lee and M. Lampe [5]). The plasma temperature was taken equal to 5 kev and the cases of mobile (H + ) and immobile ions were considered. The Weibel instability causes the beam filamentation, and the filaments coalesce until the distance between them becomes of the order of 10 c / ω p. In order to resolve the skin depth ( c / ω p ), the mesh size was taken x = y = 0.4c / ω in our simulations. Periodic boundary p conditions were assumed. We noticed a very good agreement between LSP-PIC (explicit and implicit) and OSIRIS simulations for the time step satisfying the Courant condition. (In Fig.1 our results are shown for the case of LSP implicit and OSIRIS simulations with mobile ions.) Particularly, the number of filaments is approximately the same at the same moments of time and balance between electron beam, plasma electron and magnetic field energies are similar. Particle simulations provide sufficiently good energy conservation. LSP hybrid simulations with background electrons and ions in fluid mode and beam electrons in particle mode, with the same time step, show a similar behavior except for degradation in energy conservation. In addition, a higher plasma density develops around the filaments, at the late stage of the evolution, in the simulations with mobile ions. We found that reducing the numerical parameter representing the fraction of the fluid particle momentum averaging on the grid improves the energy conservation. However, small values of the averaging parameter complicate the grid noise stabilization. Our implicit LSP simulations with a time step exceeding the Courant limit (not shown in the figure) showed an excellent agreement with the simulations for small time steps during the early stage of the beam filamentation. At the late stage of the Weibel instability, more filaments were observed, with a distorted shape, and the simulation failed for time steps exceeding a critical value. That is caused by an increase in the transversal beam temperature due to the Weibel instability, resuting in electron traversing more than one mesh size in a time step thus violating the implicit scheme applicability condition. 25

26 Fig. 1. Simulation of the Weibel instability using codes LSP (implicit) and OSIRIS. Simulation parameters are given in the text. LSP hybrid simulation: beam electrons are in particle mode, plasma electrons and ions are fluid, large momentum averaging factor is used to stabilize the grid instability. LSP particle simulations: all species are in particle mode. t Beam electron density Plasma electron density = 47 ω p t = 188 ω p t = 1504 ω p t = 188 ω p t = 1504 ω p LSP hybrid LSP particle OSIRIS (a) Beam and plasma electron densities at different moments of time. An agreement in number of beam filaments is observed in the simulations. Higher plasma compression develops in LSP hybrid simulations at the late stage of the Weibel instability. LSP hybrid LSP particle OSIRIS (b) Energy balance in the simulations: beam electron energy (dashed line), plasma electron energy (dotted line), magnetic field energy (dash-dotted line), and total energy (solid line). The energy conservation is poor in LSP hybrid simulation. 26

27 The second benchmarking problem is concerned with two-dimensional simulations of the 22-3 plasma wake field excitation by an electron bunch in plasma with density n0 = 10 cm and temperature 50 ev. The wake was excited by a Gaussian beam of relativistic electrons (with velocity close to the speed of light) with a maximum density of cm -3 and width 0.5c / ω p = µ m. For such parameters, the wake field is excited in a linear regime and theoretical prediction for the amplitude of the electron density perturbations is [6] n = 0.08n0. Note that OSIRIS simulations do not include particle collisions. For comparison, we first performed LSP simulations with electrons only in order to eliminate plasma wave damping due to electron-ion collisions. LSP and OSIRIS simulations showed an excellent agreement and the plasma wave amplitude was equal to the theoretical value for a sufficiently high spatial and temporal resolution (see Fig. 2, a). More precisely, the plasma wave period and the electron beam profile need to be well resolved or an unphysical numerical damping of the plasma wave will occur causing the wave amplitude to decrease below the theoretically predicted value. This is applicable to both LSP explicit and implicit simulations, and fluid and particle modes for the background plasma. The value of the averaging parameter in the fluid mode can also influence the results in such a way that for heavy averaging, a two times higher (or more) spatial and temporal resolution is needed to prevent numerical damping of the plasma wave. Additional LSP simulations have been carried out with both electrons and ions (Fig. 2, b) in order to compare the plasma wave damping rate due to electron-ion collisions (resulting in plasma heating) with the theoretical predictions. We found the damping rate to be in agreement with the Spitzer electron-ion collision rate except for a slight difference not exceeding 10%, associated with a different definition of the Coulomb logarithm in the code. The classical definition in the code should be replaced with a quantum mechanical one that is valid for plasma temperatures exceeding a few tens ev. We implemented this modification in the code and observed a better agreement with the theory for large temperatures. 1. D. R. Welch, D. V. Rose, B. V. Oliver, R. E. Clark, Nucl. Instrum. Methods Phys. Res. A 464, 134 (2001). 2. D. R. Welch, D. V. Rose, W. M. Sharp, C. L. Olson, S. S. Yu, Laser Part. Beams 20, 621 (2002); D. R. Welch, T. C. Genoni, D. V. Rose, B. V. Oliver, R. E. Clark, C. L. Olson, S. S. Yu, Phys. Plasmas 10, 2442 (2003); D. V. Rose, D. R. Welch, C. L. Olson, S. S. Yu, S. Neff, W. M. Sharp, Fusion Sci. Technol. 46, 470 (2004); D. R. Welch, D. V. Rose, T. V. Genoni, S. S. Yu, J. J. Barnard, Nucl. Instrum. Methods Phys. Res. A 544, 236 (2005). 3. R. P. J. Town, C. Chen, L. A. Cottrill, M. H. Key, W. L. Kruer, A. B. Langdon, B. F. Lasinski, R. A. Snavely, C. H. Still, M. Tabak, D. R. Welch, S. C. Wilks, Nucl. Instrum. Methods Phys. Res. A 544, 61 (2005); R. B. Campbell, R. Kodama, T. A. Mehlhorn, K. A. Tanaka, D. R. Welch, Phys. Rev. Lett. 94, (2005). 4. R. A. Fonseca, L. O. Silva, R. G. Hemker, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam: OSIRIS: A Three-Dimensional, Fully Relativistic Particle in Cell Code for Modeling Plasma Based Accelerators. In P.M.A. Sloot et al., editors, ICCS 2002, LNCS 2331, pp , R. Lee and M. Lampe, Phys. Rev. Lett. 31, 1390 (1973). 6. E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE Trans. Plasma Sci. 24, 252 (1996). 27

