# AFRL/RD Kirtland AFB, NM and AMOS Site, Maui, HI

### SF.10.01.B1213: Adaptive Control for Improved Laser Beam Pointing & Tracking

#### (505) 846-2711

Aircraft-based laser tracking systems are subjected to a range of disturbances that originate from the aircraft, the optical train, aero-optics effects, and the dynamics nature of the atmosphere. The existence of these disturbances, coupled with the unknowns associated with the targets of interest, combine to make pointing and tracking with a laser beam tracking system a formidable task. Aircraft platform disturbances are particularly troublesome because system modeling and system identification approaches do not accurately capture a sufficiently true representation of this dynamic plant. The objective of this solicitation is to have research conducted into developing adaptive control approaches to mitigate laser beam pointing and tracking errors generated by these disturbances while maintaining at least the minimum required bandwidth. In addition, it is desired that the application of advanced adaptive control techniques result in the extension of this bandwidth to more desirable values. All developed techniques should be robust to uncertainties in the system models as well as to sensor noise, and be shown to be stable in the sense of Lyaunov. Performance of techniques developed under this solicitation must be tested against current state-of-the-art algorithms to demonstrate their improved performance.

References:

Liu, Yu-Tai and Gibson, J. Steve. “Adaptive control in adaptive optics for directed-energy systems." Optical Engineering (2007): 046601-1 - 13.

Ioannou, Petros and Fidan, Baris. Advances in Design and Control: Adaptive Control Tutorial. SIAM, 2006

Narendra, Kumpati S. and Annaswamy, Anuradha M. Stable Adaptive Systems. New York: Dover Publications, 2005

### SF.10.01.B2132: Spectral Coherence Analysis Techniques for Improved Laser Beam Control of Jitter

#### (505) 846-2711

Many laser beam control systems are quite complicated and are constructed of many sub-systems. All these different distinctive subsystems can be very well individually characterized. However, the combination of all the different subsystems to form the larger complex beam control system and the coupling of the mechanical disturbances to this larger systems can be very difficult to quantify. This research topics explores the application of advanced Spectral Coherence, Multiple Coherence and Partial Coherence Analysis techniques to accurately identify disturbance sources, perform system and model identification to further mitigate the sources of the disturbance. Complicating the analysis further, the laser beam control system is usually on a mobile platform. The platform can either be a mobile ground platform, an airborne platform or a naval vessel. The addition of the platform dynamics and the unknowns of the complex laser beam control system, contributes to a direct effect of jittering the laser beam on target. Jitter smears the HEL beam on target, reducing its integrated intensity and therefore its target damage capability. This is generically referred as jitter error.

The objective of this solicitation is to have research conducted into developing quantitative, analytical tools using Spectral Coherence, Multiple Coherence and Partial Coherence Analysis approaches to extend resolution techniques in identifying uncertainties from unknown disturbances which in turn create laser jitter errors. In addition, since the application of these advanced analysis techniques will improve the resolution of the disturbances, it is desired that more accurate model identification of the plan would naturally occur. Therefore, knowing an accurate model of the disturbances and an accurate model of the plant would then give the researcher the ability to develop more precise, robust and optimal compensation designs.

References:

Petre Stoica, Randolph Moses, Spectral Analysis of Signals, Peason/Prentice Hall, 2005

Julius S. Bendat, Allan G. Piersol, Random Data, Analysis and Measurement Procedures, Second Edition, Wiley-Interscience1986.

T.T. Georgiou, “An intrinsic metric for power spectral density functions”, IEEE Signal Processing Letters, 14(8): 561-563, August 2007.

### SF.10.01.B3452: Experimental Investigation of Ultra-short Lasers, Nonlinear Matter Interactions, and Propagation

#### (505) 853-4957

Our research involves experimental studies of ultra-short pulse lasers (USPL) capable of producing extremely high peak electric fields; their nonlinear propagation and eventual interaction with different materials. This research is aided by theoretical predictions and numerical simulation of USPL generation, propagation, and eventual interaction with materials. Femtosecond pulses at Terawatt and Petawatt power levels are at the center of our work, including the use of single or multiple pulses to produce filaments. Candidates with demonstrated experience in the field of experimental short pulse laser physics (or applicable associated research) are desired from a variety of fields including, but not limited to: physics, electrical engineering, or optical sciences. Selected applicants should expect to work with USAF staff, collaborating university faculty, and summer students at the graduate and undergraduate level. The goal of this work is to develop and integrate experiments with newly developed theories and to improve the applicability of this resulting research across the optical spectrum.

