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DOE OSTI2017

The ICF National Diagnostic Plan (NDP) 9/19/17

A major goal of the Stockpile Stewardship Program (SSP) is to deliver validated numerical models, benchmarked against experiments that address relevant and important issues and provide data that stress the codes and our understanding. DOENNSA has made significant investments in major facilities and high-performance computing to successfully execute the SSP. The more information obtained about the physical state of the plasmas produced, the more stringent the test of theories, models, and codes can be, leading to increased confidence in our predictive capability. To fully exploit the world-leading capabilities of the ICF program, a multi-year program to develop and deploy advanced diagnostics has been developed by the expert scientific community. To formalize these activities NNSA’s Acting Director for the Inertial Confinement Fusion Program directed the formation and duties of the National Diagnostics Working Group (NDWG) in a Memorandum 11/3/16 (Appendix A). The NDWG identified eight transformational diagnostics, shown in Table 1, that will provide unprecedented information from experiments in support of the SSP at NIF, Z and OMEGA. Table 1 shows how the missions of the SSP experiments including materials, complex hydrodynamics, radiation flow and effects and thermo-nuclear burn and boost will produce new observables, which will be measured using a variety of largely new diagnostic technologies used in the eight transformational diagnostics. The data provided by these diagnostics will validate and improve the physics contained within the SSP’s simulations and both uncover and quantify important phenomena that lie beyond our present understanding.

42 ENGINEERING↗

NASA NTRS1998

An Adaptable Power System with Software Control Algorithm

A low cost, flexible and modular spacecraft power system design was developed in response to a call for an architecture that could accommodate multiple missions in the small to medium load range. Three upcoming satellites will use this design, with one launch date in 1999 and two in the year 2000. The design consists of modular hardware that can be scaled up or down, without additional cost, to suit missions in the 200 to 600 Watt orbital average load range. The design will be applied to satellite orbits that are circular, polar elliptical and a libration point orbit. Mission unique adaptations are accomplished in software and firmware. In designing this advanced, adaptable power system, the major goals were reduction in weight volume and cost. This power system design represents reductions in weight of 78 percent, volume of 86 percent and cost of 65 percent from previous comparable systems. The efforts to miniaturize the electronics without sacrificing performance has created streamlined power electronics with control functions residing in the system microprocessor. The power system design can handle any battery size up to 50 Amp-hour and any battery technology. The three current implementations will use both nickel cadmium and nickel hydrogen batteries ranging in size from 21 to 50 Amp-hours. Multiple batteries can be used by adding another battery module. Any solar cell technology can be used and various array layouts can be incorporated with no change in Power System Electronics (PSE) hardware. Other features of the design are the standardized interfaces between cards and subsystems and immunity to radiation effects up to 30 krad Total Ionizing Dose (TID) and 35 Mev/cm(exp 2)-kg for Single Event Effects (SEE). The control algorithm for the power system resides in a radiation-hardened microprocessor. A table driven software design allows for flexibility in mission specific requirements. By storing critical power system constants in memory, modifying the system code for other programs is simple. These constants can be altered also by ground command, or in response to an anomolous event. All critical power system functions have backup hardware functions to prevent a software or computer glitch from propagating. A number of battery charge control schemes can be implemented by selecting the proper control terms in the code. The architecture allows the design engineer to tune the system response to various system components and anticipated load profiles without costly alterations. A design trade was made with the size, weight and power dissipation of the electronics versus the performance of the power bus to load variations. Linear, fine control is maintained with a streamlined electronics design. This paper describes the hardware design as well as the software control algorithm. The challenges of closing the system control loop digitally is discussed. Control loop margin and power system performance is presented. Lab measurements are shown and compared to the system response of a hardware model running actual flight software.