28 Fig.2. Simulation of the plasma wake field using codes LSP (implicit) and OSIRIS. The mesh size 1 x =.25c / ω, y =.063c / ω, time step t = 0.03ω, other parameters are given in the text. LSP 0 p 0 p hybrid simulation: beam electrons are in particle mode, plasma electrons and ions are fluid. LSP particle simulations: all species are in particle mode. Electron density, longitudinal and transversal electric field distributions are shown for the moment of time when the electron beam injected at the left hand side plasma boundary reaches the right hand side boundary of the simulation box. p n / n ee / m ω c ee / m ω c x p y p LSP hybrid LSP particle OSIRIS (a) Electron plasma. A fine-scale noise in the pictures for density distributions is a consequence of particle nature of the simulations (a slightly different number of particles in the adjacent cells). n / n ee x / m ω p c ee y / m ω p c T e, ev (c) Plasma with electrons and ions. LSP hybrid simulation (LSP particle simulation shows similar results). In addition to electron density and field distributions, electron temperature distribution is also shown. 28

29 FAST-ELECTRON TRANSPORT Transport in wires and at laser-plasma interfaces F. Beg (UCSD), R. Stephens (GA), R.R. Freeman (OSU), J. Pasley (UCSD), F. He (UCSD), M Wei (UCSD), E. Baranova( UCSD), E. Shipton (UCSD), T. Ma (UCSD) The goal of our work is to design and field experiments designed to directly test components of the modeling codes we rely on in Fast Ignition experiments. We focus on two critical areas: electron transport and the laser-plasma interface. Until now, the modeling for those components have been descriptive; they contain enough heuristically determined free parameters that the experimental results cannot be used to validate the codes (as described by R.R. Freeman at IFSA 2005). We intend to change that using carefully characterized experiments on simple geometries. And we are joining our efforts among GA, UCSD, OSU, LLNL, and SNL in order to carry them out. The proposed experiments that we have developed are: 1) Probe electron transport in a nearly 1-D geometry to test hybrid code descriptions of electron transport at the high current levels in a FI experiment. Specifically, we would use an imaging Cu-K α diagnostic with ~10 µm resolution along with fluorescence spectrometry, and backlight interferometry and Faraday rotation to simultaneously measure hot electron propagation length, temperature, magnetic field and expansion rate along the length of a wire. This will be modeled with a hybrid code (hot electron particles in a fluid background). The targets necessary for these experiments have been developed over the last year, and are being constructed now. We have facility time at Sandia s Z-Petawatt (ZPW) facility in February 06 for the initial experiments; January/February is available for installing the necessary diagnostics. Later in the year, when ZPW can deliver two energetic short-pulse beams, we can add proton beam magnetic deflectometry to look at the magnetic field deeper in the plasma. 2) Characterize the electron behavior at the laser plasma interface. In this case we would diagnose the laser-plasma interface with a reflectivity probe that would give the timedependent electron response at the critical surface, and add a shallowly buried Cu layer to measure the total hot electron production. In addition we will install diagnostics to measure the spatial and temporal characteristics of the beam on a shot-by-shot basis. These experiments will test details of electron response predicted by PIC codes. In addition to LSP and OSIRIS, we intend to use the PICLS2d (by collaboration with Yasuhiko Sentoku), which includes collisions and the capability to model full density solids. The laser-pulse characterization and reflectivity diagnostics are under development; these experiments will be ready to be fielded in late Summer 06. They will utilize the split beam capability to deliver a controlled prepulse to the flat metal foil target. The Southwest Consortium (of which, OSU, UCSD, UTA, and GA are the primary actors), have been developing the ZPW at Sandia National Lab as the platform on which 29

30 to do these experiments. Because we are intimately involved in its activation, this facility will be uniquely suitable for our experiments given our easy and abundant access to the facility, adequate beam diagnostics (lack of shot-by-shot beam characterization has been a perennial problem at all the other facilities we have used), and uniquely controllable prepulse. The laser is being built by SNL using their funds for components, their personnel to assemble the laser, and our personnel for diagnostic construction. It will be available about 3 weeks/quarter for University collaboration experiments. It is being constructed with a 100 TW, 50 J beam that can be split, delayed and delivered collinearly to make a controlled prepulse, and by mid-summer will be delivered as two independently oriented 50 TW beams. It also splits off a much weaker beam (~100 mj) that can be used for short-pulse backlighting at controlled delays. The experimental development of this facility has, on the OSU/UCSD/GA side, been under the direction of the FSC-funded UCSD post-doc John Pasley (GA). He has established safety systems and training for the students, defined beam and diagnostic needs and, on the diagnostic side, led the student teams who are assembling the components into usable instruments (SNL pays for all the components through their Southwest consortium funding), and coordinated our experimental plans with the SNL beam development team. It is limited to some extent by Z-backlighter (ZBL) activity; although the ZPW system is physically independent, it is in the same building and we cannot operate simultaneously. Schedules are not known with any detail past March. The experimental program began this Fall as soon as the laser beam could be delivered to the target chamber and is supported by the combined FSC efforts of OSU, UCSD, and GA, which include substantial amounts of their own resources. The low power available then (~1 J) was not sufficient for the experiments listed below. The effort at that time concentrated on diagnostics. Enam Chowdhury (Postdoc, OSU) is leading gas jet experiments intended to give, for the first time, a direct measure of the laser intensity at the focus. Figure 1: Ion Time of Flight diagnostic for measuring ratio of ion charge states induced by laser-plasma interaction with gas jet target. This measurement allows focal spot intensity to be inferred. 30

31 This will be one of the critical diagnostics needed for our benchmarking experiments, and is a substantial improvement. Current practice is to infer the incident intensity on target from measurements of beam energy combined with overall spot size and duration. Structure within the spot can cause intensities substantially different from that estimate. In our approach, the intensity is inferred from the ratio of various ion charge states induced in a gas jet (one or more noble gases). These are detected using an ion time-offlight (TOF) diagnostic (Fig. 1), in which ions are accelerated towards a micro-channel plate (MCP) based detector. Different ion charge species arrive at the MCP at different moments, and the signal strength induced by each bunch of unique ion species reflects the yield at target chamber center, given that the very low gas pressure does not afford much chance of recombination. Some preliminary data is exhibited in Fig. 2. Figure 2: Preliminary ion time of flight data. Peaks around 11 microseconds are from variously charged neon ions. Peaks on the far left are from hydrogen (contaminant). 31

