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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Current potential patches

A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element basis, called current potential patches. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 22% of the winding surface are sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is generated by an exterior coil set.

Elder, Todd↗
NASA NTRS2003

Embedded Wing Propulsion Conceptual Study

As a part of distributed propulsion work under NASA's Revolutionary Aeropropulsion Concepts or RAC project, a new propulsion-airframe integrated vehicle concept called Embedded Wing Propulsion (EWP) is developed and examined through system and computational fluid dynamics (CFD) studies. The idea behind the concept is to fully integrate a propulsion system within a wing structure so that the aircraft takes full benefits of coupling of wing aerodynamics and the propulsion thrust stream. The objective of this study is to assess the feasibility of the EWP concept applied to large transport aircraft such as the Blended-Wing-Body aircraft. In this paper, some of early analysis and current status of the study are presented. In addition, other current activities of distributed propulsion under the RAC project are briefly discussed.

Kim, Hyun D.↗
NASA NTRS2010

Dst Index in the 2008 GEM Modeling Challenge - Model Performance for Moderate and Strong Magnetic Storms

The GEM 2008 modeling challenge efforts are expanding beyond comparing in-situ measurements in the magnetosphere and ionosphere to include the computation of indices to be compared. The Dst index measures the largest deviations of the horizontal magnetic field at 4 equatorial magnetometers from the quiet-time background field and is commonly used to track the strength of the magnetic disturbance of the magnetosphere during storms. Models can calculate a proxy Dst index in various ways, including using the Dessler-Parker Sckopke relation and the energy of the ring current and Biot-Savart integration of electric currents in the magnetosphere. The GEM modeling challenge investigates 4 space weather events and we compare models available at CCMC against each other and the observed values of Ost. Models used include SWMF/BATSRUS, OpenGGCM, LFM, GUMICS (3D magnetosphere MHD models), Fok-RC, CRCM, RAM-SCB (kinetic drift models of the ring current), WINDMI (magnetosphere-ionosphere electric circuit model), and predictions based on an impulse response function (IRF) model and analytic coupling functions with inputs of solar wind data. In addition to the analysis of model-observation comparisons we look at the way Dst is computed in global magnetosphere models. The default value of Dst computed by the SWMF model is for Bz the Earth's center. In addition to this, we present results obtained at different locations on the Earth's surface. We choose equatorial locations at local noon, dusk (18:00 hours), midnight and dawn (6:00 hours). The different virtual observatory locations reveal the variation around the earth-centered Dst value resulting from the distribution of electric currents in the magnetosphere during different phases of a storm.

Rastaetter, Lutz↗
NASA NTRS1981

A four-dimensional primitive equation model for coupled coastal-deep ocean studies

A prototype four dimensional continental shelf/deep ocean model is described. In its present form, the model incorporates the effects of finite amplitude topography, advective nonlinearities, and variable stratification and rotation. The model can be forced either directly by imposed atmospheric windstress and surface pressure distributions, and energetic mean currents imposed by the exterior oceanic circulation; or indirectly by initial distributions of shoreward propagation mesoscale waves and eddies. To avoid concerns over the appropriate specification of 'open' boundary conditions on the cross-shelf and seaward model boundaries, a periodic channel geometry (oriented along-coast) is used. The model employs a traditional finite difference expansion in the cross-shelf direction, and a Fourier (periodic) representation in the long-shelf coordinate.

Haidvogel, D. B.↗
DOE OSTI2024

Distribution Grid Impact Study in Highland Park, Michigan: Understanding Rooftop Solar, Behind-the-Meter Energy Storage, Electric Vehicle Charging, and Building Electrification [Slides]

