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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Gamma-rays from supernova remnants and the signatures of diffusive shock acceleration

A nonlinear shock acceleration model which generates non-thermal proton distributions and includes a self-consistent determination of shock hydrodynamics, is considered. Gamma ray spectra are obtained for supernova remnants, allowing for the cessation of acceleration to high energies due to the finite ages and the sizes of the remnants. Gamma ray spectral cutoffs can be observed in the TeV range for reasonable remnant parameters and deviations from power law behavior are found at all energies from 1 MeV to cutoff. Correlated observations by the International Gamma Ray Astrophysics Laboratory, Whipple and other instruments may provide stringent constraints to understanding supernova remnants.

Baring, Matthew G.↗
DOE OSTI2017

Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Numerical simulations of time-dependent cosmic ray mediated shocks

Recent research in unsteady shocks that are influenced by nonlinear aspects of diffusive particle acceleration and that involve multidimensional flows is outlined, and some of the difficulties in making further progress are discussed. It is suggested that in many situations it is probably not appropriate to assume steady states for astrophysical CR shocks. This results both from the need to be concerned about the finite rate at which CR pressure builds and modifies a shock and from the existence of instabilities. Even so, it seems likely that CR-modified shocks can develop to a state with substantial CR pressure. The overall acceleration efficiency and the CR particle momentum distribution produced in time-dependent flows typically depend on several details such as the ratio of various time scales and the initial proportion of relativistic to nonrelativistic particles in the CR populations.

Jones, T. W.↗
NASA NTRS1990

Particle simulations in magnetospheric plasmas

In view of the recent remarkable advancement of computer technology and simulation software, simulation studies are one of the most powerful academic tools for establishment of quantitative space physics and modelling of our space environment. The complex nature encountered in space plasma physics has motivated considerable development in computer simulations, which have played an essential role in the development of space plasma theory. This report describes research undertaken to understand physical processes involved in plasma waves observed in the magnetospheric plasmas, and associated nonlinear phenomena such as heating, diffusion, and acceleration of particles due to excited waves. The research explains and clarifies the observational data both qualitatively and quantitatively.

Nishikawa, Ken-Ichi↗
DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS2002

Broadband Observations and Modeling of the Shell-Type Supernova Remnant G347.3-0.5

The supernova remnant G347.3-0.5 emits a featureless power law in X-rays, thought to indicate shock acceleration of electrons to high energies. We here produce a broadband spectrum of the bright northwest limb of this source by combining radio observations from the Australia Telescope Compact Array (ATCA), X-ray observations from the Advanced Satellite for Cosmology and Astrophysics (ASCA), and TeV gamma-ray observations from the CANGAROO imaging Cerenkov telescope. We assume that this emission is produced by an electron population generated by diffusive shock acceleration at the remnant forward shock. The nonlinear aspects of the particle acceleration force a connection between the widely different wavelength bands and between the electrons and the unseen ions, presumably accelerated simultaneously with the electrons. This allows us to infer the relativistic proton spectrum and estimate ambient parameters such as the supernova explosion energy, magnetic field, matter density in the emission region, and efficiency of the shock acceleration process. We find convincing evidence that the shock acceleration is efficient, placing greater than 25% of the shock kinetic energy flux into relativistic ions. Despite this high efficiency, the maximum electron and proton energies, while depending somewhat on assumptions for the compression of the magnetic field in the shock, are well below the observed 'knee' at 10(exp 15) eV in the Galactic cosmic-ray spectrum.

Ellison, Donald C.↗
DOE OSTI2017

Anderson acceleration and application to the three-temperature energy equations

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton–Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Test-Particle Simulations of Linear and Nonlinear Interactions Between a 2-D Whistler-Mode Wave Packet and Radiation Belt Electrons

