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At least 127 records · Page 7

Low-dimensional de Sitter quantum gravity

We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering. Along the way, we show that JT gravity in dS2 is an analytic continuation of JT gravity in Euclidean AdS2, and that pure gravity in dS3 is a continuation of pure gravity in Euclidean AdS3. We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Detection of high-frequency gravitational waves using SRF cavities

Today, apart from some isolated R\&D efforts, there are no GW experiments, yet which explore a large part of the vast frequency range above the LIGO/Virgo band. It is planned to establish an experiment at DESY and Fermilab to search for high-frequency GWs in the frequency range of 10\,kHz to 100\,MHz. The basic idea is to use superconducting radiofrequency (SRF) cavities to detect tiny harmonic deformations induced by GWs which change the boundary conditions of the oscillating electromagnetic field. This paper summarizes the challenging environmental boundary requirements, and the R\&D to operate a cavity using a LLRF system which pushes beyond state-of-the-art accuracy and resolutions and a seismic noise mitigated cryostat at 1.8\,K. The focus of this paper is the warm and cold commissioning of a prototype cavity, built 20 years ago during the MAGO collaboration, and its first measurement in our collaborative research project.

Giaccone, Bianca [Fermilab]↗

Minkowski Functionals of SDSS-III BOSS: Hints of Possible Anisotropy in the Density Field?

We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with masked regions and survey boundaries, validating our methodology with Gaussian random fields and mock galaxy snapshot data. From the BOSS galaxy data, we generate a set of four density fields in three dimensions corresponding to the northern and southern skies of LOWZ and CMASS catalogs, smoothing over large scales (Gaussian smoothing scale of 35 Mpc) such that the field is perturbatively non-Gaussian. We extract the Minkowski functionals from each data set separately, and measure their shapes and amplitudes by fitting a Hermite polynomial expansion. For the shape parameter of the Minkowski functional curves a0, that is related to the bispectrum of the field, we find that the LOWZ-South data presents a systematically lower value of a 0 = –0.080 ± 0.040 than its northern sky counterpart a 0 = 0.032 ± 0.024. Although the significance of this discrepancy is not very high, it potentially indicates some systematics in the data or that the matter density field exhibits anisotropy at low redshift. By assuming a standard isotropic flat ΛCDM cosmology, the amplitudes of the Minkowski functionals from the combination of northern and southern sky data give the constraints Ω c h 2 n s = 0.110 ± 0.006 and 0.111 ± 0.008 for CMASS and LOWZ, respectively, which is in agreement with the Planck ΛCDM best-fit Ω c h 2 n s = 0.116 ± 0.001.

79 ASTRONOMY AND ASTROPHYSICS↗

Detection of high-frequency gravitational waves using SRF cavities

Today, apart from some isolated R&D efforts, there are no gravitational wave (GW) experiments, yet which explore a large part of the vast frequency range above the LIGO/Virgo band. It is planned to establish an experiment at Deutsches Elektronen-Synchrotron (DESY) and at the Superconducting Quantum Materials and Systems (SQMS) Center at Fermi National Accelerator Laboratory (Fermilab) to search for high-frequency GWs in the frequency range of 10 kHz to 100 MHz. The basic idea is to use superconducting radiofrequency (SRF) cavities to detect tiny harmonic deformations induced by GWs which change the boundary conditions of the oscillating electromagnetic field. This paper summarizes the challenging environmental boundary requirements, and the R&D to operate a cavity using a low level RF (LLRF) system which pushes beyond state-of-the-art accuracy and resolutions and a seismic noise mitigated cryostat at 1.8 K. The focus of this paper is the warm and cold commissioning of a prototype cavity, built 20 years ago during the MAGO collaboration, and its first measurement in our collaborative research project.

Wenskat, M. [DESY; Hamburg U.] (ORCID:000000016546↗

Effects of scattering on the field-induced T c enhancement in thin superconducting films in a parallel magnetic field

The problem of the normal-superconducting phase boundary for films in a parallel magnetic field, discussed in the classical paper by Ginzburg and Landau for temperatures close to the critical, is revisited with the help of the microscopic BCS theory for arbitrary temperatures taking pair-breaking and transport scattering into account. Although confirming experimental findings of the T c enhancement by the magnetic field, we find that the transport scattering pushes the phase transition curve to higher fields and higher temperatures for nearly all practical scattering rates. Still, the T c enhancement disappears in the dirty limit. Here, we also consider intriguing changes, such as reentrant superconductivity, caused to the phase boundary by pair-breaking magnetic ions spread on one of the film faces. These features await experimental verification.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Identifying Strain Stacking Boundaries between Multiphase Domains in Atomically Thin Two-Dimensional Magnets

