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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolaï, and Busquet’s [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the helium gas-fill by a factor of ∼2 despite predicting the peak heat flux to within 16%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Measuring heat flux from collective Thomson scattering with non-Maxwellian distribution functions

Here, heat flux was measured in coronal plasmas using collective Thomson scattering from electron-plasma waves. A laser-produced plasma from a planar aluminum target created a temperature gradient along the target normal. Thomson scattering probed electron-plasma waves in the direction of the temperature gradient with phase velocities relevant to heat flux. The heat-flux measurements were reduced from classical values inferred from the measured plasma conditions in regions with large temperature gradients and agreed with classical values for weak gradients. In regions where classical theory was invalid, the heat flux was determined by reproducing the measured Thomson-scattering spectra using electron distribution functions consistent with nonlocal thermal transport. Lastly, full-scale hydrodynamic simulations using flux-limited thermal transport ( FLASH ) and the multigroup nonlocal Schurtz, Nicolai, and Busquet (SNB) models both underestimated the heat flux at all locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MG Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses

This work presents an application of Cacuci’s Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the simplified Boltzmann equation that models the transport of uncollided particles through a medium to compute efficiently and exactly all of the first- and second-order derivatives (sensitivities) of a detector’s response with respect to the system’s isotopic number densities, microscopic cross sections, source emission rates, and detector response function. The off-the-shelf PARTISN multigroup discrete ordinates code is employed to solve the equations underlying the 2nd-ASAM. The accuracy of the results produced using PARTISN is verified by using the results of three test configurations: (1) a homogeneous sphere, for which the response is the exactly known total uncollided leakage, (2) a multiregion two-dimensional (r-z) cylinder, and (3) a two-region sphere for which the response is a reaction rate. For the homogeneous sphere, results for the total leakage as well as for the respective first- and second-order sensitivities are in excellent agreement with the exact benchmark values. For the nonanalytic problems, the results obtained by applying the 2nd-ASAM to compute sensitivities are in excellent agreement with central-difference estimates. The efficiency of the 2nd-ASAM is underscored by the fact that, for the cylinder, only 12 adjoint PARTISN computations were required by the 2nd-ASAM to compute all of the benchmark’s 18 first-order sensitivities and 224 second-order sensitivities, in contrast to the 877 PARTISN calculations needed to compute the respective sensitivities using central finite differences, and this number does not include the additional calculations that were required to find appropriate values of the perturbations to use for the central differences.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

A Review of Molten Salt Reactor Kinetics Models

Interest in circulating fuel reactors (CFRs), particularly molten salt reactors (MSRs) of the fluid fuel type, has been growing in the last two decades. Starting with a resurgence of interest in Europe, there have been a growing number of methods proposed and codes developed to model the kinetics of CFRs, which is a capability essential to the design and evaluation of such reactors. This work first reviews the physical phenomena unique to CFRs in light of current research and how CFR kinetics are impacted by these considerations. In general, it is found that the movement of delayed neutron precursors (DNPs) through the primary loop has significant impacts on transients at low reactor powers or those with significant spatial components such as a change in the primary loop mass flow rate. Effects on the neutron flux are exceedingly minimal and entirely negligible. An extensive review of published models and methods for simulating CFR kinetics is presented, along with transient simulations in fast and thermal neutron flux systems using representative codes from each of the main modeling categories. Comparisons among methods are presented as are recommendations for their use or nonuse in various transient and work-flow scenarios. In general, it is recommended that time-resolved, multigroup neutron diffusion approaches be used to establish ranges of applicability for point reactor kinetics (PRK)–based approaches that themselves may not be applicable for all modeling situations. In such cases, it is suggested that quasi-static approaches be used where PRK-based approaches cannot be used. Finally, a review of common assumptions used in these models is presented, along with an evaluation of their impact on model performance. It is found that neglecting turbulent diffusion in open core–type CFRs is a poor assumption that leads to an underestimation of the reduction of the delayed neutron fraction. Furthermore, it is seen that exclusion of secondary heat transfer loops in models leads to underestimation of transient peaks and troughs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Multilevel-in-Space-and-Energy CMFD in VERA

For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.

