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Affordable Development and Qualification Strategy for Nuclear Thermal Propulsion

A number of recent assessments have confirmed the results of several earlier studies that Nuclear Thermal Propulsion (NTP) is a leading technology for human exploration of Mars. It is generally acknowledged that NTP provides the best prospects for the transportation of humans to Mars in the 2030's. Its high Isp coupled with the high thrusts achievable, allow reasonable trip times, thereby alleviating concerns about space radiation and "claustrophobia" effects. NASA has embarked on the latest phase of the development of NTP systems, and is adopting an affordable approach in response to the pressure of the times. The affordable strategy is built on maximizing the use of the large NTP technology base developed in the 1950's and 60's. The fact that the NTP engines were actually demonstrated to work as planned, is a great risk reduction feature in its development. The strategy utilizes non-nuclear testing to the fullest extent possible, and uses focused nuclear tests for the essential qualification and certification tests. The perceived cost risk of conducting the ground tests is being addressed by considering novel testing approaches. This includes the use of boreholes to contain radioactive effluents, and use of fuel with very high retention capability for fission products. The use of prototype flight tests is being considered as final steps in the development prior to undertaking human flight missions. In addition to the technical issues, plans are being prepared to address the institutional and political issues that need to be considered in this major venture. While the development and deployment of NTP system is not expected to be cheap, the value of the system will be very high, and amortized over the many missions that it enables and enhances, the imputed costs will be very reasonable. Using the approach outlined, NASA and its partners, currently the DOE, and subsequently industry, have a good chance of creating a sustained development program leading to human missions to Mars within the next few decades.

Gerrish, Harold P., Jr.↗

Evaluation of Human and Anthropomorphic Test Device Finite Element Models under Spaceflight Loading Conditions

In an effort to develop occupant protection standards for future multipurpose crew vehicles, the National Aeronautics and Space Administration (NASA) has looked to evaluate the test device for human occupant restraint with the modification kit (THOR‐K) anthropomorphic test device (ATD) in relevant impact test scenarios. With the allowance and support of the National Highway Traffic Safety Administration, NASA has performed a series of sled impact tests on the latest developed THOR‐K ATD. These tests were performed to match test conditions from human volunteer data previously collected by the U.S. Air Force. The objective of this study was to evaluate the THOR‐K finite element (FE) model and the Total HUman Model for Safety (THUMS) FE model with respect to the tests performed. These models were evaluated in spinal and frontal impacts against kinematic and kinetic data recorded in ATD and human testing. Methods: The FE simulations were developed based on recorded pretest ATD/human position and sled acceleration pulses measured during testing. Predicted responses by both human and ATD models were compared to test data recorded under the same impact conditions. The kinematic responses of the models were quantitatively evaluated using the ISO‐metric curve rating system. In addition, ATD injury criteria and human stress/strain data were calculated to evaluate the risk of injury predicted by the ATD and human model, respectively. Results: Preliminary results show well‐correlated response between both FE models and their physical counterparts. In addition, predicted ATD injury criteria and human model stress/strain values are shown to positively relate. Kinematic comparison between human and ATD models indicates promising biofidelic response, although a slightly stiffer response is observed within the ATD. Conclusion: As a compliment to ATD testing, numerical simulation provides efficient means to assess vehicle safety throughout the design process and further improve the design of physical ATDs. The assessment of the THOR‐K and THUMS FE models in a spaceflight testing condition is an essential first step to implementing these models in the computational evaluation of spacecraft occupant safety. Promising results suggest future use of these models in the aerospace field.