Stacking engineering of van der Waals materials is an important strategy to control the materials’ properties, such as electronic correlations, ferroelectricity, and layer-dependent two-dimensional magnetism. A timely testbed for the study of the latter is atomically thin chromium trihalides (CrX 3 , X = Cl, Br, I). Notably, by understanding the sliding mechanism between different stacking sequences, control of the stacking arrangement, and thus magnetic properties in CrX 3 , can be achieved. Such insight, however, is currently lacking. Here, in this study, advanced electron microscopy methods are used to identify multiple stacking sequences corresponding to different bulk phases in atomically thin CrX 3 (X = Cl and Br) down to bilayer thickness and with lateral domain sizes as small as tens of nanometers. Indications of nanometer scale transitions and interactions at the stacking boundaries are found, including a universally preferred sliding direction that is consistent with density functional theory calculations and the strain fields at lateral heterostructure boundaries. This study demonstrates the necessity to consider local stacking structures when interpreting averaged magnetic properties measured with macroscale probes. Additionally, the preferred sliding direction insight from this study provides a strategy to control stacking sequence in atomically thin CrX 3 samples during the exfoliation and sample fabrication process.

DFT calculations↗

Plasma Wall Interaction with 3-D Plasma Boundaries

The interaction of the edge plasma and the material surfaces is one of the most critical challenges on the path to harness fusion power as new, fundamental energy source. This challenge typically combines the thrust to reach high density, low temperature (detached) plasmas in front of the divertor target plates as well as understanding the plasma material interaction (PMI) in particular in this regime. The combination of both research thrusts represents an extraordinarily challenging subject encompassing spatial scales spanning nanometers to meters in all states of matter and across a broad energy range. Modeling capabilities, which help to interpret data from nowadays experiments and enable extrapolation to future devices are urgently required. This is in particular true for toroidal magnetic confinement devices with three-dimensional (3D) plasma boundaries. Such plasma boundary geometries occur in tokamaks, when small amplitude magnetic perturbations are used to stabilize the unruly edge plasma or in stellarators, that are inherently 3D plasma confinement devices. In this project, the impact of 3D plasma boundaries on the plasma material interaction (PMI) was assessed. This work focused on plasma boundary conditions, in which high-density conditions at the material surfaces yield mitigation of the otherwise immense heat and particle loads that these materials would see. These so-called high recycling and eventually detached plasma regimes are of great interest for future reactor operation. In the project, key features that are unique to 3D boundaries were explored in comparison to canonically assumed axisymmetric plasma edge situations in tokamaks. In particular, the relevance of the 3D boundary situation in the extrapolation to the plasma boundary solution at ITER, the next step fusion energy experiment under construction as a multi-national, world-wide large-science experiment in southern France, has been explored. The EMC3-EIRENE plasma edge fluid and kinetic neutral transport code has been advanced to cope with the challenging and unprecedented conditions in the ITER boundary plasma including 3D fields that are planned to be used to suppress harmful edge instabilities, the so-called edge localized modes. This is a vital integration challenge for ITER and the results from this grant have provide a leading capability for this assessment. It was shown that the detachment process in a 3D edge solution for ITER follows the recycling regimes that are known from axisymmetric solutions, but that multiple plasma exhaust channels connected to the material surfaces are established which feature individual recycling characteristics. Because these channels touch the material surfaces in the divertor in a 3D geometry, the compatibility with the plasma material interaction (PMI), including erosion and impurity generation has been found to be an important part of the integration challenge. To address this, the fully 3D plasma material interaction code ERO2 has been adapted to these ITER specific geometries and a homogeneous mixing model was implemented, that allows to consider the mixing of Be and Was used at ITER in the PMI modeling. This model enhancement has been used to study non-local migration of Be in the JET ITER like wall configuration and it has been shown that with this model such complex migration processes in ITER relevant plasma shapes and with ITER relevant plasma boundary conditions can be addressed. The combined modeling approach using EMC3-EIRENE as a plasma boundary transport code and the ERO2 specialized PMI model will be an asset for the continued preparations of ITER operation as well as for Fusion Pilot Plant efforts that have emerged in the U.S. during the evolution of this grant. The predictive capability of this numerical tool has been validated at the DIII-D US national fusion facility. Here, dedicated plasma edge diagnostics were implemented to measure the impurity household around a 3D edge plasma during ELM suppression by 3D fields. Dedicated experiments with local material probes using these diagnostics and the state-of-the-art suite of boundary measurements at DIII-D have shown that the 3D perturbation of the plasma edge that is excreted by such 3D control fields yield a perturbation of the plasma boundary flux structure and hence also of the resulting PMI. The 3D boundary plasma is composed out of helical magnetic flux channels that intersect the divertor targets at an angle relative to the main guiding field, i.e., the toroidal magnetic field component of the tokamak. A similar effect has been measured as well on limiter surfaces during the startup campaign at the new stellarator experiment Wendelstein 7-X. These experiments ad initial analysis with the ERO plasma material interaction model, suggested that the place of erosion for a given particle from the surface and its re-deposition can be different in such 3D field geometries yielding potentially a significant level of net-erosion. This is not the case for axisymmetric solutions, where it was shown in the past that the eroded particles are effectively re-deposited into gaps produced by erosion at the same position and hence the net-erosion levels are small. For ITER, the quest to suppress the ELMs and at the same time maintain the integrity of the divertor is an issue, which these fundamental findings will help to resolve. The coupling of this work to the extrapolation in the ITER program has been addressed by both the PI and the lead numerical scientist being ITER Science Fellows in the duration of the contract and forward. A second focus in the exploration of 3D boundary effects on tokamaks and stellarators has been set on the measurement of helium exhaust features with such 3D fields. This is important because He represents the ash of the fusion process and needs to be exhausted. It was shown that 3D field application compatible with suppression of ELMs yields an increase of the helium exhaust performance. The ratio of the effective helium confinement time over the energy confinement time was reduced by almost 50% which demonstrated that the impact of helium accumulation in the plasma core with respect to the confinement of energy to sustain the fusion reaction is significantly improved with such 3D control fields. It was shown that this is the case for tokamaks as well as stellarators. At the Large helical Device in Japan, a similar enhancement of the helium exhaust features when small amplitude additional 3D fields were applied was measured. This is an important additional function of 3D field application and its impact on ITER is presently being studied in combination with investigations of helium exhaust in 3D field geometries of stellarator devices.