42 ENGINEERING↗
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗
DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗
DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

SHOCK BREAKOUT IN TYPE II PLATEAU SUPERNOVAE: PROSPECTS FOR HIGH-REDSHIFT SUPERNOVA SURVEYS

Shock breakout is the brightest radiative phenomenon in a supernova (SN) but is difficult to be observed owing to the short duration and X-ray/ultraviolet (UV)-peaked spectra. After the first observation from the rising phase reported in 2008, its observability at high redshift is attracting enormous attention. We perform multigroup radiation hydrodynamics calculations of explosions for evolutionary presupernova models with various main-sequence masses M {sub MS}, metallicities Z, and explosion energies E. We present multicolor light curves of shock breakouts in Type II plateau SNe, being the most frequent core-collapse SNe, and predict apparent multicolor light curves of shock breakout at various redshifts z. We derive the observable SN rate and reachable redshift as functions of filter x and limiting magnitude m {sub x,lim} by taking into account an initial mass function, cosmic star formation history, intergalactic absorption, and host galaxy extinction. We propose a realistic survey strategy optimized for shock breakout. For example, the g'-band observable SN rate for m {sub g',lim} = 27.5 mag is 3.3 SNe deg{sup -2} day{sup -1} and half of them are located at z {>=} 1.2. It is clear that the shock breakout is a beneficial clue for probing high-z core-collapse SNe. We also establish ways to identify shock breakout and constrain SN properties from the observations of shock breakout, brightness, timescale, and color. We emphasize that the multicolor observations in blue optical bands with {approx}hour intervals, preferably over {>=}2 continuous nights, are essential to efficiently detect, identify, and interpret shock breakout.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

RADIATION TRANSPORT FOR EXPLOSIVE OUTFLOWS: OPACITY REGROUPING

Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) are methods used to stochastically solve the radiative transport and diffusion equations, respectively. These methods combine into a hybrid transport-diffusion method we refer to as IMC-DDMC. We explore a multigroup IMC-DDMC scheme that in DDMC, combines frequency groups with sufficient optical thickness. We term this procedure ''opacity regrouping''. Opacity regrouping has previously been applied to IMC-DDMC calculations for problems in which the dependence of the opacity on frequency is monotonic. We generalize opacity regrouping to non-contiguous groups and implement this in SuperNu, a code designed to do radiation transport in high-velocity outflows with non-monotonic opacities. We find that regrouping of non-contiguous opacity groups generally improves the speed of IMC-DDMC radiation transport. We present an asymptotic analysis that informs the nature of the Doppler shift in DDMC groups and summarize the derivation of the Gentile-Fleck factor for modified IMC-DDMC. We test SuperNu using numerical experiments including a quasi-manufactured analytic solution, a simple 10 group problem, and the W7 problem for Type Ia supernovae. We find that opacity regrouping is necessary to make our IMC-DDMC implementation feasible for the W7 problem and possibly Type Ia supernova simulations in general. We compare the bolometric light curves and spectra produced by the SuperNu and PHOENIX radiation transport codes for the W7 problem. The overall shape of the bolometric light curves are in good agreement, as are the spectra and their evolution with time. However, for the numerical specifications we considered, we find that the peak luminosity of the light curve calculated using SuperNu is ∼10% less than that calculated using PHOENIX.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A Study of Low-Temperature Neutron Star Atmospheres

We present a study of how a low-temperature accreted atmosphere influences the emitted X-ray spectrum of a neutron star. The atmosphere models and spectra were computed with Zcode, a multigroup radiation transfer code developed at the Los Alamos National Laboratory. Though the underlying hot neutron star behaves as a blackbody, the atmosphere shifts the peak of spectrum away from a blackbody and toward higher energies, producing an emitted spectrum similar to a dilute blackbody. Quantifying the effects of this atmosphere will remove a source of uncertainty in X-ray observations and better constrain the mass-radius relation for neutron stars and thus the equation of state of dense matter. We present a suite of these atmospheres with varying compositions and temperatures as well as the resulting spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Observation of Nonlocal Heat Flux Using Thomson Scattering

Here, nonlocal heat flux was measured in laser-produced coronal plasmas using a novel Thomson scattering technique. The measured heat flux was smaller than the classical values inferred from the measured plasma conditions in regions with large temperature gradients and agreed with classical values for weak gradients. Vlasov–Fokker–Planck simulations self consistently calculated the electron distribution functions used to reproduce the measured Thomson scattering spectra and to determine the heat flux. Multigroup nonlocal simulations overestimated the measured heat flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Investigations of laser plasmas dynamics by means of real and virtual Langmuir probes