References:

Rulliere C: Femtosecond Laser Pulses: Principles and Experiments in Advanced Texts in Physics 2nd Edition. Springer, 2004

Couairon A, Mysyrowicz A: Science Direct, Physics Reports 441: 2007

Keywords:

Nonlinear optics; Terawatt laser; Ultra-short pulse lasers; Laser-induced filamentation; Petawatt laser; Femtosecond interaction; Optical system design; Optical Kerr effect; High peak electric fields; Laser-plasma interactions, Laser-material interactions.

### SF.10.02.B0165: Compact, Portable Pulsed Power

#### (505) 385-7767

Research focuses on technology for compact, portable pulsed power and its applications. This includes capacitor based and pulse forming line circuits. The research deals with technologies suitable for driving high power microwave tubes, vacuum diodes, and particle accelerators. The research spans the range from component technologies, such as dielectrics, capacitors, gas switches, and solid state switches, to system level innovations that enable advancements in compact, portable pulsed power. In the field of dielectrics, advances that enable either an increase in energy storage density or reductions in the volume of dielectric standoff internally or at the vacuum interface are sought. Switching technologies that deliver current with minimal losses, highly precise timing, high reliability, and high shot life are sought; while gas switch technologies have traditionally been used because of the stringent requirements for high current (10's of kA), high hold-off voltage (10's of kV), and fast closure rate (resistive decay in 10's of ns), solid state switch technologies are beginning to become competitive while offering better reliability and control. Experimental facilities consist of two laboratory buildings with a variety of capacitor banks and pulse forming lines used for load development and pulsed power evaluation. Dedicated laboratory spaces for switch and energy storage component evaluation are equipped with the power supplies, diagnostic hardware, fast digitizers and safety systems necessary to conduct advanced research. There are extensive complementary theoretical/computational abilities and resources, including three-dimensional fully electromagnetic particle-in-cell codes, which have been developed, and are being further developed to guide and interpret experiments.

### SF.10.02.B2015: Sources for High Energy Density Physics Research

#### (505) 853-4507

Research focuses on the overall source design of experimental hardware to produce high energy density states of matter for exploring extreme environments and radiation for hardness testing of electronic systems. Source designs can incorporate magnetic flux compression with solid and plasma armatures; magnetized plasma formation and compression, solid liner implosion or propulsion, and coaxial plasma gun variants. Experimental facilities consist of two laboratory buildings with several capacitor banks ranging from tens of kilojoule; tens of kilovolt to 9 megajoules; tens of megamps; a variety of compact Marx banks; RF shielded enclosures with numerous fast transient digitizer and analog recorders for data acquisition; substantial vacuum and power supply hardware; pulsed current, voltage, and magnetic field diagnostics; rotating mirror and gated microchannel plate tube fast photography; and optical, RF, vacuum-ultraviolet, x-ray, gamma, and neutron spectroscopy equipment. There are extensive complementary theoretical/computational abilities and resources in the division, including one-, two-, and three-dimensional radiation magnetohydrodynamic and particle-in-cell codes, which have been developed, and are being further developed to guide and interpret experiments. We are developing parallel versions of these codes, parallel processing, and high-performance computing techniques.

### SF.10.02.B1122: Theory of High Peak Ultra-short Pulse Laser Propagation and Nonlinear Matter Interaction

#### (505) 853-4957

This work involves determining the mathematical and physical nature of high peak intensity laser pulse generation, propagation, and eventual laser-matter interaction. Femtosecond pulses at Terawatt and Petawatt power levels are at the center of our work, including single or multiple pulses at high repetition rates. Our research includes theoretical physics studies coupled with numerical simulation to understand how ultra-short laser pulses propagate and interact with matter. For example, one of our goals is to examine the deterministic and statistical nature of femtosecond laser-induced plasma filaments in air and the resultant propagation process. Proposed work under this topic should focus on applied mathematics and computational development (coupled systems of nonlinear partial differential equations of the nonlinear Schrodinger type); as well as the theoretical physics necessary to describe the process of laser-induced plasma formation and electromagnetic field coupling to plasma filaments. Candidates with demonstrated experience in this field (or applicable associated research) are desired from a variety of fields including, but not limited to: mathematics, applied mathematics, and theoretical physics. Selected applicants should expect to work with USAF staff, collaborating university faculty, and summer students at the graduate and undergraduate level. The goal of this work is to develop and integrate theory and computational model components, and to improve the applicability of this resulting research across the optical spectrum.