Castell, Karen↗

DOE OSTI2023

Bison Verification and Validation Activities for TRISO

Numerical modeling and simulation (M&S) tools play a key role in the research, development, and overall safety assessments of next-generation nuclear energy systems. One such tool, Bison, is a nuclear fuel performance code that is applicable to many fuel forms (e.g., light-water reactor fuel, oxide and metallic fuel for fast reactors, tri-structural isotropic (TRISO) fuel, and plate fuel), and it uses the finite element method to model the thermo- mechanical response of nuclear fuels. One fuel form widely utilized in Generation-IV high-temperature gas-cooled and fluoride- salt-cooled nuclear reactor concepts is TRISO fuel. Recently, Bison’s capabilities were significantly expanded to enable it to model the performance of TRISO particles and compacts. It is important that Bison’s computational results be reliable and predictive, since this code is used to inform high-consequence decisions. The various processes developed to address this issue generally entail two fundamental steps: verification and validation (V&V). Verification ensures that the code functions correctly and is reliable. Code/solution verification, code benchmark, and software quality assurance exercises are examples of verification activities. On the other hand, validation is the process of assessing a code’s capability to accurately model physical problems. Comparisons between code results and experiments quantify the validation level. Application of V&V procedures is crucial to the development of computational tools that are free of coding mistakes and can accurately represent reality. The current study presents an overview of Bison V&V activities relevant to the TRISO fuel concept, which include code/solution verification exercises, CRP-6 Benchmark—a Coordinated Research Program through the International Atomic Energy Agency (IAEA)—exercises, and validation exercises with the Advanced Gas Reactor (AGR)- 1/2/3/4 experiment series.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Towards reverse mode automatic differentiation of Kokkos-based codes

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and the solving of nonlinear problems. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years, has been integrated into programming environments such as Jax, PyTorch, and TensorFlow to support derivative computations needed for training of machine learning models, facilitating wide-spread use of these technologies. The C++ language has become the de facto standard for scientific computing due to numerous factors, yet language complexity has made the wide-spread adoption of AD technologies for C++ difficult, hampering the incorporation of powerful differentiable programming approaches into C++ scientific simulations. This is exacerbated by the increasing emergence of architectures, such as GPUs, with limited memory capabilities and requiring massive thread-level concurrency. C++ AD tools must effectively use these environments to bring novel scientific simulations to next-generation DOE experimental and observational facilities. In this project, we investigated source transformation-based automatic differentiation using LLVM compiler infrastructure to automatically generate portable and efficient gradient computations of Kokkos-based code. We have demonstrated that our proposed strategy is feasible by investigating the usage of a prototype LLVM-based source transformation tool to generate gradients of simple functions made of sequences of simple Kokkos parallel regions. Speedups of up to 500x compared to Sacado were observed on NVIDIA V100 GPU.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Rich-Text based PSA Model Transformation and Verification in RiskA

Nuclear Energy is one of the most possible alternative to fossil energy in large-scale. Nuclear safety is the lifeline of nuclear energy development, and has been an important part of national security, especially after the accident of Fukushima. On the basis of computer codes, reliability engineering and Probabilistic Risk Assessment (PSA) is effective methods to improve the safety of nuclear power plants. After many years of development, the methodologies, applications and relevant soft programs have been quite sufficient in the area of nuclear safety. However, it is still difficult for the current PSA technologies and software to meet the needs of dealing with the problems of quantitatively public risk assessment in the digital society. Especially, there are so many software that adopted different modeling and analyzing methods, which brings difficulties to the comparison, evaluation or verification for different software and models. By using its own academic advantages, the advanced nuclear energy research team, i.e., FDS Team has invested a few hundreds person-years of independent research and development of a reliability and probabilistic safety assessment software system RiskA. The system consists of three main functions: device reliability optimization management, probabilistic safety assessment and instantaneous risk monitoring, and the comprehensive public risk assessment in digital society. RiskA establishes an integrated risk evaluation system for the device reliability, nuclear power plant (NPP) risk monitoring and public risk assessment. Currently, RiskA has successfully been applied in more than 600 organizations and institutes from a variety of fields in 39 countries, involving nuclear, aerospace, defense and so on. For example, RiskA has been used in the safety analysis of International Thermonuclear Experimental Reactor (ITER), FDS series fusion reactor, and the Strategic Priority Research Program of Chinese Academy of Sciences 'the Future Advanced Nuclear Fission Energy - Accelerator Driven Sub-critical (ADS) transmutation system'. Also, RiskA has been used in public risk communication and risk assessment. Among them, Third Qinshan nuclear power plant Risk Monitor (TQRM), which is the China's first domestic nuclear safety analysis software used in the actual online operation, has been highly apprised by renowned experts in the field. Meanwhile, it has been identified as the first domestic nuclear power plant risk monitoring system with completely independent intellectual property rights, and has reached the international advanced level. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Toward a high-fidelity tritium transport modeling for retention and permeation experiments