3D plasma edge transport↗

Phase-field modeling of radiation-induced composition redistribution: An application to additively manufactured austenitic Fe–Cr–Ni

Multicomponent alloys undergoing irradiation damage develop radiation-induced composition redistribution at point defect sinks such as grain boundaries (GBs) and dislocations. Such redistribution results in undesired changes to their mechanical behavior and corrosion resistance. Additively manufactured alloys proposed for future nuclear applications are expected to demonstrate a distinct response to irradiation owing to their unique microstructure with as-solidified dislocation density and chemical microsegregation. To capture the composition redistribution in such systems, we develop a mesoscale model with coupled evolution of atomic and point defect components in the presence of dislocation density, dislocation heterogeneity, and thermodynamic interactions at the GB. The model is parameterized for an FCC Fe–Cr–Ni alloy as a representative system for austenitic stainless steels, and simulations are performed in 1D and 2D as a function of irradiation temperature, dose, dislocation density, and grain size. Radiation-induced segregation (RIS) characterized by Cr depletion and Ni enrichment is predicted at both the GB and the dislocation cell wall, with RIS being lower in magnitude but wider at the cell wall. Strongly biased absorption of self-interstitials by dislocations is found to suppress Ni enrichment but slightly enhance Cr depletion under certain conditions. Thermodynamic segregation at the GB is predicted to be narrower and opposite in sign to RIS for both Cr and Ni. Importantly, non-monotonic segregation is found to occur when both thermodynamic and RIS mechanisms are considered, providing a novel physical interpretation of experimental observations. The model is expected to serve as a key tool in accelerated qualification of irradiated materials.

additively manufactured microstructure↗

The Effects of Field Line Curvature (FLC) Scattering on Ring Current Dynamics and Isotropic Boundary