Using test-particle simulations, we describe (in 2-D) the interaction of an ensemble of electrons with a discrete whistler-mode wave packet, which propagates with a moderate wave-normal angle with respect to the background magnetic field. We evaluate both the average transport coefficients used in quasi-linear diffusion transport and also the full nonlinear wave-particle interactions. The magnitude of the calculated diffusion coefficients is found to increase proportionally to the wave amplitude squared, in agreement with quasi-linear diffusion theory. Cyclotron resonance of counterstreaming electrons (n = 1 harmonic number) is more important for pitch angle scattering than Landau resonance. Landau resonance of costreaming electrons (n = 0) is comparable to cyclotron resonance for energy diffusion and advection. Strong acceleration of high pitch angle, costreaming electrons arises in nonlinear wave-particle interactions with high-amplitude waves. In our simulations with zero parallel electric field, the energy source for electron acceleration is the wave’s perpendicular electric field, in both the cyclotron and Landau resonances. The Landau resonance can happen even with zero parallel electric field, if the wave packet propagates with a finite wave-normal angle. This resonance between the particle’s azimuthal velocity and the wave fields leads to trapping and substantial parallel acceleration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Simple Analytical Forms of the Perpendicular Diffusion Coefficient for Two-component Turbulence. III. Damping Model of Dynamical Turbulence

In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper we derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Diffusive shock re-acceleration

Here, we have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We determine that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can later trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value $J\simeq en_{\text{CR}}v_{\text{sh}}$ , where $en_{\text{CR}}$ is the seed charge density and $v_{\text{sh}}$ is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than ${\sim}10~\text{yr}$ , thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1985

Selfsimilar time dependent shock structures

Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.

Beck, R.↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Properties of Intense Field-Aligned Lower-Band Chorus Waves: Implications for Nonlinear Wave-Particle Interactions: INTENSE FIELD-ALIGNED CHORUS WAVE-PACKETS

Resonant interactions between electrons and chorus waves are responsible for a wide range of phenomena in near-Earth space (e.g., diffuse aurora and acceleration of > 1 MeV electrons). Although quasi-linear diffusion is believed to be the primary paradigm for describing such interactions, an increasing number of investigations suggest that nonlinear effects are also important in controlling the rapid dynamics of electrons. However, present models of nonlinear wave-particle interactions, which have been successfully used to describe individual short-term events, are not directly applicable for a statistical evaluation of nonlinear effects and the long-term dynamics of the outer radiation belt, because they lack information on the properties of intense (nonlinearly resonating with electrons) chorus waves. In this paper, we use the Time History of Events and Macroscale Interactions during Substorms and Van Allen Probes data sets of field-aligned chorus waveforms to study two key characteristics of these waves: effective amplitude Β w (nonlinear interaction can occur when Β w >2) and wave packet length β (the number of wave periods within it). While as many as 10–15% of chorus wave packets are sufficiently intense (Β w >2–3) to interact nonlinearly with relativistic electrons, most of them are short (β < 10) reducing the efficacy of such interactions. Revised models of nonlinear interactions are thus needed to account for the long-term effects of these common, intense but short chorus wave packets. We also discuss the dependence of Β w , β on location (MLT and L-shell) and on the properties of the suprathermal electron population.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Diffuse ions produced by electromagnetic ion beam instabilities

The evolution of the electromagnetic ion beam instability driven by the reflected ion component backstreaming away from the earth's bow shock into the foreshock region is studied by means of computer simulation. The linear and quasi-linear stages of the instability are found to be in good agreement with known results for the resonant mode propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude delta B approximately B, sinusoidal transverse waves and 'intermediate' ion distributions, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and 'diffuse' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks.

Winske, D.↗
NASA NTRS1994

Electron injection and acceleration at nonlinear shocks: Results of numerical simulations

We present results of numerical simulations of electron injection and acceleration at nonlinear high Mach number shocks. The electrons are assumed to be heated at the thermal subshock to an energy E(sub inj), which is treated as a free parameter, above which they are injected by self-generated whistlers to momentum m(sub p) x V(sub A). This injection mechanism requires Mach numbers greater than (43/(beta(sub -)))(((k T(sub e))/(E(sub inj)))(exp 1/2)), where T(sub e) and beta (sub -) are the upstream electron temperature and plasma beta parameter. Above m(sub p) x V(sub A) electrons are trapped in the shock by Alfven waves. In the proton precursor region the Alfven waves are assumed to be generated by protons accelerated at the shock, and have nonlinear intensities. Below GeV, however, electrons of a given rigidity propagate faster than protons with a similar rigidity and therefore diffuse to regions ahead of the proton precursor. In those regions the Alfven waves are generated by the electrons themselves. The diffusion coefficient appears to increase with decreasing acceleration efficiency. As a result, the number of electrons accelerated to energies GeV and above and, hence, the electron to proton ratio, depend only weakly on the extent of electron heating at the subshock. The negative feedback also renders the electron spectra insensitive to shock compression ratio and smoothing length scale. The estimated e/p ratio at GeV is between approximately 1%-10%.