We report Tritium Migration Analysis Program version 8 (TMAP8), the latest version of TMAP, was developed within the framework of the Multiphysics Object-Oriented Simulation Environment (MOOSE). Created at Idaho National Laboratory (INL), MOOSE is an open-source, dimension-agnostic, fully coupled, and fully implicit multiphysics platform featuring massively parallel computation capabilities. Using TMAP8, tritium transport in a divertor monoblock was analyzed to elucidate the effects of pulsed operation (up to fifty 1,600 s plasma discharge and cool-down cycles) on the tritium in-vessel inventory source term and ex-vessel release term (i.e., tritium retention and permeation) for safety analysis. With its built-in Message Passing Interface capability, TMAP8 can, in under 2 h, simulate tritium transport in three different layered materials (i.e., tungsten, copper, and copper-chromium-zirconium alloy) in 2D geometry, using a single device/computer with 10 cores. The MOOSE-based TMAP8 code can leverage other MOOSE tools developed under the Nuclear Energy Advanced Modeling and Simulation program to perform tritium and thermal transport in complex geometries and multiphysics environments. And via its massively parallel computation, MOOSE will enable the fusion pilot plant designers to conduct high-fidelity multiphysics modeling for the design of the divertor and blanket systems as well as for the safety analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Highlights of X-Stack ExM Deliverable Swift/T

Swift/T is a key success from the ExM: System support for extreme-scale, many-task applications1 X-Stack project, which proposed to use concurrent dataflow as an innovative programming model to exploit extreme parallelism in exascale computers. The Swift/T component of the project reimplemented the Swift language from scratch to allow applications that compose scientific modules together to be build and run on available petascale computers (Blue Gene, Cray). Swift/T does this via a new compiler and runtime that generates and executes the application as an MPI program. We assume that mission-critical emerging exascale applications will be composed as scalable applications using existing software components, connected by data dependencies. Developers wrap native code fragments using a higherlevel language, then build composite applications to form a computational experiment. This exemplifies hierarchical concurrency: lower-level messaging libraries are used for fine-grained parallelism; highlevel control is used for inter-task coordination. These patterns are best expressed with dataflow, but static DAGs (i.e., other workflow languages) limit the applications that can be built; they do not provide the expressiveness of Swift, such as conditional execution, iteration, and recursive functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

SPEL: Software tool for Porting E3SM Land Model with OpenACC in a Function Unit Test Framework

Most high-end computers adopt hybrid architecture, porting a large-scale scientific code onto accelerators is necessary. The paper presents a generic method for porting large-scale scientific code onto accelerators using compiler directives within a modularized function unit test platform. We have implemented the method and designed a software tool (SPEL) to port the E3SM Land Model (ELM) onto the GPUs in the Summit computer. SPEL automatically generates GPU-ready test modules for all ELM functions, such as CanopyFlux, SoilTemperature, and EcosystemDynamics. SPEL breaks the ELM into a collection of standalone unit test programs for easy code verification and further performance improvement. We further optimize several ELM test modules with advanced techniques, including memory reduction, reconstructed parallel loops, and asynchronous GPU kernel launch. We hope our study will inspire new toolkit developments that expedite large-scale scientific code porting with compiler directives.

Schwartz, Peter↗

NASA NTRS1994

A Portable Debugger for Parallel and Distributed Programs

In this paper, we describe the design and implementation of a portable debugger for parallel and distributed programs. The design incorporates a client-server model in order to isolate non-portable debugger code from the user interface. The precise definition of a protocol for client-server interaction permits a high degree of portability of the client user interface. Replication of server components permits the implementation of a debugger for distributed computations. Portability across message passing implementations is achieved with a protocol that dictates the interaction between a message passing library and the debugger. This permits the same debugger to be used both on PVM and MTI programs. The process abstractions used for debugging message-passing programs can be easily adapted to debug HPF programs at the source level. This allows the debugger to present information hidden in tool-generated code in a meaningful manner.