References:

W.L. Boyd, Nonlinear Optics, 3rd Edition. Boston: Elsevier Inc, 2008

A.C. Newell and J.V. Moloney, Nonlinear Optics, Westview Press, 2003.

Keywords:

Nonlinear optics; Terawatt laser; Ultra-short pulse lasers; Plasma channels; Laser-induced filamentation; Nonlinear propagation; Petawatt laser; Optical Kerr effect; High peak electric fields; Laser-plasma interactions; Laser-material interactions; Laser simulations.

### SF.10.02.B1189: Fiber Laser and Beam Combination Research

#### (505) 846-6339

AFRL has ongoing experimental and theoretical research aimed at achieving high brightness high-power fiber lasers. Such research requires detailed experience in laser physics, fiber optics, solid state physics, beam combination, thermal and thermo-optic effects, and nonlinear optical phenomena. Experimental as well as theoretical studies and simulations of physical phenomena and processes relevant to power scaling and innovative beam combining methods proposed for diverse fiber laser systems and aimed at achieving high beam brightness and ultra-high power levels (100 kW and higher) are of great interest. The following are among the potential research areas for fiber laser and beam combination:

Efforts involving methods of generating high-power near diffraction-limited beams in the near-IR or mid-IR regions through rare earth doped or Raman fiber lasers. Detailed investigations of these laser systems including any advantageous or deleterious linear or non-linear processes. Stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), four-wave mixing (FWM), and modal instabilities (MI) are some of the phenomena that are relevant to high-power fiber lasers. Also of interest are specialty fiber designs that can potentially lead to power scaling including photonic crystal and photonic bandgap fibers. Detailed investigations of novel coherent or spectral beam combination techniques scalable to 100 kW. Novel techniques that can enable robust operation of compact fiber-based high-power phased arrays. The research effort can be theoretical, experimental, or both in the areas discussed above. State of the art experimental and computational facilities are available for this research.

University faculty well-versed in all aspects of laser science, physical and non-linear optics, and optical engineering, are invited to apply.

### SF.10.02.B3915: High Power Microwave Source Research

#### (505) 853-3915

Vacuum electronic sources over a wide range of wavelengths at high power density represent a current area of research interest for the Air Force Research Laboratory. These sources span the range from 1GHz L-band sources at gigawatts of power to 90GHz W-band sources at megawatts of power to THz sources at hundreds of watts of power. Each of these technology areas shares the extreme difficulties of coping with large power densities that stress current materials technology as well as the physical understanding of basic physics phenomenology of the sources operation. As such, this research area requires a strong coupling between experimental work, theory, and modeling and simulation.

This research area consists of the following foci of interest: 1) Novel vacuum electronic sources, operating in the range from 1 GHz to the THz regime; 2) New technologies, such as nonlinear transmission lines, that provide wide ranges of frequency tunability and agility; 3) Supporting technologies to enable these devices. This area comprises technologies such as new cold cathode materials, new electron collectors, new vacuum window technologies, new vacuum pumping technologies, and new pulsed power materials and topologies; 4) Adoption of advanced materials modeling to investigate new materials for all aspects of these sources. Efforts to improve each of these areas, with strong coupling between theory, experiment, and modeling, comprise a vital aspect of these research goals.

### SF.10.02.B4707: High Performance Compact Pulsed Power Components

#### (505) 853-4707

Compact, reliable pulsed power for high power microwave (HPM) generation is of particular interest to the Air Force. These generators require either high peak power at relative low duty cycle and high field strengths, or high average power at high duty cycle and lower field strengths. Development of each specific HPM generator has its own unique challenges. However, all have in common problems associated with the exposure of various devices materials to extreme electromagnetic, thermal and mechanical environments. This topic focuses on studying and utilizing new materials - dielectrics, insulators, metals and interface coatings in the design of components of the compact pulsed power systems such as modulators, capacitors, switches and anodes for cold cathode sources. Fundamental studies on compact pulsed power generation and innovative material and engineering techniques are needed to reduce the size and mass of these pulsed power components. An effective research effort in any of these component systems will require a combination of theory, experiment and modeling.