Through the Communities LEAP (Local Energy Action Program) Pilot, the National Renewable Energy Laboratory (NREL) engaged the Highland Park Stakeholder Coalition to scope four technical assistance work areas to address their energy needs and goals. This slide deck addresses the highlighted tasks under work area "B" related to policy analysis, due diligence, and case studies for removing barriers and providing best practices for local clean energy development. Highland Park community members face frequent, long-duration power interruptions due largely to the aging distribution system serving the area and the legacy design standards used in its construction. While degrading physical infrastructure such as poles, crossarms, and transformers can result in this substandard reliability, another notable characteristic of this legacy system is the lower, 4.8 kV, voltage class. This is a legacy construction standard which many utilities, DTE included, are phasing out in favor of higher, 15 or 25 kV, voltage classes instead. The existing 4.8 kV distribution system serving Highland Park may limit significant adoptions of clean-energy technologies like high percentages of building electrification or electric vehicle adoption. The following analysis seeks to quantify these limitations under a variety of clean-energy technology adoption scenarios. It compares the overall system risks of the present system to those of a hypothetical, upgraded 13.2 kV system, using NREL-developed risk metrics and offers upgrade cost considerations. The legacy 4.8 kV voltage class serving Highland park is not, as we have modeled it, a major limitation to the widespread adoption of cost-optimal rooftop solar and/or behind-the-meter energy storage. Within our modeling framework, these technologies namely impact secondary, low-voltage assets, which may be remedied without the need for a system-wide upgrade to a 13.2 kV voltage class. Our model of the current 4.8kV system indicates it is not capable of supporting community-wide electrification efforts. Widespread building electrification, and the resulting large increase in wintertime load, dramatically increases the prevalence of voltage violations and thermal overloading on the current 4.8 kV distribution system. These impacts illustrate the need for system-wide upgrades to a 13.2 kV voltage class to accommodate these technologies. Low to Moderate DER adoption does not adversely impact the grid but does improve undervoltage and asset overloading issues. However, these benefits are insufficient to defer grid upgrades. Higher DER penetration is shown to increase overvoltage and asset overloading in future electrification scenarios.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1995

Star formation activity in spiral galaxy disks and the properties of radio halos: Observational evidence for a direct dependence

In this article we address observationally the questions: how does star formation (SF) in the disks of galaxies lead to the creation of radio halos, and what minimum energy input into the interstellar medium (ISM) is needed to facilitate this? For the investigation we use a sample of five edge-on galaxies exhibiting radio continuum emmission in their halos and enhanced SF spread over large parts of their disks. In a detailed study of the two galaxies in our sample for which we have the best data, NGC 891 and NGC 4631, we show that the radio halos cut off abruptly at galactocentric radii smaller than those of the underlying thin radio disks. Our most important result is that the halo cutoffs are spatially coincident with the radii where the SF activity in the underlying disks drops sharply. The difference in radius of the emission distributions tracing ongoing SF in the disks (IRAS 50 micrometers, H alpha) versus that of the nonthermal radio continuum thin disks (tracing the distribution of cosmic-ray (CR) electrons) is typically a few kpc. This difference in extent is caused by CR diffusion. We have measured the CR diffusion coefficients in the thin disks of both NGC 891 and NGC 4631. For radial diffusion of CR electrons within the galactic disks the values are D(sub r) = 1.1-2.5 x 10 (exp 29) sq cm/s (NGC 4631) and D(sub r) = 1.2 x 10(exp 29) sq cm/s (NGC 891). For motions in the z-direction in areas within the thin disks where no outflows occur, we derive a firm upper limit of D(sub z) less than or equal to 0.2 x 10(exp 28) sq cm/s for NGC 891. The value for NGC 4631 is D(sub z = 1.4 x 10 (exp 28) sq cm/s. The other three galaxies in our sample, NGC 3044, NGC 4666, and NGC 5775 show (at the sensitivity of our data) less extended, more filamentary radio halos. Isolates spurs or filaments of nonthermal radio continuum emission in their halos are traced only above the most actively star-forming regions in the disks. This, in conjuction with the results obtained for NGC 891 and NGC 4631, suggests a direct connection between the shapes and radial extents of radio halos of normal galaxies and the level and the spatial distribution of the current SF in their disks. The existence of filamentary structures implies that expansion and convection of CR-heated plasma plays an important role even at low z-distances above the plane. Based on radio data we derive the disk-averaged mean energy input rates into the ISM due to supernova explosions per unit surface area in nine galaxies, including the ones in our sample. We find a clear trend in the sense that the galaxies with the highest mean energy input rates in the underlying disks have the most extended and pervasisve radio halos. Below a certain threshohld, outflows are inhibited. As a lower limit for this threshhold we derive an energy input rate of approximately 10 (exp -4) erg/s sq cm. The fact that radio halo emission is found only above the most luminous giant H 2 regions in late-type 'normal' galaxies (of type Sbc or later) indicates that only these are capable of initiating disk-halo interactions by locally exceeding the threshold. The distribution of the local outflows determines the overall shapes of the CR halos and leads to the observed filamentary structures.

