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DOE OSTI2016

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Weak convergence to equilibrium of statistical ensembles in integrable Hamiltonian systems

This article explores the long-time behavior of the bounded orbits associated with an ensemble of initial conditions in a nondegenerate integrable Hamiltonian system. Such systems are inherently nonlinear and subject to highly regular phase space filamentation that can drive the ensemble of orbits toward a stationary state. Describing the statistical ensemble by a probability density on a neighborhood of a family of invariant tori, it is proved that the probability density describing the ensemble at time t converges weakly to an invariant density as t → ∞. More generally, we provide sufficient conditions for convergence to equilibrium of a multiphase system in action-angle form. These ideas are applied to an illustrative exactly soluble example. Finally, this work is relevant for understanding the statistical mechanics of integrable and near-integrable Hamiltonian systems

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Effects of temperature and density evolution in MHD simulations of HIT-SI

The helicity injected torus-steady inductive (HIT-SI) experiment uses steady inductive helicity injection to form a spheromak equilibrium and sustain the structure against resistive decay. Helicity injection is performed using two half-tori “injectors” connected to the main plasma volume, whose fields are oscillated in an AC manner. The properties of the sustained spheromak equilibrium have been experimentally observed to vary with the frequency of the injector oscillation, producing higher current gains and more-symmetric and outwardly shifted current centroids with higher frequency. A computational scan of injector frequency using the 3D MHD code PSI-Tet, which models the entire HIT-SI plasma volume including the injectors, has been performed, including a comparison of the results using the full Hall MHD model to those obtained using a simplified “zero-beta” (constant temperature and density) model. The results of both PSI-Tet models are also compared with experimental data and with simulations using the NIMROD code, which does not model the injector regions. The results of the PSI-Tet simulations show that the average temperature and current gain increase with injector frequency, in agreement with experimental trends. The simulations also show qualitative changes in the dynamics of several quantities with increasing injector frequency, such as density oscillations and current evolution. However, the outward shift and symmetrizing of the current centroid, observed experimentally, are not observed in these MHD simulations, indicating that unresolved or excluded dynamics may be important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Magnetic turnstiles in nonresonant stellarator divertor

Nonresonant stellarator divertors have magnetic flux tubes, called magnetic turnstiles, that cross cantori, which are fractal remnants of destroyed invariant tori with holes, that lie outside the outermost confining surface. The exiting and entering flux tubes can be adjacent as is generally expected but can also have the unexpected feature of entering or exiting at separate locations of the cantori. Not only can there be two types of turnstiles but pseudo-turnstiles can also exist. A pseudo-turnstile is formed when a cantorus has a sufficiently large, although limited, radial excursion to strike a surrounding chamber wall. The existence of non-adjacent and adjacent turnstiles and pseudo-turnstiles resolves issues that arose in earlier simulations of nonresonant stellarator divertors [A. Punjabi and A. H. Boozer, Phys. Plasmas 27, 012503 (2020)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Laboratory study of the failed torus mechanism in arched, line-tied, magnetic flux ropes

Coronal mass ejections (CMEs) are some of the most energetic and violent events in our solar system. The prediction and understanding of CMEs are of particular importance due to the impact that they can have on Earth-based satellite systems and, in extreme cases, ground-based electronics. CMEs often occur when long-lived magnetic flux ropes (MFRs) anchored to the solar surface destabilize and erupt away from the Sun. One potential cause for these eruptions is an ideal magnetohydrodynamic (MHD) instability, such as the kink or torus instability. Previous experiments on the magnetic reconnection experiment revealed a class of MFRs that were torus-unstable but kink-stable, which failed to erupt. These “failed-tori” went through a process similar to Taylor relaxation, where the toroidal current was redistributed before the eruption ultimately failed. Herein we have investigated this behavior through additional diagnostics that measure the current distribution at the foot points and the energy distribution before and after an event. These measurements indicate that ideal MHD effects are sufficient to explain the energy distribution changes during failed torus events. This excludes Taylor relaxation as a possible mechanism of current redistribution during an event. A new model that only requires non-ideal effects in a thin layer above the electrodes is presented to explain the observed phenomena. This work broadens our understanding of the stability of MFRs and the mechanism behind the failed torus through the improved prediction of the torus instability and through new diagnostics to measure the energy inventory and current profile at the foot points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