32 Electron acceleration in cones T. Ditmire, B. Ick Cho, S. Kneip, G. Dyer (UT) The FSC has supported a research project at the University of Texas at Austin to elucidate the mechanisms of hot electron generation in cone targets. In collaboration with the group at the University of Nevada at Reno, the UT group led by Prof. T. Ditmire has undertaken a an experimental study of x-ray production from micro-cone targets irradiated by a femtosecond laser. These experiments are motivated by recent PIC simulations from Reno suggesting that free wave electron acceleration and hot electron guiding by magnetic fields will occur in tapering targets [Y. Sentoku, et al, Phys. Plasmas 11, 6 (2004)]. This experimental effort supports the fast ignition work of the FSC because of the likelihood of using cone targets in fast ignition experiments [i] and ultrafast x-ray generation [ii]. These experiments were designed to validate these PIC simulations and elucidate the acceleration mechanisms of electrons in the cone. Under FSC support, guiding structures such as pyramidal and wedge shaped targets made from silicon have been developed. Sub-micron tips of pyramids are etched anisotropically into silicon wafers using the fact that different planes of Si etch at different rates. By judiciously choosing the initial wafer thickness, after etching, the thickness of the silicon wafer near the tip is less than 10 µm. Titanium foils are adhered to the backside of the wafer to act as an x-ray converter for the hot electrons accelerated in the cone structure toward the tip. For these experiments two target configurations have been used (figure 1): pyramidal cones and 1-D wedges. In the case of pyramid cones, the laser polarization interacts with two pairs of opposing walls. In the case of a wedge, the interaction is restricted to one pair of opposing walls. Hence, a wedge can be regarded as a twodimensional pyramid. This geometry was chosen to allow us to investigate polarization effects of the micro shaped targets by rotating the orientation of the target with respect to the polarization direction of the laser. Fig. 1. SEM images of pyramid (left) and wedge (right) target which are etched in silicon wafers. Experiments have been conducted by irradiating these targets using the THOR laser at the University of Texas at Austin (delivering 800nm, 600mJ, 38fs, pulses focused to a 10µm diameter focal spot, yielding focused intensities greater than W/cm 2 ). The titanium K α emission from the Ti foil was measured using x-ray pinhole cameras and 32

33 two crystal spectrometers: a von-hamos for survey spectra and a spherical crystal x-ray spectrometer to yield spatial information in one dimension. Hard x-rays were also measured using a six-channel hard x-ray spectrometer with various cut-off filters (0.1 2 MeV). Additional diagnostics are scheduled for implementation in early 2006, including an electron spectrometer and an x-ray penumbral imaging camera. In the first set of experiments, a pinhole camera was used to image the x-ray emission from flat, 25µm thick titanium foils. The emission was compared to pyramid targets backed with these same foils. The foils were shot with the laser being incident at an angle of 45º in p-polarization. Pyramid targets were shot along the pyramid axis of symmetry. The data show both an enhancement in overall signal as well as a sharper peak in the region of x-ray emission for the pyramid targets as compared to plain flat targets. During this last year, x-ray emission spectra have been examined to derive some information on hot electron temperature with various target configurations (ie, flat, pyramid and wedge targets). Figure 2 illustrates the measured Ti K α spectrum from three different target configurations: pyramid targets, and wedge targets with laser polarization parallel (S) and perpendicular (P) to the wall surface. Surprisingly the P-polarized wedges exhibit lower K α yield than the other two target configurations. Fig. 2. Comparison of Kα spectrum from pyramid target (2.4 Å~ 10 9 photons/ shot/srad), s-wedge target (3.3Å~10 9 photons/shot/srad) and p-wedge target (0.9Å~10 9 photons/shot/srad). Each target was based on 25 m m thick titanium foil. It turns out that this behavior is a result of producing much higher electron temperature ion the case of P-pol irradiated wedges. This was determined by examining the hard x- ray spectra from these targets. To do this measurement a combination of scintillator / photomultiplier detectors with various cut off filters was used to measure hard x-ray yield. Results are shown in figure 3. Our data show the highest hard x-ray yield for p- polarized wedges and the lowest yield for s-polarized wedges. This result indicates an enhancement of very hot (MeV) electrons for p-polarized wedge targets and is also in accordance with the PIC simulation that predicts a higher electron temperature for the p- polarized wedge. It is found that there is a significant difference in the Kα source size between flat Ti targets and Ti targets laid on a Si cone. Figure 4 illustrates the spatial 33

34 profile of Ti Kα when a flat Ti target of 25 mm thickness is irradiated and the profile when a Si cone is irradiate (with Ti backing layer) the flat target exhibits wings that spread the source to >0.5 mm. Fig. 3. Hard x-ray yield from p and s-polarized wedges and pyramid targets. P-polarized illumination of the wedge exhibits the highest hard x-ray yield around 1MeV and the s- polarized wedge has lowest yield. The pyramid target results in an x-ray yield intermediate to the two wedge configurations. It has to be noted that these pyramids and wedges have a larger opening angle than the cone targets that were studied recently for fast ignition. The opening angle of guiding structures made from silicon is determined by the crystalline structure of the silicon. As results, surface guiding of electrons with moderate energy was not significant. We, therefore, plan to examine the electron spectra directly with a magnetic electron spectrometer. In fact, we have preliminary data which are under analysis. Fig. 4. Line outs of spatial profiles of Ti K taken with the bent crystal spectrometer 34

35 Electron stopping in HED plasmas R. D. Petrasso, C. K. Li, F. H. Séguin, C. Chen, D. Casey (MIT) A basic problem in plasma physics, with applications to Fast Ignition [1] and to fuel preheat [2], is the energy deposition of energetic charged particles into a dense plasma. A fundamental difference exists, however, between energetic electron and ion stopping, in that the profound effects of electron scattering [3], which manifest themselves in pronounced straggling and blooming, needs to be treated in the energy deposition. This scattering, present for both plasma and cold matter, but, until recently, only treated analytically in the latter case [4], is illustrated in Fig MeV e 0.34 g/cm g/cm MeV p g/cm g/cm 2 FIG. 1. Illustrated here is the pronounced difference in blooming and straggling, a consequence of scattering effects, for equally penetrating electrons and protons (mean penetration of 0.45 g/cm 2 ) into DT ice of 0.25 g/cc. Both cold matter and CELSA model calculations, though differing in specific details, display this same general behavior, i.e. both find the electron blooming (or straggling) is ~ 100 times that of the protons. As noted in Fig. 1, straggling and and blooming for equally penetrating electrons and protons, is ~ 100 times larger for electrons. And for the case of 1-MeV and lower energy electrons, blooming and straggling are always a significant fraction of the penetration (ρx), with, in fact, the ratio of blooming (or straggling) to penetration (ρx) significantly increasing as the energy decreases. With these issues in mind, C. K. Li and coworkers recently developed a model of energetic electron stopping which couples together both scattering and energy loss as the electrons slow in the background plasma [5-7]. (Details of the calculations, referred to henceforth as Coupled Energy Loss and Scattering Analysis, or CELSA, are contained in 35