Putnam, Jacob P.↗

Analysis of Water Recovery Rate from the Heat Melt Compactor

Human space missions generate trash with a substantial amount of plastic (20% or greater by mass). The trash also contains water trapped in food residue and paper products and other trash items. The Heat Melt Compactor (HMC) under development by NASA Ames Research Center (ARC) compresses the waste, dries it to recover water and melts the plastic to encapsulate the compressed trash. The resulting waste disk or puck represents an approximately ten-fold reduction in the volume of the initial trash loaded into the HMC. In the current design concept being pursued, the trash is compressed by a piston after it is loaded into the trash chamber. The piston face, the side walls of the waste processing chamber and the end surface in contact with the waste can be heated to evaporate the water and to melt the plastic. Water is recovered by the HMC in two phases. The first is a pre-process compaction without heat or with the heaters initially turned on but before the waste heats up. Tests have shown that during this step some liquid water may be expelled from the chamber. This water is believed to be free water (i.e., not bound with or absorbed in other waste constituents) that is present in the trash. This phase is herein termed Phase A of the water recovery process. During HMC operations, it is desired that liquid water recovery in Phase A be eliminated or minimized so that water-vapor processing equipment (e.g., condensers) downstream of the HMC are not fouled by liquid water and its constituents (i.e., suspended or dissolved matter) exiting the HMC. The primary water recovery process takes place next where the trash is further compacted while the heated surfaces reach their set temperatures for this step. This step will be referred to herein as Phase B of the water recovery process. During this step the waste chamber may be exposed to different selected pressures such as ambient, low pressure (e.g., 0.2 atm), or vacuum. The objective for this step is to remove both bound and any remaining free water in the trash by evaporation. The temperature settings of the heated surfaces are usually kept above the saturation temperature of water but below the melting temperature of the plastic in the waste during this step to avoid any encapsulation of wet trash which would reduce the amount of recovered water by blocking the vapor escape. In this paper, we analyze the water recovery rate during Phase B where the trash is heated and water leaves the waste chamber as vapor, for operation of the HMC in reduced gravity. We pursue a quasi-one-dimensional model with and without sidewall heating to determine the water recovery rate and the trash drying time. The influences of the trash thermal properties, the amount of water loading, and the distribution of the water in the trash on the water recovery rates are determined.

Heat Melt Compactor↗

Viscoplastic Characterization of Ti-6-4: Experiments

As part of a continued effort to improve the understanding of material time-dependent response, a series of mechanical tests have been conducted on the titanium alloy, Ti-6Al-4V. Tensile, creep, and stress relaxation tests were performed over a wide range of temperatures and strain rates to engage various amounts of time-dependent behavior. Additional tests were conducted that involved loading steps, overloads, dwell periods, and block loading segments to characterize the interaction between plasticity and time-dependent behavior. These data will be used to characterize a recently developed, viscoelastoplastic constitutive model with a goal toward better estimates of aerospace component behavior, resulting in improved safety.

mechanical properties↗

NASA Advances Technologies for Additive Manufacturing of GRCop-84 Copper Alloy

The Low Cost Upper Stage Propulsion project has successfully developed and matured Selective Laser Melting (SLM) Fabrication of the NASA developed GRCop-84 copper alloy. Several parts have been printed in house and at a commercial vendor, and these parts have been successfully machined and have undergone further fabrication steps to allow hot-fire testing. Hot-fire testing has demonstrated parts manufactured with this technique can survive and perform well in the relevant environments for liquid rocket propulsion systems.