SUZAKU VIEW OF THE SWIFT/BAT ACTIVE GALACTIC NUCLEI. IV. NATURE OF TWO NARROW-LINE RADIO GALAXIES (3C 403 AND IC 5063)

We report the results of Suzaku broadband X-ray observations of the two narrow-line radio galaxies, 3C 403 and IC 5063. Combined with the Swift/Burst Alert Telescope (BAT) spectra averaged for 58 months, we are able to accurately constrain their spectral properties over the 0.5-200 keV band. The spectra of both nuclei are well represented with an absorbed cutoff power law, an absorbed reflection component from cold matter with an iron-K emission line, and an unabsorbed soft component, which gives a firm upper limit for the scattered emission. The reflection strength normalized to the averaged BAT flux is R {identical_to} {Omega}/2{pi} {approx} 0.6 in both targets, implying that their tori have a sufficiently large solid angle to produce the reprocessed emission. A numerical torus model with an opening angle of {approx}50{sup 0} well reproduces the observed spectra. We discuss the possibility that the amount of the normal gas responsible for Thomson scattering is systematically smaller in radio galaxies compared with Seyfert galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

MID- AND FAR-INFRARED PROPERTIES OF A COMPLETE SAMPLE OF LOCAL ACTIVE GALACTIC NUCLEI

We investigate the mid- (MIR) to far-infrared (FIR) properties of a nearly complete sample of local active galactic nuclei (AGNs) detected in the Swift/Burst Alert Telescope (BAT) all-sky hard X-ray (14-195 keV) survey, based on the cross correlation with the AKARI infrared survey catalogs complemented by those with Infrared Astronomical Satellite and Wide-field Infrared Survey Explorer. Out of 135 non-blazer AGNs in the Swift/BAT nine-month catalog, we obtain the MIR photometric data for 128 sources either in the 9, 12, 18, 22, and/or 25 {mu}m band. We find good correlation between their hard X-ray and MIR luminosities over three orders of magnitude (42 < log {lambda}L{sub {lambda}}(9, 18 {mu}m) < 45), which is tighter than that with the FIR luminosities at 90 {mu}m. This suggests that thermal emission from hot dusts irradiated by the AGN emission dominate the MIR fluxes. Both X-ray unabsorbed and absorbed AGNs follow the same correlation, implying isotropic infrared emission, as expected in clumpy dust tori rather than homogeneous ones. We find excess signals around 9 {mu}m in the averaged infrared spectral energy distribution from heavy obscured 'new type' AGNs with small scattering fractions in the X-ray spectra. This could be attributed to the polycyclic aromatic hydrocarbon emission feature, suggesting that their host galaxies have strong starburst activities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

MULTIPOLAR PLANETARY NEBULAE: NOT AS GEOMETRICALLY DIVERSIFIED AS THOUGHT

Planetary nebulae (PNe) have diverse morphological shapes, including point-symmetric and multipolar structures. Many PNe also have complicated internal structures such as tori, lobes, knots, and ansae. A complete accounting of all the morphological structures through physical models is difficult. A first step toward such an understanding is to derive the true three-dimensional structure of the nebulae. In this paper, we show that a multipolar nebula with three pairs of lobes can explain many such features, if orientation and sensitivity effects are taken into account. Using only six parameters-the inclination and position angles of each pair-we are able to simulate the observed images of 20 PNe with complex structures. We suggest that multipolar structure is an intrinsic structure of PNe and the statistics of multipolar PNe have been severely underestimated in the past.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