Levinson, Amir↗
DOE OSTI2019

eSHIVA in IOTA: Experiment on Stochasticity in High Intensity Variable Accelerators

Nonlinear integrable optics, the basis of IOTA, is a very special form of Hamiltonian system, called completely integrable. The consequences are many, most importantly the absence of fixed points that are in one-to-one correspondence with (overlapping) resonances. This, in turn, does not limit the dynamic aperture and allows large amplitude dependent tune shifts without adverse effects. In fact, it helps significantly in alleviating issues with collective instabilities. We developed and tested different numerical methods to give a more complete picture of the dynamics of integrable and near-integrable nonlinear Hamiltonian systems consisting of motion of charged particles in electromagnetic fields. Comparison of the results allowed us to discern real phenomena from numerical artifacts and come up with conclusions that will facilitate pushing the intensity frontier in beam dynamics even further for the benefit of the accelerator community as a whole and society as the consequence of the science and technological advancements it will make possible. We concluded that, while novel structure preserving integrators would be ideal, symplectic methods under mild restrictions offer adequate invariant preservation. We especially highlighted the very good performance of the Stormer-Verlet method at low accuracy and a modified Lobatto method at high accuracy for the Integrable Optics Test Accelerator (IOTA). However, we showed that symplectic integrators are limited by numerically induced resonances, which make interpretation of some simulation results challenging. These limitations and workarounds have been addressed.The nonlinear integrable optics test accelerator IOTA at Fermilab -- a very special experimental accelerator designed to investigate nonlinear optics under severe space-charge conditions – has recently completed its construction and initial commissioning of the ring has begun. We report first, under 2 (a) below: the progress on the nonlinear tune-shift measurements for various values of the nonlinear strength potential and their comparison with theoretical expectations, thus benchmarking the nonlinear characteristics of the ring; then, under 2 (b) below: the progress on simulation and design of a gas-jet monitor to measure beam profile and in particular its diffusive halo, expected to develop during stochastic diffusion of large amplitude particles under nonlinear forces of the magnetic lattice and Coulomb space-charge. Since the development of a proton beam source in IOTA is delayed and to be completed only in the future pending financial support, the gas-jet monitor is planned for testing with real proton beams elsewhere at Fermilab (e.g. in the Main Injector or PIP-II source possibly). Once proton beams are available in IOTA, the understanding of the nonlinear properties of IOTA combined with the developed gas-jet monitor, will enable a thorough experimental analysis of nonlinear stochastic diffusion in IOTA nonlinear ring, and boosted by proper theoretical understanding of the same.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Cluster for Research Excellence (CRE) for Accelerator Physics

The purpose of this Cooperative Research and Development Agreement (CRADA) was to establish a Cluster of Research Excellence (CRE) for Accelerator Physics and broaden the accelerator physics collaboration between Northern Illinois University (NIU) and Fermilab. The CRE was based in both Fermilab’s Accelerator Division and in NIU’s Department of Physics. A research agenda and strategy for the CRE for Accelerator Physics included specific research topics, experiments, and research facility upgrades. The scope of the research program covered two thrusts with subtopics in the Accelerator Science Research Program utilizing the infrastructure of FAST, IOTA, the Fermilab Accelerator Complex, and the Illinois Accelerator Research Center (IARC). Specific areas of proposed exploration included: 1.Tests of novel “nonlinear integrable” systems including beam self-fields; 2.Experimental tests of phase-space diffusion and chaos in intense beams; 3.Investigate technically feasible approaches towards next generation intenseneutrino facilities; 4.Understanding optical control of charged particle beams; 5.Exploitation of bright electron beams from FAST for novel applications; 6. Conduct research into accelerator-based ‘precision science’, such as Muon g-2, EDM, Mu2e, etc.

43 PARTICLE ACCELERATORS↗