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Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Rotation of electrothermal-instability-driven overheating structure due to helically oriented surface magnetic field on a high-current-density aluminum rod

Experiments on the 1-MA, 100-ns-rise-time Mykonos Facility demonstrate rotation of electrothermal instability (ETI)-driven overheating structure on 1.00-mm-diameter, 10-nm-surface roughness, 99.999%-pure aluminum rods, which are pulsed with helically polarized surface magnetic field. Rods are machined to include pairs of 10-micron-scale quasi-hemispherical voids or “engineered defects (ED)” which provide the dominant current density perturbation from which ETI grows most rapidly. Experiments include an axial magnetic field component through the addition of a helically wound return-current electrode or “helical return can (HRC).” For a given HRC design, azimuthal field (B ɵ ) and axial field (B z ) components rise at a prescribed and fixed ratio, driving an increasing magnetic field of constant polarization at the rod's surface; most experiments generated surface magnetic field at a 15-degree field polarization angle (from horizontal) defined as ɸ B = arctan(B z /B ɵ ). ETI-driven emission patterns from individual ED are observed to rotate along ɸ B , while emission patterns from dielectric-coated ED pairs are shown to elongate and preferentially merge along ɸ B , in qualitative agreement with 3D-magnetohydrodynamic simulations. These data strongly support that for a randomized distribution of current density perturbations on a high-current density conductor, nearby perturbations will favorably merge about ɸ B , with the degree of merging increasing with current. Such observations offer fundamental new understanding of the seeding mechanisms of the helical magneto-Rayleigh Taylor (MRT) instabilities observed from axially magnetized magnetically driven imploding liners.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SPONTANEOUS FORMATION OF SURFACE MAGNETIC STRUCTURE FROM LARGE-SCALE DYNAMO IN STRONGLY STRATIFIED CONVECTION

We report the first successful simulation of spontaneous formation of surface magnetic structures from a large-scale dynamo by strongly stratified thermal convection in Cartesian geometry. The large-scale dynamo observed in our strongly stratified model has physical properties similar to those in earlier weakly stratified convective dynamo simulations, indicating that the α {sup 2}-type mechanism is responsible for the dynamo. In addition to the large-scale dynamo, we find that large-scale structures of the vertical magnetic field are spontaneously formed in the convection zone (CZ) surface only in cases with a strongly stratified atmosphere. The organization of the vertical magnetic field proceeds in the upper CZ within tens of convective turnover time and band-like bipolar structures recurrently appear in the dynamo-saturated stage. We consider several candidates to be possibly be the origin of the surface magnetic structure formation, and then suggest the existence of an as-yet-unknown mechanism for the self-organization of the large-scale magnetic structure, which should be inherent in the strongly stratified convective atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

Technical and personal remembrances of David A. Shirley in studies of surface magnetism, photoelectron spectroscopy, EUV lithography, and hydrogen storage

This article describes the influence of Professor David A. Shirley on the research science of one of his Ph.D. students in the diverse areas of surface magnetism, x-ray photoelectron spectroscopy (XPS), spin-resolved XPS (SRXPS), extreme ultraviolet (EUV) lithography, and hydrogen storage materials science. Examples are given from the author's work on Cr(001) surface magnetism, XPS, and SRXPS studies of multiplet-splitting in core-level photoemission from Fe. In addition, Dave's influence in understanding the radiation-induced deposition of carbon on EUV optics is described, along with the use of XPS in deciphering how hydrogen storage materials are modified by repeated hydrogen adsorption/desorption cycling. The current status of these particular topics is briefly summarized. These technical remembrances are combined with some fond personal stories about Dave, in recognition of his passing on March 29, 2021.

Klebanoff, L. E.↗

Loss of relativistic electrons when magnetic surfaces are broken

Relativistic runaway electrons in ITER could be confined in a broad annulus of stochastic magnetic field lines bounded by an annulus of magnetic surfaces. The outer confining annulus can be broken by either an evolution of the magnetic field or by the drift of the plasma into the walls. Both possibilities are studied, and in both cases, the relativistic electrons in the stochastic region are lost to the walls in a short pulse of length $\tau$ ℓ along a narrow tube, which carries a flux f ψ st , where f ~ 10 -3 and ψ st is the toroidal flux in stochastic annulus. Both $\tau$ ℓ and f are determined by two parameters: the time it takes for a toroidal transit of a relativistic electron $\tau$ t = 2πR/c, which is approximately 0.1 μs in ITER, and the evolution time $\tau$ ev , which is of order 100 ms in most conditions of interest for ITER. The concept of turnstiles in Hamiltonian mechanics is then used to obtain the relation between $\tau$ ℓ and f and $\tau$ t and $\tau$ ev . The turnstile concept is also important in the theory of divertors for stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Surface Magnetism of Cobalt Nanoislands Controlled by Atomic Hydrogen

Controlling the spin states of the surface and interface is key to spintronic applications of magnetic materials. We report the evolution of surface magnetism of Co nanoislands on Cu(111) upon hydrogen adsorption and desorption with the hope of realizing reversible control of spin-dependent tunneling. Spin-polarized scanning tunneling microscopy reveals three types of hydrogen-induced surface superstructures, 1H-(2 × 2), 2H-(2 × 2), and 6H-(3 × 3), with increasing H coverage. The prominent magnetic surface states of Co, while being preserved at low H coverage, become suppressed as the H coverage level increases, which can then be recovered by H desorption. First-principles calculations reveal the origin of the observed magnetic surface states by capturing the asymmetry between the spin-polarized surface states and identify the role of hydrogen in controlling the magnetic states. This study offers new insights into the chemical control of magnetism in low-dimensional systems.