MODELING THE NUCLEAR INFRARED SPECTRAL ENERGY DISTRIBUTION OF TYPE II ACTIVE GALACTIC NUCLEI

We present results from model fitting to the spectral energy distribution (SED) of a homogeneous sample of Seyfert II galaxies drawn from the 12 {mu}m Galaxy Sample. Imaging and nuclear flux measurements are presented in an accompanying paper. Here we add Spitzer/IRS observations to further constrain the SEDs after careful subtraction of a starburst component. We use the library of CLUMPY torus models from Nenkova et al. and also test the two-phase models recently produced by Stalevski et al. We find that photometric and spectroscopic observations in the mid-IR ({lambda} {approx}> 5 {mu}m) are crucial to properly constrain the best-fit torus models. About half of our sources show clear near-IR excess of their SEDs above the best-fit models. This problem can be less severe when using the Stalevski et al. models. The nature of this emission is not clear since best-fitted blackbody temperatures are very high ({approx}1700-2500 K) and the Type II classification of our sources would correspond to a small probability to peer directly into the hottest regions of the torus. Crucially, the derived torus parameters are quite robust when using CLUMPY models, independently of whether or not the sources require an additional blackbody component. Our findings suggest that tori are characterized by N{sub 0}{approx}>5, {sigma} {approx}> 40, {tau} {approx}< 25, Angle i {approx}> 40 Degree-Sign , Y {approx}< 50, and A {sup los} {sub v} {approx} 100-300, where N{sub 0} is the number of clouds in the equatorial plane of the torus, {sigma} is the characteristic opening angle of the cloud distribution, {tau} is the opacity of a single cloud, Angle i is the line-of-sight orientation of the torus, Y is the ratio of the inner to the outer radii, and A {sup los} {sub v} is the total opacity along the line of sight. From these, we can determine typical torus sizes and masses of 0.1-5.0 pc and 10{sup 4}-10{sup 6} M {sub Sun }, respectively. We find tentative evidence that those nuclei with detected hidden broad-line regions are characterized by lower levels of extinction than those without one. Finally, we find no correlation between the torus properties and the presence of circumnuclear or more global star formation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

BROADBAND X-RAY SPECTRA OF TWO LOW-LUMINOSITY ACTIVE GALACTIC NUCLEI NGC 1566 AND NGC 4941 OBSERVED WITH SUZAKU

We report the first broadband X-ray spectra of the low-luminosity active galactic nuclei (LLAGNs), NGC 1566 (type 1.5) and NGC 4941 (type 2), observed with Suzaku and Swift/BAT covering the 0.5-195 keV band. Both targets have hard X-ray luminosities of {approx}10{sup 41-42} erg s{sup -1} in the 15-55 keV band. The spectra of the nucleus are well reproduced by a sum of partially or fully covered transmitted emission and its reflection from the accretion disk, reprocessed emission from the torus accompanied by a strong narrow iron-K{alpha} line, and a scattered component (for NGC 4941). We do not significantly detect a broad iron-K{alpha} line from the inner accretion disk in both targets, and obtain an upper limit on the corresponding solid angle of {Omega}/2{pi} < 0.3 in NGC 1566. The reflection strength from the torus is moderate, {Omega}/2{pi}=0.45{sup +0.13}{sub -0.10} in NGC 1566 and {Omega}/2{pi}=0.64{sup +0.69}{sub -0.27} in NGC 4941. Comparison of the equivalent width of the narrow iron-K{alpha} line with a model prediction based on a simple torus geometry constrains its half-opening angle to be {theta}{sub oa} {approx_equal} 60 Degree-Sign -70 Degree-Sign in NGC 4941. These results agree with the obscured AGN fraction obtained from hard X-ray and mid-infrared selected samples at similar luminosities. Our results support the implication that the averaged covering fraction of AGN tori is peaked at L {approx} 10{sup 42-43} erg s{sup -1} but decreases toward lower luminosities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

SUZAKU VIEW OF THE SWIFT/BAT ACTIVE GALACTIC NUCLEI. V. TORUS STRUCTURE OF TWO LUMINOUS RADIO-LOUD ACTIVE GALACTIC NUCLEI (3C 206 AND PKS 0707-35)

We present the results from broadband X-ray spectral analysis of 3C 206 and PKS 0707-35 with Suzaku and Swift/BAT, two of the most luminous unobscured and obscured radio-loud active galactic nuclei (AGNs) with hard X-ray luminosities of 10{sup 45.5} erg s{sup -1} and 10{sup 44.9} erg s{sup -1} (14-195 keV), respectively. Based on the radio core luminosity, we estimate that the X-ray spectrum of 3C 206 contains a significant ({approx}60% in the 14-195 keV band) contribution from the jet, while it is negligible in PKS 0707-35. We can successfully model the spectra with the jet component (for 3C 206), the transmitted emission, and two reflection components from the torus and the accretion disk. The reflection strengths from the torus are found to be R{sub torus}({identical_to} {Omega}/2{pi}) = 0.29 {+-} 0.18 and 0.41 {+-} 0.18 for 3C 206 and PKS 0707-35, respectively, which are smaller than those in typical Seyfert galaxies. Utilizing the torus model by Ikeda et al., we quantify the relation between the half-opening angle of a torus ({theta}{sub oa}) and the equivalent width of an iron-K line. The observed equivalent width of 3C 206, < 71 eV, constrains the column density in the equatorial plane to N{sub H}{sup eq} <10{sup 23} cm{sup -2}, or the half-opening angle to {theta}{sub oa} > 80 Degree-Sign if N{sub H}{sup eq} =10{sup 24} cm{sup -2} is assumed. That of PKS 0707-35, 72 {+-} 36 eV, is consistent with N{sub H}{sup eq} {approx}10{sup 23} cm{sup -2}. Our results suggest that the tori in luminous radio-loud AGNs are only poorly developed. The trend is similar to that seen in radio-quiet AGNs, implying that the torus structure is not different between AGNs with jets and without jets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