Abstract In the ring current dynamics, various loss mechanisms contribute to the ring current decay, including losses to the upper atmosphere through particle precipitation. This study implements the field line curvature (FLC) scattering mechanism in a kinetic ring current model and investigates its role in precipitating ions into the ionosphere during the 17 March 2013 storm. Simulation results indicate that (1) the FLC scattering process exerts on energetic ions on the nightside where the magnetospheric configuration is more stretching. It is more effective on heavy ions (e.g., O + ). These ion losses thereafter lead to a faster recovery of the ring current. (2) The FLC‐associated ion precipitation mainly occurs in the outer region (L > 5 for protons and L > 4.5 for oxygen ions) on the nightside. The O + precipitation takes places in a wider region than protons although its intensity is much lower. Comparisons with POES observations suggest that more proton precipitation is needed in the inner region. This is probably caused by the less stretched configuration in the simulation that prevents more precipitation. It may also imply that other loss process is required in the model such as wave‐particle interactions. (3) The storm time precipitating proton flux of tens of keV due to the FLC scattering sometimes becomes comparable to that of electrons on the nightside, although electrons usually dominate the ionospheric energy deposition from the midnight eastward toward the dayside. (4) The FLC scattering process seems to be capable of explaining the formation of isotropic boundary in the ionosphere during the investigated event.

79 ASTRONOMY AND ASTROPHYSICS↗

Universal tripartite entanglement signature of ungappable edge states

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this Letter we argue that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information h(A:B)=S R (A:B)-I(A:B) between two parties, we argue that for A,B being adjacent subregions in the bulk h=$\frac{c+}{3}$ ln 2, where c + is the minimal total central charge of the boundary theory. As evidence, we prove that h=0 for string-net models and numerically verify that h=$\frac{|C|}{3}$ ln 2 for a Chern-C insulator. Our Letter establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

The collisionless plasma transport in stochastic magnetic fields connecting to wall boundary has been studied to understand the underlying mechanisms of thermal quench physics in tokamak disruption. In this study, we present a comprehensive understanding of the plasma dynamics in three-dimensional stochastic open magnetic field lines, taking into account the consistent coupling of electron and ion dynamics through the ambipolar electric field. The open stochastic field lines act as a 3D magnetic mirror consisting of the magnetic well and hill regions. It was found that the magnetic hill regions play a critical role in enhancing electron thermal transport. When the plasma collapses to the wall, the 3D ambipolar potential arises in the stochastic layer to maintain the quasi-neutrality of the plasma. The E × B vortices induced by the 3D ambipolar potential mix the plasma across stochastic field lines and enhance the radial transport. Particularly, the E × B mixing between the magnetic well and hill regions provides a collisionless detrapping mechanism that plays a major role in the loss of high-energy trapped electrons. As a result, the electron temperature steadily decreases at a rate of about -0.5 keV ms -1 , comparable to the rate observed in thermal quench experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extending the operational boundaries of RMP-ELM suppression with optimized 3D field control

The use of 3D magnetic fields is one of the promising approaches to control edge localized modes (ELMs), and ITER has plans to utilize a flexible 3D coil set for ELM suppression using 3D fields. This study focuses on optimizing the 3D field spectrum to expand the operational window for n = 1 resonant magnetic perturbation (RMP) ELM suppression in KSTAR. The optimized n = 1 RMP effectively suppresses ELMs throughout the entire H-mode discharge, including the first ELM crash, while avoiding the onset of disruptive locked modes in low-density L-mode plasmas. The predicted suppression window aligns well with experimental data, highlighting the challenges and solutions of using n = 1 RMP at low densities. Moreover, the optimization successfully achieved n = 1 RMP ELM suppression for the first time in ITER-relevant q 95 and shaping conditions, including cases with q95 as low as 3.6, as well as other q 95 and shape configurations. This highlights the importance and utility of 3D coil optimization while emphasizing the potential of long-wavelength low-n RMP, which will be valuable for ex-vessel coils designed to avoid complications of nuclear degradation.

3D magnetic field control↗

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies–the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Boundary conditions manipulation of polar vortex domains in BiFeO 3 membranes via phase-field simulations

Polar vortex domains have recently become an emergent research field due to the abundant physical phenomena and potential applications in high-density memories. Here, we explore the mechanisms of creating polar vortex domains in the BiFeO3 (BFO) membranes subjected to different boundary conditions using phase-field simulations. A major difference is that the vortex in membrane can be stabilized even under short-circuit electrical boundary conditions compared to vortex in other systems, such as thin film or superlattice. We found that (a) the formation of polar vortex domains at the membrane interior under bending is mainly driven by the reduction of elastic energy under short-circuit boundary condition, and the vortex chirality (namely, clockwise and counterclockwise) could be identified by n-shape and u-shape bending; (b) in the unbent open-circuit BFO membrane case, exotic trapezoid-shaped vortex nanodomains form at the terminations of 109 degrees domain walls (DWs) and partially charged 71 degrees DWs, which is driven by the local depolarization field and the interplay among electrostatic, elastic, and gradient and Landau energies. We also examine Kittel's law by establishing the dependence of vortex periods on the membrane thickness. Furthermore, these results give further understanding of the effect of boundary conditions on the formation of polar vortex domains, guiding experimental designs of vortex-based high-density memories.