In this paper we propose a novel technique for LPP-Laser Produced Plasmas investigation, combining high time resolved measurements using compact Langmuir Probes with the output of a theoretical model called HYBLAS developed on purpose, which is able to simulate the charged particles collected by a so-called virtual probe. It will be shown that with an appropriate experimental set-up and with the use of a Matlab software able to accurately analyze the experimental I-V curves, laser plasmas can be investigated properly even if the probe is placed very close to the target surface. This permits not only to study the plume expansion with a high temporal resolution, but also to estimate correctly the self-generated coulomb electric field inside the plume and to detect the inner structure of the the first upcoming expanding plasma. HYBLAS is able to predict and describe the plume expansion at relatively low power densities and is a powerful method to compare directly the experimental current signals with the numerical results if the initial conditions are settled properly. A direct comparison of the theoretical data with the experimental ones realized on different metal targets shows that our method is able to predict properly the overall plasma expansion in the nanosecond laser pulse duration regime. The virtual probe method was moreover tested by comparing the numerical results with another numerical code called MULTI, which simulate the expansion by combining the hydrodynamics equations to a multigroup method in order to include the radiation transport. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities

Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.

Engineering↗
DOE OSTI2024

Performance Portable Graphics Processing Unit Acceleration of a High-Order Finite Element Multiphysics Application

The Lawrence Livermore National Laboratory (LLNL) will soon have in place the El Capitan exascale supercomputer, based on advanced micro devices (AMD) graphics processing units (GPUs). As part of a multiyear effort under the National Nuclear Security Administration (NNSA) Advanced Simulation and Computing (ASC) program, we have been developing marbl, a next generation, performance portable multiphysics application based on high-order finite elements. In previous years, we successfully ported the Arbitrary Lagrangian–Eulerian (ALE), multimaterial, compressible flow capabilities of marbl to nvidia GPUs as described in Vargas et al. Here, in this paper, we describe our ongoing effort in extending marbl's GPU capabilities with additional physics, including multigroup radiation diffusion and thermonuclear burn for high energy density physics (HEDP) and fusion modeling. We also describe how our portability abstraction approach based on the raja Portability Suite and the mfem finite element discretization library has enabled us to achieve high performance on AMD based GPUs with minimal effort in hardware-specific porting. Throughout this work, we highlight numerical and algorithmic developments that were required to achieve GPU performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

COUPLING OF RELAP5-SCDAP MOD4.0 AND NEUTRONIC CODES

High-fidelity and accurate nuclear system codes play a key role in the design and analysis of complex nuclear power plants, which consist of multiple subsystems, such as the reactor core (and its fuel, burnable poisons, control elements, etc.), the reactor internal structures, the vessel, and the energy conversion subsystem and beyond to grid demand. Most commonly the interplay between these various subsystems is modeled using coupled codes, each of which represents one of the subsystems. And the most common direct coupling is that of thermal-hydraulics and neutronics codes. The subject of this paper is the coupling of codes that model not only thermal-hydraulics and neutronics, but also structural components damage. Furthermore, the neutronic component is not limited to the sole core solver. The coupled code system encompasses thermal-hydraulics, material performance of the fuel, neutronic solver, and neutronic data preparation. Thus, this paper presents a framework for coupling RELAP5/SCDAPSIM/MOD4.0 with a suite of neutron kinetics codes that includes NESTLE, DRAGON and a version of the ENDF library. The version of the RELAP5/SCDAPSIM/MOD4.0 code used in this work is one developed by Innovate System Software (ISS) as part of the international SCDAP Development and Training Program (SDTP) for best-estimate analysis to model reactor transients including severe accident phenomena. This RELAP5/SCDAPSIM/MOD4.0 code version is also capable of predicting nuclear fuel performance. It uses nodal power distributions to calculate mechanical and thermal parameters such as heat-up, oxidation and meltdown of fuel rods and control rods, the ballooning and rupture of fuel rod cladding, the release of fission products from fuel rods, and the disintegration of fuel rods into porous debris and molten material. On the neutronics side, this work uses the NESTLE and DRAGON codes. NESTLE is a multi-dimensional static and kinetic neutronic code developed at North Carolina State University. It solves up to four energy groups neutron diffusion equations utilizing the Nodal Expansion Method (NEM) in Cartesian or hexagonal geometry. The DRAGON code, developed at Ecole Polytechnique de Montreal, performs lattice physics calculations based on the neutron transport equation and is capable of using very fine energy group structures. In this work, we have developed a coupling approach to exchange data among the various modules. In the coupling process, the generated nuclear data (in fine multigroup energy structure) are collapsed down into two- or four-group energy structures for use in NESTLE. The neutron kinetics and thermal-hydraulics modules are coupled at each time step by using the cross-section data. The power distribution results of the neutronic calculations are transmitted to the thermal-hydraulics code. The spatial distribution of coolant density and the fuel-moderator temperature, which result from the thermal-hydraulic calculations, are transmitted back to the neutron kinetics codes and then the loop is closed using new neutronics results. Details of the actual data transfers will be described in the full length paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