BLACK HOLE-NEUTRON STAR MERGERS WITH A HOT NUCLEAR EQUATION OF STATE: OUTFLOW AND NEUTRINO-COOLED DISK FOR A LOW-MASS, HIGH-SPIN CASE

Neutrino emission significantly affects the evolution of the accretion tori formed in black hole-neutron star mergers. It removes energy from the disk, alters its composition, and provides a potential power source for a gamma-ray burst. To study these effects, simulations in general relativity with a hot microphysical equation of state (EOS) and neutrino feedback are needed. We present the first such simulation, using a neutrino leakage scheme for cooling to capture the most essential effects and considering a moderate mass (1.4 M{sub ☉} neutron star, 5.6 M{sub ☉} black hole), high-spin (black hole J/M {sup 2} = 0.9) system with the K{sub 0} = 220 MeV Lattimer-Swesty EOS. We find that about 0.08 M{sub ☉} of nuclear matter is ejected from the system, while another 0.3 M{sub ☉} forms a hot, compact accretion disk. The primary effects of the escaping neutrinos are (1) to make the disk much denser and more compact, (2) to cause the average electron fraction Y{sub e} of the disk to rise to about 0.2 and then gradually decrease again, and (3) to gradually cool the disk. The disk is initially hot (T ∼ 6 MeV) and luminous in neutrinos (L{sub ν} ∼ 10{sup 54} erg s{sup –1}), but the neutrino luminosity decreases by an order of magnitude over 50 ms of post-merger evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Toward the standard population synthesis model of the X-ray background: Evolution of X-ray luminosity and absorption functions of active galactic nuclei including Compton-thick populations

We present the most up to date X-ray luminosity function (XLF) and absorption function of active galactic nuclei (AGNs) over the redshift range from 0 to 5, utilizing the largest, highly complete sample ever available obtained from surveys performed with Swift/BAT, MAXI, ASCA, XMM-Newton, Chandra, and ROSAT. The combined sample, including that of the Subaru/XMM-Newton Deep Survey, consists of 4039 detections in the soft (0.5-2 keV) and/or hard (>2 keV) band. We utilize a maximum likelihood method to reproduce the count rate versus redshift distribution for each survey, by taking into account the evolution of the absorbed fraction, the contribution from Compton-thick (CTK) AGNs, and broadband spectra of AGNs, including reflection components from tori based on the luminosity- and redshift-dependent unified scheme. We find that the shape of the XLF at z ∼ 1-3 is significantly different from that in the local universe, for which the luminosity-dependent density evolution model gives much better description than the luminosity and density evolution model. These results establish the standard population synthesis model of the X-ray background (XRB), which well reproduces the source counts, the observed fractions of CTK AGNs, and the spectrum of the hard XRB. The number ratio of CTK AGNs to the absorbed Compton-thin (CTN) AGNs is constrained to be ≈0.5-1.6 to produce the 20-50 keV XRB intensity within present uncertainties, by assuming that they follow the same evolution as CTN AGNs. The growth history of supermassive black holes is discussed based on the new AGN bolometric luminosity function.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Hubble space telescope observations and geometric models of compact multipolar planetary nebulae

We report high angular resolution Hubble Space Telescope observations of 10 compact planetary nebulae (PNs). Many interesting internal structures, including multipolar lobes, arcs, two-dimensional rings, tori, and halos, are revealed for the first time. These results suggest that multipolar structures are common among PNs, and these structures develop early in their evolution. From three-dimensional geometric models, we have determined the intrinsic dimensions of the lobes. Assuming the lobes are the result of interactions between later-developed fast winds and previously ejected asymptotic giant branch winds, the geometric structures of these PNs suggest that there are multiple phases of fast winds separated by temporal variations and/or directional changes. A scenario of evolution from lobe-dominated to cavity-dominated stages is presented. The results reported here will provide serious constraints on any dynamical models of PNs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