36 MATERIALS SCIENCE↗

Field lines and magnetic surfaces in a two-component slab/2D model of interplanetary magnetic fluctuations

A two-component model for the spectrum of interplanetary magnetic fluctuations was proposed on the basis of ISEE observations, and has found an intriguing level of application in other solar wind studies. The model fluctuations consist of a fraction of 'slab' fluctuations, varying only in the direction parallel to the locally uniform mean magnetic field B(0) and a complement of 2D (two-dimensional) fluctuations that vary in the directions transverse to B(0). We have developed an spectral method computational algorithm for computing the magnetic flux surfaces (flux tubes) associated with the composite model, based upon a precise analogy with equations for ideal transport of a passive scalar in planar two dimensional geometry. Visualization of various composite models will be presented, including the 80 percent 2D/ 20 percent slab model with delta B/B(0) approximately equals 1 and a minus 5/3 spectral law, that is thought to approximately represent a snapshot of solar wind turbulence. Characteristically, the visualizations show that flux tubes, even when defined as regular on some plane, shred and disperse rapidly as they are viewed along the parallel direction. This diffusive process, which generalizes the standard picture of field line random walk, will be discussed in detail. Evidently, the traditional picture that flux tubes randomize like strands of spaghetti with a uniform tangle along the axial direction is in need of modification.

Matthaeus, W. H.↗

Mercury's Surface Magnetic Field Determined from Proton-Reflection Magnetometry

Solar wind protons observed by the MESSENGER spacecraft in orbit about Mercury exhibit signatures of precipitation loss to Mercury's surface. We apply proton-reflection magnetometry to sense Mercury's surface magnetic field intensity in the planet's northern and southern hemispheres. The results are consistent with a dipole field offset to the north and show that the technique may be used to resolve regional-scale fields at the surface. The proton loss cones indicate persistent ion precipitation to the surface in the northern magnetospheric cusp region and in the southern hemisphere at low nightside latitudes. The latter observation implies that most of the surface in Mercury's southern hemisphere is continuously bombarded by plasma, in contrast with the premise that the global magnetic field largely protects the planetary surface from the solar wind.

loss cone↗

Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. In conclusion, the last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Surface magnetism of the carbon foam: An ab-initio theoretical study

By means of ab-initio calculations, we study the surface magnetism of carbon foam, a carbon allotrope constructed by both the sp{sup 2} and sp{sup 3} hybridized carbon atoms. It is found that the sp{sup 3}-terminated surface and sp{sup 2}-terminated surface with hydrogen saturation (sp{sup 2}H) have the antiferromagnetic and ferromagnetic ground states, respectively. And the corresponding phase transition temperatures of these two surfaces are estimated to exceed 100 K. In addition, the magnetic moment of the sp{sup 2}H surface can be effectively modulated by strain. More interestingly, at the level of generalized gradient approximation, as the lattice are stretched, a bulk bandgap will open. And in such a bandgap, the sp{sup 2}H surface states can form spin polarized Dirac cones at K(K′) point. Thus, in the vicinity of the Fermi level, only the electron with a specific spin behaves like a Dirac Fermion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Estimating Antarctic Near-Surface Magnetic Anomalies from Oersted and CHAMP Satellite Magnetometer Observations

Significant improvement in predicting near-surface magnetic anomalies can result from the highly accurate magnetic observations of the CHAMP satellite that is orbiting at about 400 km altitude. In general, regional magnetic signals of the crust are strongly masked by the core field and its secular variations due to wavelength coupling in the spherical harmonic representation and thus are difficult to isolate in the satellite measurements. However, efforts to isolate the regional lithospheric from core field components can exploit the correlations between the CHAMP magnetic anomalies and the pseudo magnetic effects inferred from gravity-derived crustal thickness variations. In addition, we can use spectral correlation theory to filter the static lithospheric field components from the dynamic external field effects. Employing these procedures, we processed the CHAMP magnetic conservations for an improved magnetic anomaly map of the Antarctic crust. Relative to the much higher altitude Oersted and noisier Magsat observations, CHAMP magnetic anomalies at 400 km altitude reveal new details on the effects of intra-crustal magnetic features and crustal thickness variations of the Antarctic. Moreover, these results greatly facilitate predicting magnetic anomalies in the regional coverage gaps of the ADMAP compilation of Antarctic magnetic anomalies from shipborne, airborne and ground surveys. Our analysis suggests that considerable new insights on the magnetic properties of the lithosphere may be revealed by a further order-of-magnitude improvement in the accuracy of the magnetometer.

vonFrese, Ralph R. B.↗

On the surface magnetic fields of rapidly rotating stars with winds

The consistency of estimates of angular velocities and magnetic field strength obtained from magnetic rotator models is examined. Upper and lower bounds for the surface magnetic field are derived with constraints of interior theory using magnetohydrodynamic considerations. The formulas for the bounds are applied to rapidly rotating Be stars and Wolf-Rayet type stars using Eddington-Vogt speed relevant for the radiative diffusion zone. It is suggested that stars which have equatorially enhanced winds driven by magnetic rotator effects must have fields such that the Aflven speed is close to the speed of the Eddington-Vogt currents at the base of the stellar atmosphere.