36 those references.) In brief, whenever λ D < r g, L >> λ, and L >> λ r, with λ g D the Debye length, r g the gryo radius (due to, e.g. current flows), λ the mean free path, and L and L the longitudinal and lateral plasma scale lengths [8], the interaction of the energetic electrons are dominated by classical Coulomb collisions, thus collisional transport processes prevail. For the case of fast ignition, Fig. 2 illustrates the regimes in the interior of the compressed capsule (n e /cc) where collisional transport dominates and, in contradistinction, near the surface of the capsule where Weibel-like instabilities and large self-magnetic field effects dominate electron transport. For the case of preheat, which affects the fuel assembly through the adiabat, collisional transport of the CELSA model is solely important. Laser ρ n b /n e > 10-2 : self fields, instabilities,. n b /n e < 10-2 : scattering n b /n e ~10-2 FIG. 2. Schematic illustration of MeV electron transport and energy deposition in a pre-compressed target. Two distinct regions for electron transport are illustrated: First, when n b /n e > 10-2, electron transport is highly filamented due to Weibel-like instabilities which dominate energy loss and beam blooming; however, for n b /n e < 10-2, for which λ D is clearly smaller than the energetic electron gyro radius associated with the beam current, Weibel-like instabilities are stabilized and the electrons are then subject to the scattering, straggling, and blooming processes described by the CELSA model. Prediction of the model. With the previous considerations in mind, results are illustrated by applying the CELSA model to FI and preheat scenarios. Figure 3 illustrates the stopping power for 1 MeV electrons slowing in a 300 g/cc DT plasma. The nonscattering or uniform energy deposition model used, for example, by Atzeni [9] lacks the enhanced region of energy deposition, a result of straggling and blooming; furthermore, the mean penetration of the non-scattering model is about 30% farther, a natural consequence that the (non-physical) straight-line approximation for the electron path suffers no deflections while slowing. 36

37 Distance (µm) de/d(ρr) (MeV g -1 cm 2 ) Effective Bragg peak > Σ R < Σ R Traditional Bragg peak ρr (g/cm 2 ) FIG. 3. The stopping power plotted as a function of the electron penetration for 1-MeV electrons in a DT plasma (ρ=300g/cm 3 and T e =5 kev). The heavy solid line represents the mean energy loss, while the two dashed lines schematically indicate the straggling range over which energy is effectively spread. The thin line illustrates the continuous slowing-down approximation, or non-scattering model, of energy desposition. In order to more fully explore the consequences of the CELSA model for 1-MeV electrons, Fig. 4 plots, utilizing the results of Fig. 3, the energy deposition into a uniform 300g/cc DT plasma for electron beam footprints with radii from 1 to 20 µm. Also plotted are the results of the non-scattering model similar to that used by Atzeni [9]. In each case, the model deposition profiles are usually quite different, the consequence of which would be to modify, in a fashion yet to be determined (Section 6), the ignition conditions discussed by Atzeni [9]. These considerations, especially the mean penetration (ρx), are also potentially important for the electron preheat problem [2] which, if excessive, could raise the fuel adiabat and preclude proper fuel assembly. Table I tabulates the results of the CELSA model for conditions applicable to preheat, ie. densities near or a few times above solid DT, plasma temperatures of ~ 10 ev, and electrons with energies from ~ 10 to ~100 kev. The materials listed in Table 1 (CH, Be, or DT) are either being used at OMEGA in current experiments, will be used in the near future at OMEGA, or will be used for the NIF ignition experiments. Figure 5 shows the mean penetration (ρ<x>) of the CELSA model as function of the electron energy, where the DT ice thickness for the direct drive capsule, as noted, is approximately 350 µm or ~ 9 mg/cm 2. While 100 kev electrons are seen to penetrate ~ 8 mg/cm 2, electrons of substantially smaller energy will, of course, wreak significant damage on the fuel adiabat if sufficient in numbers. To this point, work that remains (Section 6) is to convolve conceivable or expected electron distributions with these stopping power calculations, and to calculate the resultant adiabat. The effects on the fuel assembly can then be quantitatively assessed. 37

38 r b = 1 µm r b = 3 µm E (kev/µm 3 ) r b = 5 µm r b = 10 µm r b = 20 µm Penetration (µm) FIG. 4. Energy deposition profiles calculated using the CELSA model (solid line) and a uniform energy deposition model, similar to that used by Atzeni [9]. The radii of the beam footprint for the 1 MeV electrons varies from 1 to 20 µm. In nearly every case, significant differences exist between the two model energy deposition profiles, the consequence of which is likely to affect details of the ignition criteria. 38

39 1.00E-02 ρ<x> g/cm E E Energy (kev) FIG. 5. The penetration of electrons, with energies between 10 and 100 kev, into a DT plasma of 0.25 g/cc and ~ 10 ev. Increasing the plasma density to 1 g/cc, as might occur after passage of a strong shock, has a small effect on these results (Table I). For the NIF direct drive capsule, the DT ice thickness corresponds to an areal density of 9 mg/cm 2, as indicated by the arrow. TABLE I. Interactions of 10-keV and 100-keV electrons with DT, Be and plastic CH plasmas, common ablator or fuel materials of ICF. The plasma T e ~10eV. (For CH, the scattering effects are calculated for carbon ions and all plasma electrons). ρ<x> or <x> is the mean penetration, Σ R (Σ B ) is the associated straggling (blooming). For fixed energy, Σ B / <x> increases with Z. Ε 0 ρ R <x> ρ<x> Σ R Σ B (kev) (g/cm 3 ) (µm) (µm) (g/cm 2 ) (µm) (µm) Σ R x Σ B x 10 DT Be CH DT Be CH M. Tabak et al., Phys. Plasmas 1, 1626 (1994). 2. M. D. Rosen, R. H. Price, E. M. Campbell et al., Phys. Rev. A 36, 247 (1987). 3. G. Molière, Z. Naturforsch, 3a, 78 (1948). 4. H. A. Bethe, Phys. Rev (1953). 5. C.K. Li and R.D. Petrasso, Stopping of Directed Energetic Electrons in High-Temperature Hydrogenic Plasmas Phys. Rev. E, 70, (2006). 6. C.K. Li and R.D. Petrasso, Stopping, Straggling, and Blooming of Directed Energetic Electrons in Hydrogenic and Arbitrary-Z Plasmas, to be published in Phys. Rev. E, 73, January C.K. Li and R.D. Petrasso, Energy deposition of MeV electrons in compressed targets of fastignition inertial confinement fusion, to be published in Phys. Plasmas (2006). 8. B. Trubnikov, Review of Plasma Physics 1 (Consultants Bureau, New York, 1965). 9. S. Atzeni, Phys. Plasmas 6, 3316 (1999). 39