Dahlem, Michael↗
NASA NTRS1997

The Nature and Evolutionary History of GRO J1744-28

GRO J1744-28 is the first known X-ray source to display bursts, periodic pulsations, and quasi-periodic oscillations. This source may thus provide crucial clues that will lead to an understanding of the differences in the nature of the X-ray variability from various accreting neutron stars. The orbital period is 11.8 days, and the measured mass function of 1.31 x 10(exp -4) solar mass is one of the smallest among all known binaries. If we assume that the donor star is a low-mass giant transferring matter through the inner Lagrange point, then we can show that its mass is lower than approximately 0.7 solar mass and probably closer to 0.25 solar mass. Higher mass, but unevolved, donor stars are shown to be implausible. We also demonstrate that the current He core mass of the donor star lies in the range of 0.20-0.25 solar mass. Thus, this system is most likely in the final stages of losing its hydrogen-rich envelope, with only a small amount of mass remaining in the envelope. If this picture is correct, then GRO J1744-28 may well represent the closest observational link that we have between the low-mass X-ray binaries and recycled binary pulsars in wide orbits. We have carried out a series of binary evolution calculations and explored, both systematically and via a novel Monte Carlo approach, the range of initial system parameters and input physics that can lead to the binary parameters of the present-day GRO J1744-28 system. The input parameters include both the initial total mass and the core mass of the donor star, the neutron-star mass, the strength of the magnetic braking, the mass-capture fraction, and the specifics of the core mass/radius relation for giants. Through these evolution calculations, we compute probability distributions for the current binary system parameters (i.e., the total mass, core mass, radius, luminosity, and K-band magnitude of the donor star, the neutron star mass, the orbital inclination angle, and the semimajor axis of the binary). Our calculations yield the following values for the GRO J1744-28 system parameters (with 95% confidence limits in parentheses): donor star mass: 0.24 solar mass (0.2-0.7 solar mass); He core mass of the donor star: 0.22 solar mass (0.20-0.25 solar mass); neutron-star mass: 1.7 solar mass (1.39-1.96 solar mass); orbital inclination angle: 18deg (7deg-22deg); semi- major axis: 64 lt-s (60-67 lt-s); radius of the donor star: 6.2 solar radius(6-9 solar radius); luminosity of donor star: 23 solar luminosity (15-49 solar luminosity), and long-term mass transfer rate at the current epoch: 5 x 10(exp -10)solar mass/yr (2 x 10(exp -10) to 5 x 10(exp -9)solar mass/yr). We deduce that the magnetic field of the underlying neutron star lies in the range of approximately 1.8 x 10(exp 11)G to approximately 7 x 10(exp 11)G, with a most probable value of 2.7 x 10(exp 11)G. This is evidently sufficiently strong to funnel the accretion flow onto the magnetic polar caps and suppress the thermonuclear flashes that would otherwise give rise to the type 1 X-ray bursts observed in most X-ray bursters. We present a simple paradigm for magnetic accreting neutron stars where X-ray pulsars, GRO J1744-28, the Rapid Burster, and the type 1 X-ray bursters may form a continuum of possible behaviors among accreting neutron stars, with the strength of the neutron-star magnetic field serving as a crucial parameter that determines the mode of X-ray variability from a given object.