Gradl, Paul↗

Advances in Rodent Research Missions on the International Space Station

A Research platform for rodent experiment on the ISS is an essential tool for advancing biomedical research in space. The Rodent Research allows for experiments of much longer duration that experiments on the Shuttle. NASA’s Rodent Research (RR)-1 mission was successfully completed, including post-flight analysis and achieved a number of objectives including validation of flight hardware, on-orbit operations, and science capabilities that were developed at the NASA Ames Research Center. Briefly, twenty C57BL/6J adult female mice were launched on the SpX4 Dragon vehicle, which thrived for up to 37 days in microgravity. Daily health checks of the mice were performed during the mission via downlinked video; all animals were healthy and displayed normal behavior without any significant signs of stress. Behavioral analysis demonstrated that Flight and Ground Control mice exhibited the same range of behaviors, including eating, drinking, exploratory behavior, self- and allo-grooming, and social interactions indicative of healthy animals. The animals were euthanized and select tissues were collected from some of the mice on orbit to assess the long-term sample storage capabilities of the ISS. The data obtained from the flight mice were comparable to those from the 3 groups of control mice (baseline, vivarium and ground controls), suggesting that the ISS has adequate capability to support long-duration rodent experimentations. We recovered over 35 tissues from 40 RR1 frozen carcasses, yielded over 3200 aliquots of tissues, and distributed to the scientific community, including NASA’s GeneLab and scientists in the U.S. through Biospecimen Sharing Program via Ames Life Science Data Archive. Tissues were also distributed to Russian research colleagues at the Institute for Biomedical Problems. The expression levels of select genes including albumin, catalase, GAPDH, HMGCoA Reductase, and IGF1 were determined using RNA isolated from the livers by qPCR and no significant differences by one factor ANOVA were found between flight and ground control groups. In addition, some of the liver samples were subject to transcriptomics, epigenomics and proteomics. The data are now available to the scientific community through GeneLab’s open science data website. Since the RR1 mission, another long duration mission (Rodent Research-2) was completed on the ISS in 2015 in which 20 female C57 BL/6J mice were successfully maintained on the ISS for varying time points, with the last group of 5 animals being on-orbit for 54 days. This second Rodent Research flight expanded the program’s capabilities with the introduction of new technologies including blood collection and separation and bone densitometry scanning. Furthermore, we have continued to expand the ISS’s capabilities by running a series of ground-based verification testing using male mice. Our next step is to fly male mice for Rodent Research-4 on SpaceX-10 to study the effects of microgravity on bone healing and regeneration. It will be the first long-duration mission using male mice using Rodent Hardware. In addition, the number of mice will increase from 20 mice (on RR-1 and RR-2) to 40 for RR-4. When samples return to Earth, a number of tissues will be dissected from the frozen carcasses and select tissue samples will become available to the scientific community via BSP. Altogether, we have continued to expand our capabilities for performing long-duration missions on the ISS as emphasized in the National Research Council’s Decadal Survey released in 2011 and to maximize science return from each mission.

Choi, S.↗

The 13th Technology of Deep Space One

On October 24th, 1998, the Deep Space One (DS-1) spacecraft launched aboard a Delta II rocket as the first step towards the bold task of testing and validating 12 new technologies for future missions. This launch also represented yet another thrilling event; namely, the successful test and validation of a 13th heretofore undisclosed technology: model-base-code-generation of the spacecraft's system-level fault-protection (FP) software from behavioral state diagrams and structural models.

model-based-code-generation↗

Design, Instrumentation, and Data Analysis for the SLS Core Stage Green Run Test Series

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. The actuators are powered by a Shuttle-derived hydraulic Core Auxiliary Power Unit (CAPU), and integrated with an all-new Core Stage thrust structure. The actuators are interfaced to the SLS Vehicle Management (VM) software via an all-new TVC Actuator Control (TAC) avionics subsystem. Despite the significant test and flight experience of the Shuttle hardware, the SLS Green Run ambient and hot fire test activities revealed a number of new findings associated with the dynamic response of the TVC integrated system. Test responses suggested that the TVC system did not meet its performance specifications and its step and frequency responses exhibited unexpected departures from prior lab tests and modeled behavior. This paper is the fifth installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. In this paper, the design of the TVC analyses conducted during the Core Stage Green Run test series are discussed in detail. Throughout the course of the test activities, the SLS flight control team worked diligently with the Core Stage contractor to revise test command profiles and ensure sufficient instrumentation was available to collect data. Post-test analysis combined the Green Run modal, ambient, and hot fire test data, MSFC 2- axis Core Stage TVC Inertial Load Simulator (ILS) data, Hardware-In-the-Loop (HWIL) Systems Integration Lab (SIL) results, and actuator Acceptance Testing Procedure (ATP) responses. These data were used to characterize the response, validate critical math models of the TVC subsystem, and isolate the probable cause of the unexpected responses. Through comprehensive analysis of the available test data sources, the integrated team identified the dominant contributors to the observed response and developed test-correlated rationale for vehicle flight control system performance, ultimately leading to a confident posture for the Artemis I mission.