40 FUEL ASSEMBLY FOR FAST IGNITION Fuel Assembly for Fast Ignition: Theory and Simulations R. Betti (UCSD), C. Zhou, (UR), J. Delettrez (UR) The energy gain [1] G of a direct-drive implosion is defined as the ratio between the thermonuclear energy yield and the laser energy on target. The gain is directly related to G = 2 η θe m, where VI is the implosion velocity, the capsule implosion velocity ( V ) 1 I h f i η h = EK E L is the hydrodynamic efficiency representing the ratio between the shell kinetic energy and the laser energy on target, Ef = 17.6 MeV is the energy of the fusion products for a DT fusion reaction, and mi = 2.5 mh is the average ion mass. The function θ represents the fraction of burned fuel depending on the fuel areal density ρr R ρdr. 0 The function θ = θ(ρr) is commonly approximated [1] by θ ( 1+ 7 ρr) 1, where ρr is given in g/cm2. If the driver energy is kept constant, higher implosion velocities require lower masses. In this case, the effect on the ρr of a lower mass balances the effect of higher velocity, thus making ρr independent of velocity. The hydrodynamic efficiency [1] depends on the ratio between the initial M0 and final mass M1 of the capsule; η 2 ( M M )( ln M M ) ( ). The difference Ma = M0 M1 is the ablated mass, h M1 M0 and the approximation η ( M M ) 0.87 can be used for Ma < 0.8 M0. The ablated mass h a 0 is proportional to the ablation velocity Va, the in-flight shell density ρ if, the implosion 2 time ti, and the ablation surface area ~R2; M a ~ ρifvrt a I. By setting M 2 0 ~ ρifr i f ( if is the in-flight thickness) and by using the well-known scaling relation [1] V ~ α I, where α if is the in-flight adiabat and IL is the laser intensity, one can easily rewrite ( ) a ~ if if L M M α A V I, I where Aif is the in-flight aspect ratio and the relation ti ~ a if L R V I has been used. Since the aspect ratio [1] 2 scales as Aif ~ M if (where Mif is the in-flight Mach number), the final scaling of the hydroefficiency can be easily derived by substituting ρ ~ ( p α ) 35 into the Mach number, and [1] 23 p P I, where PL is if if if if ~ L ~ the laser-driven ablation pressure. A straightforward manipulation yields η h ~ VI I L, which compares favorably with the following numerical fit of 1-D simulations of UV laser (λl = 0.35 µm) driven implosions η fit h I ( cm s) V = I, L (1) 40

41 where I15 is the laser intensity in 1015 W/cm2. The simulations are for ten direct-drive cryogenic targets with UV laser energies varying from 25 kj to 1.5 MJ and are carried out using the 1-D code LILAC [2]. The targets used in the simulations are either all DT ice or wetted-foam CH(DT)6 capsules with a 2-µm CH overcoat. Substituting the hydroefficiency into the gain formula yields a thermonuclear gain that increases with lower implosion velocities θ G I V 15 I ( cm s) 0.2 (2) Equation (2) shows that, if ignited, slow targets yield high gains. The energy required for ignition from a central hot spot, however, increases rapidly as the velocity decreases hot-spot 6 [3] ( ~1 V This is because the hot-spot temperature increases with the velocity. E ign ). Since the fusion cross section is a strong function of the temperature, slow targets have a relatively cold hot spot and therefore require greater energy for ignition. If the implosion velocity is below cm/s, the hot spot cannot be ignited regardless of the shell energy since the radiation losses dominate the hot-spot energy balance. However, such slow targets can be optimal for fast ignition [4] since the hot-spot size and energy decreases with the implosion velocity. Fast ignition with *1 MeV electrons requires [4,5] large ρr s, densities greater than 200 g/cc, and assemblies with small hot spots. Scaling Laws for Density and Areal Density. We start our analysis by deriving a scaling law for the shell density, areal density, and hot-spot size as a function of characteristic implosion parameters such as shell energy, implosion velocity, and in-flight adiabat. By indicating with s the stagnating shell thickness, with Rh the hot-spot radius, and with Ms the shell mass, the compressed shell areal density scales as ( ) ( ) ρs s ~ M s Rh As ~ EK RhVI As, where EK is the shell kinetic energy at the end of the acceleration phase, As = Rh s is the 2 stagnation aspect ratio, and ( x) = 1+ 1 x+ 1 3x is a volume factor. The hot-spot radius Rh can be derived by setting the total shell internal energy at stagnation equal to the shell kinetic energy E 3 K ~ ps( R h + s), where the stagnation pressure ps has been assumed to be approximately uniform through the hot spot and shell. This energy conversion 53 condition (from kinetic to internal) can be rewritten by setting p ~ α ρ, where α s is s s s the stagnation adiabat that is related [6] to the in-flight adiabat α if through the in-flight 23 Mach number αs ~ α if Mif, leading to α ~ s α if VI PL. It follows that the shell density and the shell areal density can be rewritten as and ρ ~ Φ( A ) E V I α s s s k I L if (3) 41

