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Results for “chaotic field lines”

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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16 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Do chaotic field lines cause fast reconnection in coronal loops?

Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the Boozer–Elder coronal loop model driven by sub-Alfvénic footpoint motions [A. H. Boozer and T. Elder, Phys. Plasmas 28, 062303 (2021)]. In this work, our simulation results significantly differ from their predictions. The ideal simulation shows that Boozer and Elder under-predict the intensity of current density due to missing terms in their reduced model equations. Furthermore, resistive simulations of varying Lundquist numbers show that the maximal current density scales linearly rather than logarithmically with the Lundquist number.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Electric field effects during disruptions

Tokamak disruptions are associated with breaking magnetic surfaces, which makes magnetic field lines chaotic in large regions of the plasma. The enforcement of quasi-neutrality in a region of chaotic field lines requires an electric potential that has both short and long correlation distances across the magnetic field lines. The short correlation distances produce a Bohm-like diffusion coefficient ∼Te/eB and the long correlation distances aT produce a large scale flow ∼Te/eBaT. This cross-field diffusion and flow are important for sweeping impurities into the core of a disrupting tokamak. The analysis separates the electric field in a plasma into the sum of a divergence-free, E→B, and a curl-free, E→q, part, a Helmholtz decomposition. The divergence-free part of E→ determines the evolution of the magnetic field. The curl-free part enforces quasi-neutrality, E→q=−∇→Φq. Magnetic helicity evolution gives the required boundary condition for a unique Helmholtz decomposition and an unfortunate constraint on steady-state tokamak maintenance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

On heat conduction in an irregular magnetic field. Part 1

Anisotropic heat conduction in a plasma embedded in a magnetic field with irregular, possibly chaotic, field lines is discussed. If the collisional mean free path exceeds the electron gyroradius, the heat conductivity is much larger along the field lines than across them, and this enhances the transport across a domain where good flux surfaces do not exist. Recognising that anisotropic heat conduction may be cast in a variational form, and by constructing increasingly sophisticated trial functions that are based on invariant and almost-invariant structures under the magnetic field-line flow, bounds are derived on this enhancement and on the temperature variation along the magnetic field. In this way, remarkably accurate approximations for the temperature can be rapidly constructed without solving the diffusion equation, even in the small perpendicular-diffusion limit when the solution for the temperature is dominated by the fractal structure the magnetic field lines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Flattening of the tokamak current profile by a fast magnetic reconnection with implications for the solar corona

During tokamak disruptions, the profile of the net parallel current is observed to flatten on a time scale that is so fast that it must be due to a fast magnetic reconnection. After a fast magnetic reconnection has broken magnetic surfaces, a single magnetic field line covers an entire volume and not just a magnetic surface. The current profile, given by K ≡ μ 0 j | | / B , relaxes to a constant within that volume by Alfven waves propagating along the chaotic magnetic field lines. The time scale for this relaxation determines the commonly observed disruption phenomena of a current spike and a sudden drop in the plasma internal inductance. An efficient method for studying this relaxation is derived, which allows a better understanding of the information encoded in the current spike and the associated sudden drop in the plasma internal inductance. Implications for coronal heating are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Fast neural Poincaré maps for toroidal magnetic fields

Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. Furthermore, this structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