An example of a research area that is within the scope of this topic is high energy density pulsed power capacitors. The energy density of pulsed power systems for high power microwave (HPM) systems remains limited by the storage capabilities of the dielectric sub-system, which may consist of either capacitors or solid dielectric lines. Gigawatt-class HPM systems generally operate from megavolts to hundreds of kilovolts with pulse durations no more than several hundred nanoseconds long. The state-of-the-art for commercially available pulsed power capacitors approaches 2 J/cc. However, in practice, repetition rate (as high as 100 pps), discharge rate <0.1 microseconds and lifetime requirements for HPM systems limit the energy density of these capacitors to less than 0.5 J/cc. However, advances in pulsed power switches, capacitors and cold cathode anode materials are necessary to develop compact, reliable electric power on directed energy systems as well as advanced air and space platforms. All these areas are within the scope of this topic.

### SF.10.02.B9076: Advanced Gas Lasers and High Performance Computing Simulation of Multi-Physics

#### (505) 846-9076

This research is comprised of the physical processes that underlie gas lasers: laser physics, optics, physical chemistry, spectroscopy, and fluid dynamics. Gas lasers use various mechanisms for generating a population inversion within the gas: chemical reactions, electric discharges, rapid gas dynamic expansion, and optically pumping. As a part of the generation of the population inversion, chemical kinetic processes may support or erode the inversion, having a significant impact upon laser performance in conjunction with spontaneous and stimulated emission of photons. Spectroscopy plays an important role here with broadening processes associated with the lineshape of the lasing transmission, measurement of intermediate species populations, determination of gas temperature, and visualization of the flow structure providing critical roles. With a population inversion in place, lasing action occurs with the optical physics interplay with the laser gain generated in the gas media dictating power extraction from the gas. Stable and unstable resonator configurations are used with novel resonator configurations being of interest. As all of these processes occur within a gas, fluid dynamics play a critical role with flow stability, unsteadiness, and transition in subsonic through supersonic flows from very low to high Reynolds numbers being significant. Research opportunities exist related to all of the above areas in both experimental and theoretical capacities. Within the theoretical discipline, modeling of these complex physical processes utilizing high performance computing on very large parallel architectures is a significant activity with research opportunities in the various associated disciplines being available.

### SF.10.03.B4320: Algorithm Development for Electromagnetic Plasma Simulation

#### (505) 853-8172

Electromagnetic and low density plasma simulations have been dominated by the finite difference time domain technique coupled with a particle-in-cell approach. This dominance has been fueled by the relative ease of implementation combined by the nominal second order accuracy the scheme provides. The robustness of the scheme, combined with highly efficient parallel programming has allowed researchers to solve challenging problems with high confidence. However, due to the increased resolution available through high performance computing, many limitations have been reached with the aforementioned scheme, such as accurate geometric representation, physically realistic representation of particle emission, correct simulation of subgrid forces, and efficient simulation of high density plasmas. Many of these issues are observable in real-world simulations as an increased error, dropping a nominally second order scheme to first order or below. This tendency is often seen in many of problems of interest to the Air Force Research Laboratory's Directed Energy Directorate (AFRL/RDH). For example, it is seen in simulations of high power microwave devices, and it represents a major issue in the design process.

The goal of this research is to advance the state-of-the-art in EM/EM-PIC/EM-Fluid/EM-PIC-Fluid hybrid/parallel computing for improved simulation capabilities of HPM sources. This work spans the realm from basic to applied research and should result in both publications and potential incorporation into our in-house 3D highly parallel EM-PIC code. The candidate will have the unique opportunity to develop algorithms from scratch, incorporate the algorithm in a multiphysics code, and validate against real-world problems currently being studied in the laboratory.

### SF.10.03.B4500: Analysis of Strong Turbulence Effects on Laser and Speckle Propagation

#### (808) 875-4500

NOTE: This opportunity will take place at the research facility in Maui.