Maheswaran, Murugesapillai↗

A COUPLED 2 × 2D BABCOCK–LEIGHTON SOLAR DYNAMO MODEL. I. SURFACE MAGNETIC FLUX EVOLUTION

The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series of papers we present one such dynamo model, and document its behavior and properties. This first paper focuses on one of the model’s key components, namely surface magnetic flux evolution. Using a genetic algorithm, we obtain best-fit parameters of the transport model by least-squares minimization of the differences between the associated synthetic synoptic magnetogram and real magnetographic data for activity cycle 21. Our fitting procedure also returns Monte Carlo-like error estimates. We show that the range of acceptable surface meridional flow profiles is in good agreement with Doppler measurements, even though the latter are not used in the fitting process. Using a synthetic database of bipolar magnetic region (BMR) emergences reproducing the statistical properties of observed emergences, we also ascertain the sensitivity of global cycle properties, such as the strength of the dipole moment and timing of polarity reversal, to distinct realizations of BMR emergence, and on this basis argue that this stochasticity represents a primary source of uncertainty for predicting solar cycle characteristics.

79 ASTRONOMY AND ASTROPHYSICS↗

Contribution of Surface Magnetic Recordings to Planetary Exploration

The transient variations of the magnetic field at the surface of a planet has a primary external source, the interaction between the environment of the planet and solar radiation, and a secondary source, the electric currents induced in the conductive planet. The continuous recording of the time variations of the magnetic fields at the surface of Mars by means of three component magnetometers installed onboard landers would therefor allow the study of both the internal structure of Mars and the dynamic of its ionized environment.

magnetic field solar radiation Mars↗

Vector potential and surface magnetic field in magnetoelectric antiferromagnetic materials

A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. Here, for antiferromagnetic materials, the study reveals a unique relation between the macroscopic potential and the orientation-dependent magnetic quadrupole as a result of the different crystalline and magnetic symmetries. In particular, at surfaces and interfaces of a truncated bulk without inversion and time-reversal symmetries, the average vector potential exhibits a discontinuity which results in an interfacial magnetic field. In general, however, due to the surface and interface electronic and atomic relaxations, additional magnetization may result. For the experimentally observed magnetoelectric antiferromagnets, in particular, our symmetry analysis suggests that the relaxation effects could well be a system response to the presence of such a potential discontinuity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effective decolorization and adsorption of contaminant from industrial dye effluents using spherical surfaced magnetic (Fe{sub 3}O{sub 4}) nanoparticles

Treatment of highly concentrated Industrial dye stuff effluents released in the environment is the major issue faced in the era of waste management as well as in water pollution. Though there is availability of conventional techniques in large numbers, there is a need of efficient and effective advance technologies. In account of that, Nanotechnology plays a prominent role to treat the heavy metals, organic and inorganic contaminants using smart materials in nano regime (1 -100 nm). Among these nanomaterials like Iron Oxide (Fe{sub 3}O{sub 4}, magnetic nanoparticle) is one of the most promising candidates to remove the heavy metals from the industrial effluent. Fe{sub 3}O{sub 4} is the widely used smart material with magnetic property having high surface area; high surface to volume ratio provides more surface for the chemical reaction for the surface adsorption. Fe{sub 3}O{sub 4} nanoparticles have been synthesized using sonochemical method using ultra frequency in aqueous solution under optimized conditions. The as-synthesized nanoparticle was analyzed using different characterization tool. The Transmission Electron microscope (TEM) images revealed 10-12 nm spherical shape nanoparticles; crystal phase and surface morphology was confirmed by X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM), respectively. The functional group were identified by Fourier Transform-Infra Red Spectroscopy (FT-IR), revealed the bending and stretching vibrations associated with Iron Oxide nanoparticle. In present study, for the efficient removal of contaminants, different concentration (10-50 ppm) of dye stuff effluent has been prepared and subjected to adsorption and decolourization at definite time intervals with Fe{sub 3}O{sub 4} nanoparticles. The concentration of Iron oxide and the time (45 mins) was kept fixed for the reaction whereas the concentration of dye stuff effluent was kept varying. It was found that the spherical shaped Fe{sub 3}O{sub 4} proved to be the potential material for the adsorption of corresponding contaminants due to its highly active adsorbing surfaces. The result concluded that the effective adsorption and decolourization of contaminants is observed in different concentration with the maximum time period of 45 mins with the optimized concentration of Fe{sub 3}O{sub 4}.

54 ENVIRONMENTAL SCIENCES↗