John H. Wall↗

Plans for an Integrated Front-End Test Stand at the Spallation Neutron Source

A spare Radio-Frequency Quadrupole (RFQ) is presently being fabricated by industry with delivery to Oak Ridge National Laboratory planned in late 2012. The establishment of a test stand at the Spallation Neutron Source site is underway so that complete acceptance testing can be performed during the winter of 2012-2013. This activity is the first step in the establishment of an integrated front-end test stand that will include an ion source, low-energy beam transport (LEBT), RFQ, medium-energy beam transport, diagnostics, and a beam dump. The test stand will be capable of delivering an H- ion beam of up to 50 mA with a pulse length of 1 ms and a repetition rate of 60 Hz or a proton beam of up to 50 mA, 100us, 1Hz. The test stand will enable the following activities: complete ion source characterization; development of a magnetic LEBT chopper; development of a two-source layout; development of beam diagnostics; and study of beam dynamics of high intensity beam.

Champion, Mark S↗

EMPIRICAL VALIDATION OF MULTI-ZONE BUILDING AND HVAC SYSTEM MODELS UNDER UNCERTAINTY

This study implemented a framework of empirical validation of building energy models under uncertainty to a set of controlled experiments that aim to validate multi-zone building and HVAC system models. Energy models were created through iterative acquisitions of information and data and uses measurement data from various types of sensors as both inputs and as observations to validate predictions. Experimental and modeling uncertainties were quantified and propagated accordingly, and probabilistic accuracy metrics were used to evaluate the agreement between model predictions and observations under uncertainty. Sensitivity analysis was performed to identify the most influential uncertainties that will be prioritized to be addressed in the next steps. Current results of two cooling tests show an overall good agreement between predictions and observations on a set of HVAC system outputs despite considerable and influential uncertainty in DX cooling coil COP. Agreements on zone-level responses vary notably among individual rooms, likely because of significant uncertainties in room radiation heat gain and system supply air.

Li, Qi↗

PWR core and spent fuel pool analysis using scale and nestle

The SCALE nuclear analysis code system [SCALE, 2011], developed and maintained at Oak Ridge National Laboratory (ORNL) is widely recognized as high quality software for analyzing nuclear systems. The SCALE code system is composed of several validated computer codes and methods with standard control sequences, such as the TRITON/NEWT lattice physics sequence, which supplies dependable and accurate analyses for industry, regulators, and academia. Although TRITON generates energy-collapsed and space-homogenized few group cross sections, SCALE does not include a full-core nodal neutron diffusion simulation module within. However, in the past few years, the open-source NESTLE core simulator [NESTLE, 2003], originally developed at North Carolina State Univ. (NCSU), has been updated and upgraded via collaboration between ORNL and the Univ. of Tennessee (UT), so it now has a growingly seamless coupling to the TRITON/NEWT lattice physics [Galloway, 2010]. This study presents the methodology used to couple lattice physics data between TRITON and NESTLE in order to perform a three-dimensional full-core analysis employing a 'real-life' Duke Energy PWR as the test bed. The focus for this step was to compare the key parameters of core reactivity and radial power distribution versus plant data. Following the core analysis, following a three cycle burn, a spent fuel pool analysis was done using information generated from NESTLE for the discharged bundles and was compared to Duke Energy spent fuel pool models. The KENO control module from SCALE was employed for this latter stage of the project. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOME Reactor Testing User Guide

DOME User Guide History DOME User Guide Introduction User Engagement Lifecycle for DOME Phase 1 – Front End Engineering and Experiment Design (FEEED) Phase 2 – Detailed Design & Long Lead Procurement Phase 3 – Fabrication, Training, & Delivery Phase 4 – Installation & Testing Phase 5 – Removal & Disposal Next steps

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A Perspective on Development Flight Instrumentation and Flight Test Analysis Plans for Ares I-X

NASA. s Constellation Program will take a significant step toward completion of the Ares I crew launch vehicle with the flight test of Ares I-X and completion of the Ares I-X post-flight evaluation. The Ares I-X flight test vehicle is an ascent development flight test that will acquire flight data early enough to impact the design and development of the Ares I. As the primary customer for flight data from the Ares I-X mission, Ares I has been the major driver in the definition of the Development Flight Instrumentation (DFI). This paper focuses on the DFI development process and the plans for post-flight evaluation of the resulting data to impact the Ares I design. Efforts for determining the DFI for Ares I-X began in the fall of 2005, and significant effort to refine and implement the Ares I-X DFI has been expended since that time. This paper will present a perspective in the development and implementation of the DFI. Emphasis will be placed on the process by which the list was established and changes were made to that list due to imposed constraints. The paper will also discuss the plans for the analysis of the DFI data following the flight and a summary of flight evaluation tasks to be performed in support of tools and models validation for design and development.