On the non-existence of stepped-pressure equilibria far from symmetry

The Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502) has been successful in the construction of equilibria in 3D configurations that contain a mixture of flux surfaces, islands and chaotic magnetic field lines. In this model, the plasma is sliced into sub-volumes separated by ideal interfaces, and in each volume the magnetic field is a Beltrami field. In the cases where the system is far from possessing a continuous symmetry, such as in stellarators, the existence of solutions to a stepped-pressure equilibrium with given constraints, such as a multi-region relaxed MHD minimum energy state, is not guaranteed but is often taken for granted. Using SPEC, we have studied two different scenarios in which a solution fails to exist in a slab with analytic boundary perturbations. Here we found that with a large boundary perturbation, a certain interface becomes fractal, corresponding to the break up of a Kolmogorov–Arnold–Moser (KAM) surface. Moreover, an interface can only support a maximum pressure jump while a solution of the magnetic field consistent with the force balance condition can be found. An interface closer to break-up can support a smaller pressure jump. We discovered that the pressure jump can push the interface closer to being non-smooth through force balance, thus significantly decreasing the maximum pressure it can support. Our work shows that a convergence study must be performed on a SPEC equilibrium with interfaces close to break-up. These results may also provide insights into the choice of interfaces and have applications in finding out the maximum pressure a machine can support.

3D equilibrium↗
DOE OSTI2023

Exploration of non-resonant divertor features on the Compact Toroidal Hybrid

Abstract Non-resonant divertors (NRDs) separate the confined plasma from the surrounding plasma facing components (PFCs). The resulting striking field line intersection pattern on these PFCs is insensitive to plasma equilibrium effects. However, a complex scrape-off layer (SOL), created by chaotic magnetic topology in the plasma edge, connects the core plasma to the PFCs through varying magnetic flux tubes. The Compact Toroidal Hybrid (CTH) serves as a test-bed to study this by scanning across its inductive current. Simulations observe a significant change of the chaotic edge structure and an effective distance between the confined plasma and the instrumented wall targets. The intersection pattern is observed to be a narrow helical band, which we claim is a resilient strike line pattern. However, signatures of finger-like structures, defined as heteroclinic tangles in chaotic domains, within the plasma edge connect the island chains to this resilient pattern. The dominant connection length field lines intersecting the targets are observed via heat flux modeling with EMC3-EIRENE. At low inductive current levels, the excursion of the field lines resembles a limited plasma wall scenario. At high currents, a private flux region is created in the area where the helical strike line pattern splits into two bands. These bands are divertor legs with distinct SOL parallel particle flow channels. The results demonstrate the NRD strike line pattern resiliency within CTH, but also show the underlying chaotic edge structure determining if the configuration is diverted or limited. This work supports future design efforts for a mechanical structure for the NRD.

Physics↗
DOE OSTI2026

Computing nuclear response functions with time-dependent coupled-cluster theory

We compute nuclear response functions by solving the time-dependent 𝐴-body Schrödinger equation, recording the time-dependent transition moment and extracting spectral information via Fourier transforms. The solution of the time-dependent many-body problem accounts for correlations on top of the mean field by taking advantage of a time-dependent formulation of coupled-cluster theory. As a validation, we focus on electric dipole transitions in 4 He and 16 O and compare moments of the response function distribution to the results of an equivalent static framework, finding negligible discrepancies. We investigate how proton and neutron densities evolve in time, and we see the traditional picture of soft and giant dipole resonances as collective oscillations of protons and neutrons emerging from our calculations in 16 O and 24 O. Furthermore, this method also allows us to investigate the behavior of the nucleus in the presence of a strong electric field. In that regime, the behavior of the system becomes chaotic. Qualitatively, the spectral information obtained in this limit is in line with previous time-dependent mean-field results.

Ab initio calculations↗
DOE OSTI2023

Required toroidal confinement for fusion and omnigeneity

Deuterium–tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The distribution functions are given by the Fokker–Planck equation, which is an advection–diffusion equation. A large hyperbolic operator, the Vlasov operator with the particle trajectories as its characteristics, equals a small diffusive operator, the collision operator. The collisionless particle trajectories would be chaotic in stellarators without careful optimization. This would lead to rapid entropy production and transport—far beyond what is consistent with a self-sustaining DT burn. Omnigeneity is the weakest general condition that is consistent with a sufficiently small entropy production associated with the thermal particle trajectories. Omnigeneity requires that the contours of constant magnetic field strength be unbounded in at least one of the two angular coordinates in magnetic surfaces and that there be a symmetry in the field-strength wells along the field lines. Even in omnigenous plasmas, fluctuations due to microturbulence can produce chaotic particle trajectories and the gyro-Bohm transport is seen in many stellarator and tokamak experiments. The higher the plasma temperature above 10 keV, the smaller the transport must be compared to gyro-Bohm for a self-sustaining DT burn. The hot alphas of DT fusion heat the electrons. When the ion–electron equilibration time is long compared to the ion energy confinement time, a self-sustaining DT burn is not possible, which sets a limit on the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Resilient stellarator divertor characteristics in the Helically Symmetric eXperiment

Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric eXperiment are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length L C lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint’s resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection min $(\delta_N)$ of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between min $(\delta_N)$ and L C of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

divertor↗
DOE OSTI2022

Poor confinement in stellarators at high energy

High-energy particle resonances can modify particle distributions and even cause significant particle loss. Resonances can be present in any toroidal confinement device and can easily be found numerically. Many stellarators have weak magnetic shear so that large islands and large chaotic regions can be produced by resonant perturbations with small amplitudes. Additionally, while the choice of the field line helicity profile in the plasma can limit the presence of resonances at low particle energy, the resonance location is energy-dependent, and they can move into the plasma at higher energy. If resonances match the toroidal variation of the equilibrium, they can produce wide islands in the phase space of orbits even in the absence of perturbations due to instabilities. These islands increase in size with particle energy and can seriously affect the confinement of high-energy ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Towards improved neutral exhaust in the HSX stellarator

To improve our knowledge of neutral exhaust in non-resonant divertors, a particle exhaust study is performed for the Helically Symmetric eXperiment (HSX). The chaotic magnetic field topology in the plasma edge is examined with connection lengths and Lyapunov exponents. Plasma flux tubes are identified and these flux tubes deposit particles onto plasma facing components. This helps determine the areas where neutrals are generated and provides guidance on where to put baffles. As shown using EMC3-EIRENE simulations, the introduction of baffles can help increase the neutral pressure at and away from the strike line locations. Furthermore, it is demonstrated that baffle design cannot only be based on placing structures at locations with small connection lengths.

Baffles↗
DOE OSTI2024

A MUSE source-blind survey for emission from the circumgalactic medium

The recent detection of optical emission lines from the circumgalactic medium (CGM) in combined, large samples of low-redshift, normal galaxy spectra hints at the potential to map the cool (∼10 4 kelvin) CGM in individual, representative galaxies. Using archival data from a forefront instrument (MUSE) on the VLT, we present a source-blind, wide-redshift-range (z∼ 0 to 5) narrowband imaging survey for CGM emission. Our detected, resolved emission line sources are cataloged and include a 30-kiloparsec-wide Hα source likely tracing the CGM of a low-mass galaxy (stellar mass ∼ 10 8.78±0.42 solar mass) atz= 0.1723, a 60-kiloparsec-wide Ly α structure associated with a galaxy atz= 3.9076, and a 130-kiloparsec (∼r vir )–wide [O II] feature revealing an interaction between a galaxy pair atz= 1.2480. The Hα velocity field for the low-mass galaxy suggests that the CGM is more chaotic or turbulent than the galaxy disk, while that for the interacting galaxies shows large-scale (∼50 kiloparsec) coherent motions.

Science & Technology - Other Topics↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Transport Barriers in Symplectic Maps

Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be obtained from simple dynamical systems like two-dimensional area-preserving (symplectic) maps, where powerful mathematical results like KAM theory are available. In this work we review recent works on transport barriers in area-preserving maps, focusing on systems which do not obey the so-called twist property. For such systems KAM theory no longer holds everywhere and novel dynamical features show up as nonresistive reconnection, shearless curves and shearless bifurcations. After presenting some general features using a standard nontwist mapping, we consider magnetic field line maps for magnetically confined plasmas in tokamaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