36 MATERIALS SCIENCE↗

Qubit lattice algorithm simulations of the scattering of a bounded two dimensional electromagnetic pulse from an infinite planar dielectric interface

Qubit lattice algorithm (QLA) simulations are performed for a two-dimensional spatially bounded pulse propagating onto a plane interface between two dielectric slabs. QLA is an initial value scheme that consists of a sequence of unitary collision and streaming operators, with appropriate potential operators, that recover Maxwell equations in inhomogeneous dielectric media to the second order in the lattice discreteness. For the case of total internal reflection, there is transient energy transfer into the second medium due to the evanescent fields as the Poynting unit vector of the pulse is rotated from its incident to reflected direction. Because of the finite spatial extent of the pulse, a self-consistent Goos–Hanchen-type displacement along the interface is found without imposing any explicit interface boundary conditions on the fields. For normal incidence, the standard Fresnel coefficients are recovered for appropriately averaged QLA fields. Energy is conserved at all times to seven significant figures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Neural operator prediction of linear instability waves in high-speed boundary layers

Here, we investigate if neural operators can predict the linear evolution of instability waves in high-speed boundary layers. To this end, we extend the design of the DeepOnet to ensure accurate and robust predictions, and also to perform data assimilation. In particular, we train DeepONet to take as inputs an upstream disturbance and a downstream location of interest, and to provide as output the perturbation field downstream in the boundary layer. DeepONet thus approximates the linearized and parabolized Navier-Stokes operator for this flow. For successful application to the high-speed boundary layer problem, we add sample weighting and Fourier input features to the regular DeepONet formulation. Once trained, the DeepOnet can perform fast and accurate predictions of the downstream disturbances within the range of training frequencies (inside the distribution). In addition, we show that DeepONet can solve the inverse problem, where downstream wall measurements are adopted as input, and a trained network can predict the upstream disturbances that led to these observations. This capability, along with the forward predictions, allows us to perform a full data assimilation cycle efficiently: starting from wall-pressure data, we predict the upstream disturbance using the inverse DeepONet and its evolution using the forward DeepONet. Finally, we introduce three new metrics to benchmark the training, evaluation and break-even cost of neural operators.

42 ENGINEERING↗

Interface conformal anomalies

We consider two d ≥ 2 conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we compute the heat kernel coefficients and interface central charges in free theories. The results are consistent with the known boundary CFT data via the folding trick. In d = 4, two interface invariants generally allowed as anomalies turn out to have vanishing interface charges. These missing invariants are constructed from components with odd parity with respect to flipping the orientation of the defect. We conjecture that all invariants constructed from components with odd parity may have vanishing coefficient for symmetric interfaces, even in the case of interacting interface CFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Axion helioscopes as solar magnetometers

Axion helioscopes search for solar axions and axionlike particles via inverse Primakoff conversion in strong laboratory magnets pointed at the Sun. Anticipating the detection of solar axions, in this work, we determine the potential for the planned next-generation helioscope, the International Axion Observatory (IAXO), to measure or constrain the solar magnetic field. To do this we consider a previously neglected component of the solar axion flux at sub-keV energies arising from the conversion of longitudinal plasmons. This flux is sensitively dependent to the magnetic field profile of the Sun, with lower energies corresponding to axions converting into photons at larger solar radii. If the detector technology eventually installed in IAXO has an energy resolution better than 200 eV, then solar axions could become an even more powerful messenger than neutrinos of the magnetic field in the core of the Sun. For energy resolutions better than 10 eV, IAXO could access the inner 70% of the Sun and begin to constrain the field at the tachocline: the boundary between the radiative and convective zones. The longitudinal plasmon flux from a toroidal magnetic field also has an additional 2% geometric modulation effect which could be used to measure the angular dependence of the magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