Although strong atmospheric turbulence is often encountered in many space (low elevation angles) and horizontal paths, no large efforts were made to analyze the problem critically via analytical approaches. Simulations based on phase screen approaches have been done and some mitigation methods have been invented. Some work has been done in characterizing the moderately strong optical turbulence and its effects on the histograms of the intensity. But no efforts were made to arrive at analytical expressions for various optical system parameters in deep turbulence. This field was active in late1970s and early 1980s and since then, no publications have appeared except in the subtopic of the histograms of intensity and some related efforts such as coherence length. Hence, to develop a clear understanding of the problem and to optimize the methods of mitigating the strong turbulence effects in such important applications as space based imaging and the design of adaptive optics systems, a critical examination of various phenomena in strong turbulence in spatial, temporal and related spectral domains is needed. Here, we propose to examine the role of Kolmogorov spectral wave numbers in affecting the various important optical parameters such as Fried coherence length, isoplanatic angle, spectra of figure and tilt and several other optical parameters and use this information to develop analytical expressions. We expect that the resulting expressions to be multi-dimensional integrals and will use USAF super-computing resources available locally to calculate the results and complete the problem by comparing the data with simulations from the phase screen approach and experimental data if needed. This analysis work supports several on-going projects in space imaging, sodium guidestar beacons and related problems and deep turbulence mitigation.

### SF.10.03.B5386: Quantum Chemistry/Ab Initio Modeling of High Current Cathodes

#### (505) 853-3906

As part of an ongoing research effort, the Air Force Research Laboratory (AFRL) seeks to extend the state-of-the-art in this area for application of these techniques to the high electromagnetic field environments of Directed Energy devices. In this regard, AFRL would like to pursue ab initio modeling of cathodes, electron collectors, and high energy dielectric materials. Ab initio modeling techniques, or quantum chemistry, have shown a great deal of promise for not only reproducing known material behavior, but also for building predictive capabilities for condensed matter physics and surface physics. Work would initially focus on refining the understanding of existing cathodes, but would then extend to the prediction of new material properties based on computer models, with the realization that such new materials should lend themselves to synthesis as well as support the AFRL mission. Particular areas of interest consist of work function and emission threshold dependencies on surface coatings and absorbates. In the course of this work, computational researchers would be required to work closely with scientists working on existing experimental devices and platforms.

### SF.10.03.B5387: Effects on Radio Frequency (RF) Radiation on Electronics

#### (505) 846-9107

Our research focuses on modeling the interaction between continuous wave (CW) and pulsed radio frequency (RF) fields and analog and digital electronics. This includes large scale finite difference time domain (FDTD) modeling of the propagation of RF energy to an electronic device and the internal field structure that is established, as well as modeling the coupling of energy to cables and electronic components and circuit traces. It also includes predicting the effect of this coupled RF energy on the functioning of the electronic circuit. In addition, we are interested in modeling effects on large scale electronic systems comprising very large numbers of such circuits. This research involves performing electromagnetic modeling, as well as building new models describing the interaction with electronics and comparing the results from these models with experimental data to validate and improve the models.

### SF.10.03.B6642: State-of-the-Art, Massively Parallel Computational Electromagnetics

#### (505) 846-6642

Basic research in computational electromagnetics produces promising new techniques in terms of scaling and problems that can be solved. However, results for these techniques are often shown only for a few small test cases. Before the new methods can make an impact on production level simulations, more work is needed for validation and verification as well as to show that the techniques can be implemented fully in three dimensions and can scale to large numbers of processors on modern parallel architectures. Parallel implementation and scaling becomes an even larger concern with the anticipated move to multicore computer architectures with increasing numbers of cores on a single chip, but not necessarily an increase in bandwidth for transfer to off-chip memory. Areas of interest include, but are not necessarily limited to, fast matrix solution techniques (including robust preconditioners, both dense and sparse matrices as well as sparse-dense matrices from finite element-boundary integral techniques, and matrix compression techniques), finite-element time-domain analysis (including implicit time-domain techniques, efficient solution of mass matrices on massively parallel architectures, local terminating boundary conditions, higher order basis functions, complex material modeling, antenna feed network modeling, and the efficient, accurate addition of charged particles to the method), finite element tearing and interconnect (FETI) techniques (including use of FETI to accelerate interprocessor communication, continuous and non-continuous mesh analysis for multi-scale problems, and use of FETI for modeling finite periodic structures).

### SF.10.03.B9101: Simulation of Plasmas and High Power Microwave Devices

#### (505) 846-8571

The Air Force Research Laboratory is at the forefront of high-performance computing for the Department of Defense. The High Power Microwave Division has a solid record of developing plasma and electromagnetic simulation software. Researchers use these codes to investigate various concepts involving collisional and collisionless plasmas, in collaboration with investigators at other laboratories to help design and diagnose a variety of experiments. The HPM Division has access to some of the most advanced high-performance parallel computing platforms available, including machines with 1000s of CPU. Over the past few years, the division has developed portable, parallel, three-dimensional plasma physics simulation codes for complex geometries, using particle-in-cell (PIC), multi-fluid, and hybrid approaches.