Cheng, Doreen Y.↗

DOE OSTI2013

Research subjects for analytical estimation of core degradation at Fukushima-Daiichi nuclear power plant

Estimation of the accident progress and status inside the pressure vessels (RPV) and primary containment vessels (PCV) is required for appropriate conductance of decommissioning in the Fukushima-Daiichi NPP. For that, it is necessary to obtain additional experimental data and revised models for the estimation using computer codes with increased accuracies. The Japan Atomic Energy Agency (JAEA) has selected phenomena to be reviewed and developed, considering previously obtained information, conditions specific to the Fukushima-Daiichi NPP accident, and recent progress of experimental and analytical technologies. As a result, research and development items have been picked up in terms of thermal-hydraulic behavior in the RPV and PCV, progression of fuel bundle degradation, failure of the lower head of RPV, and analysis of the accident. This paper introduces the selected phenomena to be reviewed and developed, research plans and recent results from the JAEA's corresponding research programs. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1982

A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries

A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.

Lilley, D. G.↗

NASA NTRS1984

POSTOP: Postbuckled open-stiffener optimum panels-theory and capability

The computer program POSTOP was developed to serve as an aid in the analysis and sizing of stiffened composite panels that are loaded in the postbuckling regime. A comprehensive set of analysis routines was coupled to a widely used optimization program to produce this sizing code. POSTOP is intended for the preliminary design of metal or composite panels with open-section stiffeners, subjected to multiple combined biaxial compression (or tension), shear and normal pressure load cases. Longitudinal compression, however, is assumed to be the dominant loading. Temperature, initial bow eccentricity and load eccentricity effects are included. The panel geometry is assumed to be repetitive over several bays in the longitudinal (stiffener) direction as well as in the transverse direction. Analytical routines are included to compute panel stiffnesses, strains, local and panel buckling loads, and skin/stiffener interface stresses. The resulting program is applicable to stiffened panels as commonly used in fuselage, wing, or empennage structures. The analysis procedures and rationale for the assumptions used therein are described in detail.

Dickson, J. N.↗

DOE OSTI2024

An Evaluation of The Dynamic Physical Security Risk Assessment Methodology for Fleet-Wide Applications

The requirements for U.S. nuclear power plants to maintain a large onsite physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This integrated process for physical security analysis is named Modeling and Analysis for Safety Security using Dynamic EMRALD Framework (MASS-DEF). This document provides an update on the progress in applying the MASS-DEF process to an operating commercial nuclear power plant as well as additional industry feedback regarding use of the tool for other physical security risk-informed topics. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, and integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5 or MAAP. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report is an update the progress of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report also provides an update to the procedural guidance for the MASS-DEF process and an overview of the generic models available for use by utilities. This report does not contain any plant’s sensitive information and/or safeguards information. This study’s purpose was to verify that the results achieved using generic models are similar to actual plant results and refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction

Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.

Wu, Jing [Fermilab] (ORCID:0000000249460732)↗

DOE OSTI2015

An Update on NiCE Support for BISON

The Nuclear Energy Advanced Modeling and Simulation program (NEAMS) from the Department of Energy s Office of Nuclear Energy has funded the development of a modeling and simulation workflow environment to support the various codes in its nuclear energy scientific computing toolkit. This NEAMS Integrated Computational Environment (NiCE) provides extensible tools and services that enable efficient code execution, input generation, pre-processing visualizations, and post-simulation data analysis and visualization for a large portion of the NEAMS Toolkit. A strong focus for the NiCE development team throughout FY 2015 has been support for the Multiphysics Object Oriented Simulation Environment (MOOSE) and the NEAMS nuclear fuel performance modeling application built on that environment, BISON. There is a strong desire in the program to enable and facilitate the use of BISON throughout nuclear energy research and industry. A primary result of this desire is the need for strong support for BISON in NiCE. This report will detail improvements to NiCE support for BISON. We will present a new and improved interface for interacting with BISON simulations in a variety of ways: (1) improved input model generation, (2) embedded mesh and solution data visualizations, and (3) local and remote BISON simulation launch. We will also show how NiCE has been extended to provide support for BISON code development.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2012