Rappaport, S.↗
DOE OSTI2023

Automatic voltage regulation application for PV inverters in low-voltage distribution grids – A digital twin approach

This paper proposes a hierarchical coordinated control strategy for PV inverters to keep voltages in low-voltage (LV) distribution grids within specified limits. The top layer of the proposed architecture consists of the designed automatic voltage regulation (AVR) application, which has access to voltage measurements and grid parameters from the LV distribution grid, both current and historical. The AVR application solves a constrained optimization problem, which provides a set of local control set-points that bring the voltage across the grid within bounds. The middle layer consists of a local Volt/VAR controller, which is adjusted by the AVR app, while the bottom layer is the inner-loop controller of the PV inverter. The proposed method not only improves the voltage quality in the grid but also manages the reactive power outputs of PV inverters efficiently. Further, a digital twin of the cyber-physical system has also been employed that interacts with the control system to ensure its appropriate operation. The effectiveness of the proposed methodology is demonstrated on a representative low-voltage feeder located in Denmark.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2017

Vertical Profiles of Mars 1.27 Micrometer O2 Dayglow from MRO CRISM Limb Spectra: Seasonal/global Behaviors, Comparisons to LMDGCM Simulations, and a Global Definition for Mars Water Vapor Profiles

Since July of 2009, The Compact Reconnaissance Imaging Spectral Mapper (CRISM) onboard the Mars Re- connaissance Orbiter (MRO) has periodically obtained pole-to-pole observations (i.e., full MRO orbits) of limb scanned visible/near IR spectra (lambda= 0.4 - 4.0 micrometers, delta lambda approx. 10 nm- Murchie et al., 2007). These CRISM limb observations support the first seasonally and spatially extensive set of Mars 1.27 micometers O2 (1 delta(sub g)) day-glow profile retrievals (approx. 1100) over greater than or equal to 8-80 km altitudes. Their comparison to Laboratoire de Meteorologie Dynamique (LMD) global climate model (GCM) simulated O2 (1 delta(sub g)) volume emission rate (VER) profiles, as a function of altitude, latitude, and season (solar longitude, L(sub s), supports several key conclusions regarding Mars atmospheric water vapor (which is derived from O2 (1 delta(sub g)) emission rates), Mars O3, and the collisional de-excitation of O2 (1 delta(sub g)) in the Mars CO2 atmosphere. Current (Navarro et al., 2014) LMDGCM simulations of Mars atmospheric water vapor fall 2-3 times below CRISM derived water vapor abundances at 20-40 km altitudes over low-to-mid latitudes in northern spring (L(sub s) = 30-60 deg), and northern mid-to-high latitudes over northern summer (L(sub s) = 60-140 deg). In contrast, LMDGCM simulated water vapor is 2-5 times greater than CRISM derived values at all latitudes and seasons above 40 km, within the aphelion cloud belt (ACB), and over high-southern to mid-southern latitudes in southern summer (L(sub s) = 190-340 deg) at 15-35 km altitudes. Overall, the solstitial summer-to-winter hemisphere gradients in water vapor are reversed between the LMDGCM modeled versus the CRISM derived water vapor abundances above 10-30 km altitudes. LMDGCM-CRISM differences in water vapor profiles correlate with LMDGCM-CRISM differences in cloud mixing profiles; and likely reflect limitations in simulating cloud microphysics and radiative forcing, both of which restrict meridional transport of water from summer- to-winter hemispheres on Mars (Clancy et al., 1996; Montmessin et al., 2004; Steele et al., 2014; Navarro et al., 2014) and depend on uncertain cloud microphysical properties (Navarro et al., 2014). The derived low-to-mid latitude changes in Mars water vapor vertical distributions should reduce current model- data disagreements in column O3 and H2O2 abundances over low-to-mid latitudes (e.g., within the ACB; Lefevre et al., 2008; Encrenaz et al., 2015; Clancy et al., 2016). Lastly, the global/seasonal average com- parison of CRISM and LMDGCM O2 (1 delta(sub g)) VER below 20 km altitudes indicates a factor of approx. 3 times lower value (0.25 x 10(exp -20) cu cm sec(exp -1)) for the CO2 collisional de-excitation rate coefficient of O2 (1 delta(sub g)) than derived recently by Guslyakova et al. (2016).