42 ρ ( A ) V I α s ~ Ψ s I L if, (4) where ( x) ( x x 13) ( 1 x) Φ and Ψ ( x) = Φ ( x)( 1+ x) 94. Though the stagnation aspect ratio is of order unity, it is important to accurately determine its functional dependency on the implosion parameters. For reasonable values of the stagnation aspect ratio ranging between 1 < As < 4, Φ and Ψ can be approximated with a power law as Φ ( As) ~1 As and Ψ ( As) ~1 As. As grows with the implosion velocity since the mass decreases for a fixed energy leading to smaller s, while Rh depends mostly on energy. In order to determine an accurate dependence on the velocity, we fit the results of the simulations where Rh is defined as the point of maximum shell density, and s is the distance between Rh and the return shock at the time of peak areal density. The simulations show a clear dependence on the velocity and almost no dependence on energy and adiabat leading to ( cm s) 0.96 fit VI As 2.1, (5) as shown in Fig. 1. Substituting Eq. (5) into (3) and (4) yields scaling laws for the density and areal density s s ~ EL VI if, s ~ VI IL αif, ρ α ρ (6) where the hydro-efficiency from Eq. (1) has been used. These semi-analytical scaling laws compare favorably with the numerical fits of the peak values of the densities and areal densities ( ρr) fit 1.3 EL( kj) VI ( cm s) = max αif 3 10 ρ ( cm s) fit V I max = I15, α 7 if 3 10 (7) (8) where the subscript max indicates the maximum values during the implosion and ρr and ρ max are in g/cm2 and g/cc, respectively. The laser-intensity scaling in (8) is analytical from (6) since the intensity varies only within a ±15% range in the simulation, and it does not represent a good scaling parameter. The areal density in Eq. (7) includes the inner portion of the shell that has been compressed by the return shock as well as the surrounding portion that has not been shocked. Typically, the unshocked portion has significantly lower density and lower ρr with respect to the shocked portion (see Fig. 4). The time of peak ρr occurs after the time of peak density, and the average density at the time of peak ρr is slightly below 80% of Eq. (8). If fast ignition is triggered at or soon 42

43 after the time of peak ρr, the corresponding average density is significantly below its maximum value. 4 sim R f h p Δs 3 2 Figure 1. Stagnation aspect ratio from simulation compared with numerical fit (5). TC7017J (R h /Δ s ) fit 4 Laser Pulse Shaping. Other important considerations in optimizing fast-ignition targets concern the pulse length and laser power contrast ratio. It is clear from Eqs. (7) and (8) that low adiabat implosions lead to high densities and areal densities. However, very low adiabat implosions require long pulse lengths and careful pulse shaping. The long pulse length is required by the slow velocity of the low-adiabat shocks, and the careful shaping is required to prevent spurious shocks from changing the desired adiabat. Furthermore, the ratio between the peak power and the power in the foot of the laser pulse (i.e., the power contrast ratio) increases as the adiabat decreases thus leading to difficult technical issues in calibrating the pulse shape. These constraints on the pulse shape are relaxed by using the relaxation (RX) laser pulse technique [7]. The relaxation pulse consists of a prepulse followed by an interval of laser shutoff and the main pulse. The RX pulse induces an adiabat profile that is monotonically decreasing from the ablation surface to the inner shell surface. In addition to improving the hydrostability of the implosions, the RX main pulse is shorter and requires a lower contrast ratio than the equivalent flat adiabat pulse with the same inner surface adiabat. Inertial Fusion Energy FI Capsule Design. By using the results in Eqs. (5), (7), and (8), an IFE fast-ignition capsule can be designed. We start by setting a low value for the min inner-surface adiabat αif 0.7. An adiabat below unity implies that, at shock breakout, the inner portion of the shell is not fully ionized. In order to achieve a ρr 3 g/cm2, Eq. (7) yields a laser energy EL. 750 kj. Equation (8) is then used to determine the velocity required to obtain a peak density of 640 g/cc that corresponds to an average density of the shocked shell at the time of peak ρr of ρ 0.8 ρ max 500 g/cc. The corresponding velocity from (8) is VI = cm/s, leading to a hot-spot aspect ratio [Eq. (5)] of As ~ 1. Since the required laser energy of 750 kj is approximately half the NIF energy, we use a reference driver with half the energy and half the power of the NIF. For a peak power of 220 TW, the outer shell radius is chosen to keep the peak intensity at 1015 W/cm2, thus leading to Rout 1.3 mm. The target mass at stagnation is derived from the kinetic energy 2 2 with EK η h EL. Using Eq. (1) for η h and EL = M s EK V I, 750 kj, VI cm/s yields a stagnation mass of Ms 1.7 mg. Assuming that 43

44 ~20% of the mass is ablated leads to an initial mass of about M0 2 mg. In order to improve the laser energy absorption, we consider a wetted-foam target with an inner ice layer, an outer wetted-foam CH(DT)6 layer, and a 2-µm CH overcoat. Given the low density of the foam and the small thickness of the overcoat, we can assume that the average density is the same as DT ice, ρ g/cc, and determine the inner-shell radius from the volume M0 ρ 0 and the outer radius leading to Rinn. 660 µm. Figure 2 shows the FI-IFE target with a foam layer thickness that is large enough to reabsorb the coronal radiation and reduce the radiation heating of the inner ice layer. It is important to notice that the large shell thickness combined with the slow implosion velocity makes the target performance insensitive to the hydrodynamic instabilities and 1-D codes suitable for realistic simulations of the implosion. The 750-kJ RX pulse is shown in Fig. 3. The main foot-pulse length is about 22 ns, and the power contrast ratio is about 150. A LILAC simulation of the 750-kJ implosion yields the exact desired implosion parameters. Substituting the implosion parameters into the gain formula (1) yields a thermonuclear gain of about G 220 ( 1+ EPW 750 ), where EPW is the petawatt laser energy required for ignition in kilojoules. Figure 4 shows the density profiles versus the areal density at different times about the peak ρr time. The sharp drops in density shown in Fig. 4 correspond to the return shock traveling outward from the center. Notice that the density varies significantly while the total ρr remains above 2.5 g/cm2. Ignition can therefore be triggered at an average density varying from 300 to 550 g/cc without significant changes to the target gain. The density versus volume plots in Fig. 5 indicate that the hot-spot volume is less than 10% of dense core during hundreds of ps about the time of peak ρr. Notice that at 27.5 ns, the density is about 300 g/cc, and its profile is approximately uniform. The hot-spot volume is small, and values below ρ < 300 g/cc are confined within a tiny region occupying only 6% 7% of the core. CH CH(DT) 6 DT ice DT gas 657 μm 2 μm 177 μm 479 μm Power (TW) Prepulse TC7018J1 Figure 2. Fast-ignition IFE target. TC7019J Time (ns) Figure kj, α = 0.7 relaxation laser pulse. 44