Thermochimica User Manual – v1.0

A new software library called Thermochimica has been developed that determines a unique combination of phases and their compositions at thermochemical equilibrium. The development of Thermochimica in this research is aimed at direct integration in multi-physics codes and to address several concerns with using commercially available software, including: licensing entanglements associated with code distribution, access to the source code, convenient incorporation into other codes with quality assurance considerations, and computational performance. In particular, significant research efforts have been dedicated to enhance computational performance through advanced algorithm development, such as improved estimation techniques and non-linear solvers. The overall goal of this undertaking is to provide an open source computational tool to enhance the predictive capability of multiphysics codes without significantly impeding computational performance. The purpose of this document is to describe the design of Thermochimica and the basic use of the software library. A brief background to computational thermodynamics and the conditions for thermodynamic equilibrium is given in §2, details of the code development is discussed in §3, details of building and compiling Thermochimica is given in §4, specific programming details for each subroutine in the library is given in the Appendix. The open license for Thermochimica is provided with the source code. As is always the case, software quality assurance (SQA) is an extremely important subject in software development. The importance of this warrants an independent document dedicated to SQA, which has been developed in parallel to this document. The subject of thermodynamic model validation is also of extreme importance in scientific computing and must be given careful attention. To be clear, this document is concerned with the development and use of a general thermodynamic solver and the validation of any models should be included in the discussion of the development of a thermodynamic model that is specific to a particular system.

36 MATERIALS SCIENCE↗

NASA NTRS2013

Plant Habitat Telemetry / Command Interface and E-MIST

Plant Habitat (PH) is an experiment to be taken to the International Space Station (ISS) in 2016. It is critical that ground support computers have the ability to uplink commands to control PH, and that ISS computers have the ability to downlink PH telemetry data to ground support. This necessitates communication software that can send, receive, and process, PH specific commands and telemetry. The objective of the Plant Habitat Telemetry/ Command Interface is to provide this communication software, and to couple it with an intuitive Graphical User Interface (GUI). Initial investigation of the project objective led to the decision that code be written in C++ because of its compatibility with existing source code infrastructures and robustness. Further investigation led to a determination that multiple Ethernet packet structures would need to be created to effectively transmit data. Setting a standard for packet structures would allow us to distinguish these packets that would range from command type packets to sub categories of telemetry packets. In order to handle this range of packet types, the conclusion was made to take an object-oriented programming approach which complemented our decision to use the C++ programming language. In addition, extensive utilization of port programming concepts was required to implement the core functionality of the communication software. Also, a concrete understanding of a packet processing software was required in order to put aU the components of ISS-to-Ground Support Equipment (GSE) communication together and complete the objective. A second project discussed in this paper is Exposing Microbes to the Stratosphere (EMIST). This project exposes microbes into the stratosphere to observe how they are impacted by atmospheric effects. This paper focuses on the electrical and software expectations of the project, specifically drafting the printed circuit board, and programming the on-board sensors. The Eagle Computer-Aided Drafting (CAD) software was used to draft the E-MIST circuit. This required several component libraries to be created. Coding the sensors and obtaining sensor data involved using the Arduino Uno developmental board and coding language, and properly wiring peripheral sensors to the microcontroller (the central control unit of the experiment).

Walker, Uriae M.↗

DOE OSTI2015

Impact of Dutch nuclear fuel cycle scenarios on radionuclide inventory intended for disposal - 15201

One of the main subjects of Dutch five-year research program into geological disposal of radioactive waste, OPERA, is the post-closure radiological safety assessment. Reliable estimates of the radionuclide inventory and matrix composition are an important input for the safety assessment. The amounts and categories of waste foreseen to be disposed in 2130 the Netherlands have been compiled by the Dutch waste management organisation COVRA. Additionally, NRG has made a characterisation of the waste (radionuclides and matrix). This reference inventory is based on the Dutch base nuclear energy scenario of operating the Dutch single reactor, the Borssele NPP, until its presently scheduled shut-down in 2033. However, changes in the presently adopted nuclear fuel cycle strategy in the Netherlands may impact both the quantities of generated radioactive waste and its composition, and therefore the source term of the radiological safety assessment. To get a grip on this uncertainty a set of alternative future fuel cycle scenarios in the Netherlands, which are in compliance with scenarios formulated in the Dutch vision documents, has been considered and evaluated. The scenarios have been analysed with the computer code DANESS, 'Dynamic Analysis of Nuclear Energy System Strategies'. The result of the DANESS analyses concerns the amount and type of the radioactive waste to be finally disposed in a deep geological repository. This also includes the inventories of the individual radionuclides that are relevant for the post-closure safety assessment to be performed in a subsequent stage of the OPERA program. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