Clancy, R. Todd↗
DOE OSTI2021

Along the Channel Gradients Impact on the Spatioactivity of Gas Diffusion Electrodes at High Conversions during CO 2 Electroreduction

Results of a 2-D transport model for a gas diffusion electrode performing CO 2 reduction to CO with a flowing catholyte are presented, including the concentration gradients along the flow cell, spatial distribution of the current density and local pH in the catalyst layer. The model predicts that both the concentration of CO 2 and the buffer electrolyte gradually diminish along the channels for a parallel flow of gas and electrolyte as a result of electrochemical conversion and nonelectrochemical consumption. At high single-pass conversions, significant concentration gradients exist along the flow channels leading to large local variations in the current density (>150 mA/cm 2 ), which becomes prominent when compared to ohmic losses. In addition, concentration overpotentials change dramatically with CO 2 flow rate, which results in significant differences in outlet concentrations at high conversions. The outlet concentration of CO attains a maximum of 80% along with 5% CO 2 and 15% H 2 , although the maximum single-pass conversion is limited to below 60% due to homogeneous consumption by the electrolyte. Fundamental and practical implications of our findings on electrochemical CO 2 reduction are discussed with a focus on the trade-off between high current density operation and high single-pass conversion efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Redshift evolution of the underlying type Ia supernova stretch distribution

The detailed nature of type Ia supernovae (SNe Ia) remains uncertain, and as survey statistics increase, the question of astrophysical systematic uncertainties arises, notably that of the evolution of SN Ia populations. We study the dependence on redshift of the SN Ia SALT2.4 light-curve stretch, which is a purely intrinsic SN property, to probe its potential redshift drift. The SN stretch has been shown to be strongly correlated with the SN environment, notably with stellar age tracers. We modeled the underlying stretch distribution as a function of redshift, using the evolution of the fraction of young and old SNe Ia as predicted using the SNfactory dataset, and assuming a constant underlying stretch distribution for each age population consisting of Gaussian mixtures. We tested our prediction against published samples that were cut to have marginal magnitude selection effects, so that any observed change is indeed astrophysical and not observational in origin. In this first study, there are indications that the underlying SN Ia stretch distribution evolves as a function of redshift, and that the age drifting model is a better description of the data than any time-constant model, including the sample-based asymmetric distributions that are often used to correct Malmquist bias at a significance higher than 5σ. The favored underlying stretch model is a bimodal one, composed of a high-stretch mode shared by both young and old environments, and a low-stretch mode that is exclusive to old environments. The precise effect of the redshift evolution of the intrinsic properties of a SN Ia population on cosmology remains to be studied. The astrophysical drift of the SN stretch distribution does affect current Malmquist bias corrections, however, and thereby the distances that are derived based on SN that are affected by observational selection effects. We highlight that this bias will increase with surveys covering increasingly larger redshift ranges, which is particularly important for the Large Synoptic Survey Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Plasma flows during the ablation stage of an over-massed pulsed-power-driven exploding planar wire array

We characterize the plasma flows generated during the ablation stage of an over-massed exploding planar wire array, fielded on the COBRA pulsed-power facility (1 MA peak current, 250 ns rise time). The planar wire array is designed to provide a driving magnetic field (80–100 T) and current per wire distribution (about 60 kA), similar to that in a 10 MA cylindrical exploding wire array fielded on the Z machine. Over-massing the arrays enables continuous plasma ablation over the duration of the experiment without implosion. The requirement to over-mass on the Z machine necessitates wires with diameters of 75–100μm, which are thicker than wires usually fielded on wire array experiments. To test ablation with thicker wires, we perform a parametric study by varying the initial wire diameter between 33 and 100 μm. The largest wire diameter (100 μm) array exhibits early closure of the cathode-wire gap, while the gap remains open over the duration of the experiment for wire diameters between 33 and 75 μm. Laser plasma interferometry and time-gated extreme-ultraviolet (XUV) imaging are used to probe the plasma flows ablating from the wires. The plasma flows from the wires converge to generate a pinch, which appears as a fast-moving (V≈100kms−1) column of increased plasma density (n¯e≈2×1018cm−3) and strong XUV emission. Finally, we compare the results with three-dimensional resistive-magnetohydrodynamic (MHD) simulations performed using the code GORGON, the results of which reproduce the dynamics of the experiment reasonably well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Diagnosing electric and magnetic fields in laser-driven coil targets