45 ns ρ(g/cc) ns ns ρ(g/cc) TC7020J ρr(g/cm 2 ) TC7021J Volume (cm 3 ) ( 10 6 ) Figure 4. Density profiles versus areal density at three times about the time of peak areal density. Figure 5. Density profiles versus volume at three times about the time of peak areal density. [1] Atzeni S. and Meyer-ter-Vehn J., The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter, International Series of Monographs on Physics (Clarendon Press, Oxford, 2004); Lindl J. D., Inertial Confinement Fusion: The Quest for Ignition and Energy Gain Using Indirect Drive (Springer-Verlag, New York, 1998). [2] Delettrez J. and Goldman E. B., Numerical Modeling of Suprathermal Electron Transport in Laser- Produced Plasmas, Laboratory for Laser Energetics, Report No. 36, University of Rochester (1976). [3] Herrmann M. C. et al., Nucl. Fusion 41 (2001) [4] Tabak M. et al., Phys. Plasmas 1 (1994) [5] Atzeni S., Phys. Plasmas 6 (1999) [6] Betti R. et al., Phys. Plasmas 9 (2002) [7] Betti R. et al., Phys. Plasmas 12 (2005)

46 Fuel assembly experiments with cone targets D. Meyerhofer (UR), C. Stoeckl (UR), R. Stephen (GA), W. Theobald (UR) Project co-sponsored by the FSC. LLE is the main sponsor. Prior to the commencement of this grant, fuel assembly experiments using cone-in-shell targets with 70 degree opening angle cones were performed. Both x-ray radiography and charged particle spectroscopy were used to estimate the shell areal density to be ~60 mg/cm 2, approximately 80% of that predicted by symmetric 1-D simulations under similar drive conditions. Work during the recent period has extended this in three ways: Extending fuel assembly experiments to cones with 35 degree opening angles, Using self-emission images to estimate the amount of the gold cone material mixed into the compressed core, Streaked optical measurements of compression-induced shockwaves propagating through the cone material. Each of these topics will be briefly described below. It is important to note that this work is carried out jointly with LLE s internal research program and with collaborators from other FSC institutions, and international colleagues as well in some cases. Extending Fuel Assembly Experiments to 35 degree cones. X-ray radiography and nuclear diagnostics were used to study the compression of cone-in-shell targets with Au cones having 35 degree opening angles. Figure 1 shows a backlit implosion of cone-in-shell target with a 35 degree opening angle. The images are similar to those obtained for 70 degree cone-in-shell implosions. The performance of compressed core of these targets was slightly improved compared to that of 70 degree cone targets. The development of simulation capability for cone-in-shell targets will be required to understand these differences quantitatively. Figure 1: Backlit implosion of a 35 degree cone-in-shell target 46

47 Cone-Core mixing. The x-ray self-emission of a series of compressed cone-in-shell implosions was observed. Figure 2 shows the x-ray self emission of the compressed core, clearly showing separate emission regions from the gold cone tip (dashed line) and the compressed shell material. Figure 2: Self emission from the compressed core region of a cone-in-shell implosion. The original cone location is shown by the dashed lines. Two distinct regions are observed, corresponding to gold emission and that from the compressed shell material. A lineout through the centerline of Fig. 2 (black line) is shown in Figure 3. One sees that the cone and core emission are distinctly separated and that the core emission is symmetric about its center. This allows an upper limit of the amount of Au material into compressed core to be estimated to be less than 0.01% mass density (due to the very different opacities of CH and Au.) Figure 3: Lineout of the self-emission shown in Fig. 2. The symmetry of the core emission allows an upper limit of the amount of Au material into compressed core to be estimated to be less than 0.01% mass density. 47

48 Shock breakout through the Au cone due to the compressed core. One of the important issues for cone-in-shell Fast Ignition is the thickness of the Au cone. The thinner the cone, the easier it will be for the electron beam to propagate through. However, the cone must remain intact through the duration of the implosion so that the inside of the cone remains free of plasma. In particular, a shockwave is generated in the cone due to the compression of the shell material. We have measured the breakout of the compressiongenerated shockwave through the Au cone using a visible streak camera (the Streaked Optical Pyrometer). The experimental setup is shown in Figure 4. The light emission from the inside of the cone is imaged onto an optical streak camera. Prior to shock-wave breakout, there is only background emission. There is an increased intensity when the shock-wave breaks out of the Au cone, into the vacuum. Figure 5 shows the emission observed during the implosion of a cone-in-shell target with a 70 degree cone. The emission shows a characteristic conical shape, with the emission beginning at the tip of the cone and working its way up the sides. Similar measurements with 35 degree cones are less clear. It is speculated that this due to shock waves launched into the cone due to the implosion. Figure 6 shows a line-out of the light emission through the cone tip with the laser power history and predicted areal density superimposed. This clearly shows that the shock-wave breaks out the cone material after peak compression, as required for the FI concept. Figure 4: Setup for the measurement of the compression-induced shockwave through the Au cone. 48

49 Figure 5: Streaked optical emission from the interior of a 70 degree Au cone during a cone-in-shell implosion. Figure 6: Lineout of the emission from the interior of the 70 degree cone with the laser power history and predicted areal density super-imposed. 49

50 INNOVATIVE HEDP CONCEPTS Shock ignition of thermonuclear fuel with high areal densities R. Betti (UR), C. Zhou (UR), J. Perkins (LLNL) In conventional hot-spot ignition ICF, a compressed shell of thermonuclear fuel is ignited from a low-density central hot spot. For ignition to occur, the alpha particle self-heating of the hot spot must exceed all the energy losses. The radiation losses alone can only be overcome if the hot spot temperature exceeds about 4 kev. Other energy losses such as thermal losses and hydrodynamic expansion require a significant increase of the temperature needed for ignition. Since the hot spot temperature is mostly dependent on the shell velocity V I, the energy required for ignition decreases with the shell velocity. Obviously, smaller drivers require larger implosion velocities with a 200kJ driver requiring velocity of about cm/s for a 50% margin. However, high velocity implosions exhibit fast Rayleigh-Taylor instability growth during the acceleration phase leading to the shell break-up before stagnation. The number of e-foldings for the growth of the most dangerous RT modes with k =1 (k is the mode wave number and is the inflight shell thickness) during the acceleration phase can be written as 0.6 V I ( cm / s) α out N e / /15 (1) 15 α I I 15 α Observe that the ablative stabilization has only a small effect on the k =1 modes. It follows that the 200kJ target with adiabat α=1 and V I = cm/s mentioned above undergoes a RT growth of 8.3 e-foldings. Note that even using adiabat shaping (i.e. increasing <α> and α out /<α>) may not be sufficient to stabilize those highly unstable targets. Such a large RT growth is very likely to cause a major disruption of the shell and failure of the implosion. In order to reduce the impact of the acceleration phase RT, low energy drivers must adopt low velocity implosions that inevitably fail to ignite because the hot spot stays too cold. Even though low velocity implosions cannot be ignited through conventional hot-spot ignition, they can be used to assemble high density and high ρr fuel as long as the target adiabat is kept sufficiently low. Indeed the peak value of the total areal density is approximately independent of the implosion velocity and can be approximated by the following simple formula EL ( kj ) 2 ρ Rmax g / cm (2) α 0.55 inn