Huebner, Lawrence D.↗

Microreactor Agile Nonnuclear Experimental Testbed Test Plan

Microreactors are an attractive technology option for kick-starting nuclear innovation if they can be operated at high temperature, yielding high power conversion thermal efficiencies comparable or better than in commercial light water reactors. Microreactors are currently the smallest variation of Small Modular Reactors (SMRs). SMRs are “newer generation reactors designed to generate electric power up to 300 MWe and whose components and systems can be shop-fabricated and then transported as modules to the sites for installation as demand arises.” (IAEA, 2016). Vendors are developing microreactor designs to provide an affordable, potentially mobile source of electricity - see Fig. 1 for an example of a microreactor on a semi-truck. Various microreactor designs are possible including heat pipe- and gascooled options, which are the focus of the nonnuclear testing described in this document. In heat pipe microreactors, high-temperature heat pipes using liquid sodium or potassium working fluid transport fission heat from the core to a heat removal section which in turn transfers heat to the power conversion system working fluid. In a gas-cooled design, He or other gas will flow through a solid monolith of material and transfer heat as the temperature of the gas increases through a heat exchanger to a power conversion unit. The logistics of all these processes will be examined and tested through a series of articles at the nonnuclear test bed at Idaho National Laboratory (INL), the Microreactor Agile Nonnuclear Experiment Testbed (MAGNET) facility. Microreactors designed to produce power of 0.1-20 MWt offer the potential for more affordable nuclear energy for a range of applications. In a heat pipe microreactor, heat pipes, fuel rods, and/or moderator are intermixed in the reactor core assembly. Heat pipes extend from the core region into the heat removal section where the power conversion unit working fluid flows through holes or channels, transferring heat from the heat pipes to the working fluid. In a gas-cooled microreactor, gas flows through the solid monolith region and up into the heat exchanger region, transferring heat to the working fluid. For initial testing, the heat removal working fluid can be a low pressure gas for testing that addresses thermal stresses. In the final application, heat addition to the power conversion working fluid typically occurs at high pressure, supporting operation of an air-Brayton, supercritical CO 2 (SCO2), or He-recuperated Brayton cycle. Various stages of the steps above will be demonstrated through the tests described in this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Spent Crystalline Silicotitanate Storage Study

Washington River Protection Solutions is working to support initial production of immobilized low-activity waste (LAW) by feeding Hanford tank supernate from tank farms to the Hanford Waste Treatment and Immobilization Plant (WTP) LAW Facility. This goal incorporates the design of a Tank-Side Cesium Removal (TSCR) system, which filters tank waste supernate to remove suspended solids and then removes Cs by processing it through crystalline silicotitanate (CST) ion exchange media manufactured by Honeywell UOP, LLC. The 137 Cs-depleted product is intended to be sent to the WTP for vitrification. The Cs-loaded CST columns will be stored indefinitely, with a goal of eventual CST removal and treatment. Thus, the spent CST needs to be recoverable. The testing described herein looks to potential upset process conditions where CST storage may be required before various rinse steps are completed. This study evaluated upset conditions at three sequential processing steps envisioned for TSCR (feed, 0.1 M NaOH rinse, water rinse), and in-column drying with compressed air (normal end step) to assess impacts on the nature of the CST bed. Testing was conducted at the small scale (12-mL bed volume); simulated AP-105 tank waste was used as the feed. Following process disruption, the CST bed was dried in place at 70 °C. Post-dried CST bed physical properties (angle of repose, penetration depth, particle morphological changes) were measured to evaluate how CST moved and flowed. The testing is intended to provide a preliminary assessment of issues that may arise from desiccation of CST with the indicated salt solutions in place. Since these were small-scale tests, the processing conditions will not match full scale conditions exactly; however, the tests do provide insight into the impact of stopping processing at an earlier step than normal. Except for the feed that was dried in-place, all other process stop-conditions showed the CST bed flowed well after drying. At this small scale, CST beds would not present an issue for retrievability. The feed that was dried in place had solidified into a rock-hard monolith with no movement possible. Samples had to be chipped from the surface.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Fourier plane colorimetric sensing using broadband imaging of surface plasmons and application to biosensing