Laser-driven capacitor coils are widely used to generate intense magnetic fields for various applications in high-energy-density (HED) physics research. Accurate measurement of the magnetic fields is essential but challenging, due to the overlapping contributions from magnetic and electric fields in proton radiography, which is the primary tool diagnosing the field generation around the coils. In this study, we systematically analyze proton radiographs obtained from laser-driven capacitor-coil targets along two orthogonal axes under various electromagnetic field conditions, including magnetic field only, electric field only, and combined electromagnetic fields. By analyzing key features in the radiographs, we distinguish and characterize the respective contributions from magnetic and electric fields. Using detailed simulations validated by experimental benchmarks, methods to isolate and quantify the magnetic field and electric field are given. The methods are successfully applied to determine the electric current and charge distribution in a double coil configuration. Our findings provide insights into improving the diagnostic capability of proton radiography, potentially leading to more accurate measurements of electromagnetic fields and enhancing the utility of laser-driven capacitor coils in HED experiments.

electromagnetic field diagnostics↗
DOE OSTI2024

Vortex in superconducting thin-film strips of arbitrary width

We report the currents and field distributions of a vortex in a thin superconducting strip of a width W are considered. It is shown that unlike infinite films where the vortex field crosses the film only in one direction (say, from the half-space under the film to the half-space above it), in strips (as well as in finite size film samples of any shape) the field lines go back to the lower half-space not only out of the sample but also through certain strip parts. The strip patches where the magnetic lines 'dive' back to the space under the strip are situated mostly near the strip edges, at the strip and out of it. The magnetic flux through the strip associated with the vortex is shown to be less than the flux quantum and depends on the vortex position. The suppression of the vortex flux is strong in narrow strips with W $\ll$ Λ = 2λ 2 /d where λ is the bulk London penetration depth and d is the film thickness. The vortex energy scales roughly with W/Λ and depends on vortex position.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

The geometry of the ICRF-induced wave–SOL interaction. A multi-machine experimental review in view of the ITER operation

As a part of ITPA-Integrated Operational Scenario activities, this contribution reviews recent experimental characterizations of radio-frequency (RF)-induced scrape-off layer (SOL) modifications of various tokamaks worldwide and of the LArge Plasma Device at UCLA. The phenomenology, as observed using a large variety of measurement techniques, is consistent with expectations from RF sheath rectification. Emphasis is then put on the complex three-dimensional (3D) spatial patterns of the RF–SOL interaction, in relation to the magnetic topology and the spatial distribution of RF currents over the metallic structures surrounding the RF wave launchers. Dependence on the local plasma parameters in the antenna vicinity is also briefly addressed. The final part discusses implications for future devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Thermal control across a chain of electronic nanocavities

Here, we study a chain of alternating hot and cold electronic nanocavities—connected to one another via resonant-tunneling quantum dots—with the intent of achieving precise thermal control across the chain. This is accomplished by positioning the dots' energy levels such that a predetermined distribution of heat currents is realized across the chain in the steady state. The number of electrons in each cavity is conserved in the steady state which constrains the cavities' chemical potentials. We determine these chemical potentials analytically in the linear response regime where the energy differences between the dots' resonant levels and the neighboring chemical potentials are much smaller than the thermal energy. In this regime, the thermal control problem can be solved exactly, while, in the general case, thermal control can only be achieved in a relative sense, that is, when one only preassigns the ratios between different heat currents. We apply our results to two different cases: We first demonstrate that a “heat switch” can be easily realized with three coupled cavities, and then we show that our linear response results can provide accurate results in situations with a large number of cavities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