51 where E L is the laser energy on target, and ρr max represents the maximum value of the total ρr. In the past year, we have shown that such a high density fuel can be ignited with a spherically convergent shock. Shock-ignition makes use of the same fuel assembly required for conventional fast ignition, but it employs a different mechanism to trigger ignition. Since spherically convergent shocks are an ideal venue to collect energy over a large area and concentrate it in a small volume upon convergence, shock ignition uses a convergent shock to heat up the relatively cold hot spot of the fuel assembly to ignition temperatures. The key issue for a successful shock-fast ignition implosion is timing the ignitor shock with the return shock reflecting off the center. The return shock is a ubiquitous by-product of spherical shell implosions and is driven by the converging material moving towards the center. The ignitor shock can be launched by a rapid rise in laser power of the compression driver itself and needs to be timed to collide with the return shock inside the imploding capsule, preferably near the shell peak density. That implies that the ignitor shock needs be launched shortly before the fuel stagnates. The inward traveling shock resulting from the collision between the return and the ignitor shock causes an impulsive acceleration of the stagnating shell inner surface and direct shock heating of the hot spot. Ignition occurs if the hot spot becomes hot enough and if the surrounding fuel develops large areal densities to provide adequate hot spot confinement. Figures 1 shows a typical wetted foam target with a 2µm CH overcoat used for shock ignition. The targets require 100kJ and 500kJ for the fuel assembly and exhibit a peak implosion velocities of cm/s. The inner surface adiabat at shock break-out is 0.7. These targets have large peak areal densities of 1.6g/cm 2 for 100kJ and 2.9g/cm 2 for the 500kJ. Their peak central ion temperature at stagnation is about 4keV. Such cold and dense hot-spots cannot self-ignite, however, given their high densities and areal densities of the surrounding shells, their confinement time is long. CH 2µm CH 2µm CH(DT)6 80µm CH(DT)6 153µm DT ice 147µm DT ice 253µm DT gas 453µm DT gas 772µm Fig kJ and 500kJ wetted-foam targets for shock ignition What is needed to trigger ignition is simply a mechanism to heat up the hot spot to ignition temperatures in the 7-8keV range. This can be accomplished by launching a shock at the end of the assembly pulse as shown in the power "spikes" in Fig. 2 for the 51

52 100 and 500kJ fuel assembly. The energy in the shock is a significant fraction of the assembly energy varying from 30 to 60% with greater energy providing a more robust design. The shock laser energy in Fig. 2 and 3 is 60kJ and 200kJ respectively and the spike laser intensities are and W/cm. 2 The shock is timed in order to collide with the return shock in the shell and close to the inner shell surface. The collision produces an inward propagating shock with a pressure greater than the return shock pressure. Such a converging shock impulsively accelerates the inner shell surface heating the hot spot to ignition temperatures. Fig. 2. Laser pulses for the 100kJ (left) and 500kJ (left) wetted-foam targets. The power spike at the end of the pulse drives the ignitor shock Performances of the two targets are shown in the two tables below. The total energies including the power spike are 160kJ and 700kJ. The gains are large (65 and 116 respectively) due to the large areal densities induced by the low adiabats and the large initial shell masses. Energy In-flight Max. areal aspect ratio density (g/cm2) Implosion velocity (cm/s) Gain 160kJ Energy In-flight Max. areal aspect ratio density (g/cm2) Implosion velocity (cm/s) Gain 700kJ

53 E and B fields generation by laser-plasma interaction R. D. Petrasso, C. K. Li, F. H. Séguin, C. Chen, D. Casey (MIT) Project co-sponsored by the National Laser User Facility program Under the sponsorships of the FSC and the NLUF program, MIT took the first preliminary data in an ongoing series of experiments using proton radiography to study transient E and B fields generated by the interaction of OMEGA laser beams with plastic foils. In each experiment a plastic foil was illuminated by a single OMEGA laser beam, and projection radiographs were made of the foil using a backlighter providing monoenergetic 14.7-MeV protons and 3-MeV DD protons; the image recorder was a CR- 39 area detector. The protons passed through a wire mesh before impinging on the foil, and the distortion in the mesh pattern at the detector shows how the proton trajectories were deflected through interaction with the fields generated by laser-plasma interaction at the foil. Figures 1 and 2 show the experimental setup. The backlighter was formed by imploding a D 3 He-filled, glass-shell capsule with 20 OMEGA laser beams in a 10-kJ, 1-ns pulse. The capsule diameter used was unusually small, at about 440 µm, in order to provide a smaller-than-usual burn radius for optimal spatial resolution in the radiograph; the FWHM of the proton source was measured with proton emission imaging to be about 50 µm. The mesh was mounted on the foil assembly about 1 cm away, and the center-tocenter spacing of the mesh wires was either 150 µm or 200 µm. The diameter of the laser beam incident on the foil was 800 µm, and the laser intensity was about W/cm 2, and the pulse length was 1 ns. The CR-39 detector was about 36 cm away. Since the burn duration of the D 3 He implosion was short (~ 150 ps) relative to the duration of the foil illumination, and since the relative timing of the implosion and the foil illumination was adjustable, it was possible to record images at different times relative to the foil illumination. 53

54 Laser beam Laser beams Mesh 20-µm CH D 3 Hefilled capsule 1 cm 35 cm protons Detector (CR-39) FIG. 1. Physical arrangement of the proton backlighter (imploded D 3 He-filled capsule), mesh, CH foil, CR-39 imaging detector, and OMEGA laser beams, as used for radiography. FIG. 2. Photograph taken before an actual experiment, showing the backlighter capsule (left), the CH foil (right), and the wire mesh (just to the left of the foil). Sample images recorded at different times are shown in Fig. 3. These images are currently being analyzed in collaboration with LLE and LLNL coworkers in order to provide information about the time evolution of the field-induced distortion. Preliminary results are shown in Fig.4. Qualitatively, at least, they agree with LASNEX simulations that indicate formation of a plasma bubble [R. Town (private communication)]. with B field of ~ 0.5 MG at t = 0.5 ns. MIT plans to extend these measurements. 54