We demonstrate an optical technique for refractive index and thickness sensing of sub-wavelength-thick dielectric analytes. The technique utilizes the broadband, multimode, directional leakage radiation arising from the excitation of hybrid mode surface plasmons (SP) on low aspect ratio periodic plasmonic substrates with period ≈λ. The approach requires relaxed fabrication tolerances compared to extra ordinary transmission-based sensing techniques, wherein minor shifts in the fabricated dimensions result in a very large change from the designed resonant wavelength. We show that refractive index perturbations due to about 10-nm-thick dielectric can be captured optically by the usage of carefully designed plasmonic substrates, a halogen lamp source, free-space optical components, polarizers, and a low-end, consumer-grade charge coupled device camera. The plasmonic substrates were designed for converting the signature of hybrid mode SP excitation into a transmission peak by utilizing a thin homogeneous metal layer sandwiched between the periodic plasmonic structures and the substrate. The resonance is highly sensitive to the refractive index and thickness of the analyte superstrate. The excitation of hybrid mode SP results in a polarization rotation of 90° of the leaked radiation at resonant wavelength. In order to eliminate the problem of image registration (i.e., placing the same feature in the same pixel of the image, for comparison before and after a change in refractive index) for sensing, we perform the color analysis in the Fourier plane. The change in color of the bright emitted spot with highest momentum, corresponding to the leakage of fundamental SP mode, was used to measure the changes in refractive index, whereas the number and color of spots of lower momenta, corresponding to higher-order Fabry Perot modes, was used to measure the variation in thickness. We further show that the Fourier plane analysis can also be used to sense the index of thicker dielectrics, where real plane image analysis may fail to sense index perturbations, simply due to superposition of different modes in the real plane images of such substrates. Control experiments and analysis revealed a refractive index resolution of 10{sup –5} RIU. The results were correlated with simulations to establish the physical origin of the change in the fundamental mode and higher-order modes due to the refractive index and thickness of analyte. As a demonstration of an application and to test the limits of sensing, the substrates were used to image the surface functionalization using 2-nm-thick 11-mercaptoundecanoic acid and immobilization of 7-nm-thick mouse anti-human IgG antibody. In biological systems, where a priori knowledge about a process step is available, where accurate chemical composition testing is not necessary or possible, the presented method could be used to study the surface changes using a label-free sensing mechanism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Uranium Removal from Seawater by Means of Polyamide 6 Fibers Directly Grafted with Diallyl Oxalate through a Single-Step, Solvent-Free Irradiation Process

In order to test the effectiveness of oxalate-based polymeric adsorbents in the recovery of uranium from seawater, diallyl oxalate (DAOx) was grafted onto nylon 6 fabrics by exposing the fabric, immersed in pure liquid DAOx or in a surfactant-stabilized dispersion of DAOx in water, to electron beam or gamma radiation. Following drying and weighing to determine the degree of grafting (DoG), the presence of oxalate in the fabrics was verified using XPS. Zeta potential measurements showed the fabric surfaces to be negatively charged. The fabrics were tested by rotating them for 7 days in a rotary agitator with actual seawater spiked with 0.2 or 1.0 mg∙L -1 uranium. The fraction of uranium in the solution which was removed due to uptake on the fabrics was found to rise with increasing DoG at both uranium concentrations. EDS measurements were used to map the distribution of adsorbed uranium on the polymeric fibers.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Belyaev, Mikhail A. (ORCID:0000000224908887)↗