ON THE ANISOTROPY OF NUCLEI MID-INFRARED RADIATION IN NEARBY ACTIVE GALACTIC NUCLEI

In the center of active galactic nuclei (AGNs), the dusty torus absorbs the radiation from the central engine and reemits in mid-infrared (MIR). Observations have detected moderate anisotropy in the dust MIR emission, in the way that type 1 AGNs (type1s) are mildly brighter in MIR comparing with type 2 sources (type2s). However, type1s and type2s were found to follow statistically the same tight MIR-hard X-ray correlation, suggesting that the MIR emission is highly isotropic assuming that the hard X-ray radiation is inclination independent. We argue that this discrepancy could be solved considering that the hard X-ray emission in AGNs is also mildly anisotropic, as we recently discovered. To verify this diagram, we compare the subarcsecond 12 μm flux densities of type1s and type2s using the [O IV] λ25.89 μm emission line as an isotropic luminosity indicator. We find that on average type1s are brighter in nuclei 12 μm radiation by a factor of 2.6 ± 0.6 than type2s at given [O IV] λ25.89 μm luminosities, confirming the mild anisotropy of the nuclei 12 μm emission. We show that the anisotropy of the 12 μm emission we detected is in good agreement with radiative transfer models of clumpy tori. The fact that type1s and type2s follow the same tight MIR-hard X-ray correlation instead supports that both the MIR emission and hard X-ray emission in AGNs are mildly anisotropic.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

[O iii] λ5007 and X-ray properties of a complete sample of hard X-RAY selected AGNs in the local universe

We study the correlation between the [O iii] λ5007 and X-ray luminosities of local active galactic nuclei (AGNs), using a complete, hard X-ray (>10 keV) selected sample in the Swift/BAT 9-month catalog. From our optical spectroscopic observations at the South African Astronomical Observatory and the literature, a catalog of [O iii] λ5007 line flux for all 103 AGNs at Galactic latitudes of |b|>15{sup ∘} is compiled. Significant correlations with intrinsic X-ray luminosity (L{sub X}) are found for both observed (L{sub [O III] }) and extinction-corrected (L{sub [O III]}{sup cor}) luminosities, separately for X-ray unabsorbed and absorbed AGNs. We obtain the regression form of L{sub [O III] }∝ L{sub 2−10 keV}{sup 1.18±0.07} and L{sub [O III]}{sup cor} ∝ L{sub 2−10 keV}{sup 1.16±0.09} from the whole sample. The absorbed AGNs with low (<0.5%) scattering fractions in soft X-rays show on average smaller L{sub [O III]}/L{sub X} and L{sub [O III]}{sup cor}/L{sub X} ratios than the other absorbed AGNs, while those in edge-on host galaxies do not. These results suggest that a significant fraction of this population is buried in tori with small opening angles. By using these L{sub [O III] }versus L{sub X} correlations, the X-ray luminosity function (LF) of local AGNs (including Compton-thick AGNs) in a standard population synthesis model gives much better agreement with the [O iii] λ5007 LF derived from the Sloan Digital Sky Survey than previously reported. This confirms that hard X-ray observations are a very powerful tool to find AGNs with high completeness.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

RINGED ACCRETION DISKS: EQUILIBRIUM CONFIGURATIONS

We investigate a model of a ringed accretion disk, made up by several rings rotating around a supermassive Kerr black hole attractor. Each toroid of the ringed disk is governed by the general relativity hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. Properties of the tori can then be determined by an appropriately defined effective potential reflecting the background Kerr geometry and the centrifugal effects. The ringed disks could be created in various regimes during the evolution of matter configurations around supermassive black holes. Therefore, both corotating and counterrotating rings have to be considered as being a constituent of the ringed disk. We provide constraints on the model parameters for the existence and stability of various ringed configurations and discuss occurrence of accretion onto the Kerr black hole and possible launching of jets from the ringed disk. We demonstrate that various ringed disks can be characterized by a maximum number of rings. We present also a perturbation analysis based on evolution of the oscillating components of the ringed disk. The dynamics of the unstable phases of the ringed disk evolution seems to be promising in relation to high-energy phenomena demonstrated in active galactic nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