Our principal goal is to improve the state-of-the-art of plasma physics simulations to enable virtual prototyping of high-power microwave devices. As advanced Air Force weapons concepts move from the laboratory to the field, the size of the packages must generally decrease. This effective decrease in the characteristic length scale increases the relative importance of diffusive processes compared to convection. We seek applicants with strong backgrounds in physics and the application of large-scale scientific computation for plasmas and charged-particle beams that interact with complex structures.

### SF.10.13.B1205: Modeling studies of complex nonlinear systems for defense applications

#### (505) 846-4639

Participants in the program are expected to perform analysis of complex nonlinear systems, the nature of which is subject to his or her choice.

Topics of special interest will be given priority, such as, for example: atmospheric propagation of laser arrays through deep turbulence with application to targeting and destroying enemy missiles; modeling of biological and physiological systems, including sensory and cognitive behaviors of the central neural system; pattern recognition; the spread and control of pandemics; the treatment of disease by medication, radiation or other therapies; ecological and environmental studies, including predictions of climate change and its effects; political, social and economic system modeling, etc.

New mathematical and/or computational methods are sought, e.g. based on neural-net techniques, but the features in the models of nonlinearity, feedback, scaling capacity and complexity, massive interconnectivity, or others relevant to the proposed subject, are desired. Phenomena of interest include bifurcations and instabilities, chaos, and self-organization, but mathematical models should be founded on empirical precedent.

### SF.10.17.B0001: Rayleigh beacon adaptive optics on a small telescope

#### (505) 846-6699

AFSPACE needs affordable, small, portable telescopes for space situational awareness applications, such as distinguishing closely spaced objects at low-Earth orbits up to geosynchronous-Earth orbit. This research topic would model, design, and build a Rayleigh beacon adaptive optics system for a 1-m telescope. Candidates would have a background in laser beacon adaptive optics and would have at least a secret clearance (or could receive one before starting). They must also be a U.S. citizen.

### SF.10.17.B0002: Development of a Symplectic Hamiltonian formulation for planetary tides within an n-body integration package (AMOS Site, Maui, HI)

#### (808) 891-7727

This research aims to expand AFRL simulation efforts of long-term n-body integrations, for trajectory and orbit determination applications. Modeling tidal interactions due to the Earth's tidal bulge, the effects of high-order tidal harmonics and resonances can complicate "n-body plus perturbation" methods. Lower fidelity planetary science applications provide a basis for theory expansion and implementation. The objective of this solicitation is to have research conducted into (1) deriving a symplectic Hamiltonian formulation for planetary tides, (2) expanding this into a n-body formulation that calculates multiple tidal influences from multiple bodies (e.g., calculating the combined tidal contributions of Earth and Moon), and (3) integrating this with an existing symplectic n-body code. The publicly available Symplectic Massive Body Algorithm (SyMBA) is recommended but any software package that integrates mutually gravitationally interacting bodies with multiple massless particles will be acceptable. All developed algorithms should be robust to long-term integration with minimal impact to the convergence speed of the original n-body integrator. The goal of this work is to develop and integrate sympletic tidal theory with computational n-body components, and to apply these results to AFRL trajectory computation and orbit determination applications. References for tidal Hamiltonians 1. Tittemore and Wisdom (1988), Icarus 74. doi:10.1016/0019-1035(88)90038-3 2. Lithwick and Wu (2012), ApJL 756. doi:10.1088/2041-8205/756/1/L11 3. Batygin et al (2009), ApJ, 704. doi:10.1088/0004-637X/704/1/L49 References for SyMBA / Swifter (publicly available symplectic n-body integrator) 1. Levison and Duncan (2000), AJ, 120. doi: 10.1086/301553 2. http://www.boulder.swri.edu/swifter/

### AFRL/Directed Energy

Chief Scientist, Directed Energy

Air Force Research Laboratory

3550 Aberdeen Ave SE, Bldg. 497

Kirtland AFB, NM 87117-5776

Telephone: (505) 846-0862

E-mail: Robert.peterkin@us.af.mil

Dr. Diana Loree

Assistant to the Chief Scientist

AFRL/RD

3550 Aberdeen Ave SE, Bldg. 497

Kirtland AFB, NM 87117-5776

Telephone: (505) 846-5261

E-mail: Diana.Loree@us.af.mil