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At least 145 records · Page 8

Icing Encounter Duration Sensitivity Study

This paper describes a study performed to investigate how aerodynamic performance degradation progresses with time throughout an exposure to icing conditions. It is one of the first documented studies of the effects of ice contamination on aerodynamic performance at various points in time throughout an icing encounter. Both a 1.5 and 6 ft chord, two-dimensional, NACA-23012 airfoils were subjected to icing conditions in the NASA Icing Research Tunnel for varying lengths of time. At the end of each run, lift, drag, and pitching moment measurements were made. Measurements with the 1.5 ft chord model showed that maximum lift and pitching moment degraded more rapidly early in the exposure and degraded more slowly as time progressed. Drag for the 1.5 ft chord model degraded more linearly with time, although drag for very short exposure durations was slightly higher than expected. Only drag measurements were made with the 6 ft chord airfoil. Here, drag for the long exposures was higher than expected. Novel comparison of drag measurements versus an icing scaling parameter, accumulation parameter times collection efficiency was used to compare the data from the two different size model. The comparisons provided a means of assessing the level of fidelity needed for accurate icing simulation.

Addy, Harold E., Jr.↗

The response of the Goddard general circulation model to sea ice boundary conditions

The effect of variation in the location of Arctic sea ice boundaries on the model's mean monthly climatology was examined. When sea ice boundaries were at their maximum extent the differences resulted in the January-February climatology. Sea level pressure was higher over the Barents Sea, in the Davis Strait, and in the Sea of Okhotsk. Pressure was lower by as much as 8 mb in the North Atlantic between Iceland and the British Isles, and in the Gulf of Alaska. Pressure rises in the eastern subtropical regions of the North Atlantic and North Pacific accompanied pressure falls in the Gulf of Alaska and Icelandic region. Geopotential heights at 500 mb were more than 100 gpm lower in the Bering Sea, and more than 120 gpm lower in the Icelandic region. Zonally averaged temperatures were cooler by 4 deg C below 3800 mb between 50 deg and 70 deg N with little change elsewhere. Zonally averaged geopotentials were lower by as much as 70 gpm in the mid-troposphere between 50/-70 deg N and zonal winds increased by as much as 3 m s in the mid-troposphere between 35/-50 deg N.

Herman, G.↗

The Effect of Ice Formations on Propeller Performance

Measurements of propeller efficiency loss due to ice formation are supplemented by an analysis to establish the magnitude of efficiency losses to be anticipated during flight in icing conditions. The measurements were made during flight in natural icing conditions; whereas the analysis consisted of an investIgation of changes in blade-section aerodynamic characteristics caused by ice formation and the resulting propeller efficiency changes. Agreement in the order of magnitude of eff 1- ciency losses to be expected is obtained between measured and analytical results. The results indicate that, in general, efficiency losses can be expected to be less than 10 percent; whereas maximum losses, which will be encountered only rarely, may be as high as 15 or 20 percent. Reported. losses larger than 15 or 20 percent, based on reductions in airplane performance, probably are due to ice accretions on other parts of the airplane. Blade-element theory is used in the analytical treatment, and calculations are made to show the degree to which the aerodynamic characteristics of a blade section. must be altered to produce various propeller efficiency losses. The effects of ice accretions on airfoil-section characteristics at subcritical speeds and their influence on drag-divergence Mach number are examined, and. the attendant maximum efficiency losses are computed. The effect of kinetic heating on the radial extent of ice formation is considered, and its influence on required length of blade heating shoes is discussed. It is demonstrated how the efficiency loss resulting from an icing encounter is influenced by the decisions of the pilot in adjusting the engine and propeller controls.

Neel, C. B., Jr.↗

Evaluate the application of ERTS-A data for detecting and mapping sea ice

The author has identified the following significant results. The results of the analysis of data collected during the spring and summer demonstrate that ERTS-1 imagery has a high potential for monitoring arctic sea ice conditions during the time for maximum ice extent through ice-breakup season. In the eastern Beaufort Sea area, the combination of ERTS-1 orbital overlap and a high incidence of cloud-free conditions during the spring assures a high frequency of repetitive satellite coverage. In the mid-Beaufort Sea, numerous fractures and leads can be identified, even in the early spring data. Ice features that can be identified include: development of fractures leading to the formation of distinct ice floes; growth and deterioration of leads; evidence of shearing movements of ice masses; formation of new grey ice within leads; distinction between grey, grey-white, and older forms of ice; and the deterioration of the ice surface evidenced by the formation of puddles, thaw holes, and drainage patterns. Ice conditions in the Bering Sea near St. Lawrence Island reported by aircraft observers participating in the Bering Sea Expedition are in close agreement with the ice conditions mapped from the corresponding ERTS-1 imagery. Ice features identified were: boundaries between grey ice and first year ice, shear leads, and occurrence of open water.

Barnes, J. C.↗

Computational Icing Analysis on NASA’s SIDRM Geometry to Investigate Collection Efficiency

Computational icing analysis results were compared to experimental icing tunnel data including aerothermal (e.g. dry air) and supercooled water droplet rime-ice conditions from tests conducted in early 2022 at the NASA Icing Research Tunnel (IRT). The Simulated Intercompressor Duct Research Model (SIDRM) test article was used in this study, and its geometry represents the inter-compressor duct region of a turbofan engine. The test article’s purpose is to study the physics of supercooled water icing and ice crystal icing. This study compared three different icing codes: FENSAP-ICE (Eulerian approach), LEWICE3D (Lagrangian approach), and GlennICE (Lagrangian approach). All three icing codes were conducted on SIDRM’s complex body flow-field and compared to different experimental supercooled water rime runs. The test article instrumentation (pressure taps, thermocouples, etc.) and 3D laser scans of final ice shapes were used to compare against the different icing code simulations. The overall objectives are to understand how the icing codes handle capturing collection efficiency on the complex test article’s unheated surfaces. In the aerothermal cases, pressure tap readings matched the CFD results, but dry air CFD underpredicted thermocouple readings. Collection efficiency results from all three icing codes matched well together on the main body leading edge, main body slope, and the strut leading edges. All three icing codes underpredicted the final ice shape using a single-shot constant ice density approach, with more difficulty coming from the strut leading edge ice shape due to the swept wing like flow field. NASA’s overall goal for this effort is to develop computational icing tools to assist in the design and certification of engines for flight in icing conditions.

Supercooled icing, SIDRM, aerodynamics, computatio↗

The Potential of Using Landsat 7 Data for the Classification of Sea Ice Surface Conditions During Summer

During spring and summer, the Surface of the Arctic sea ice cover undergoes rapid changes that greatly affect the surface albedo and significantly impact the further decay of the sea ice. These changes are primarily the development of a wet snow cover and the development of melt ponds. As melt pond diameters generally do not exceed a couple of meters, the spatial resolutions of sensors like AVHRR and MODIS are too coarse for their identification. Landsat 7, on the other hand, has a spatial resolution of 30 m (15 m for the pan-chromatic band). The different wavelengths (bands) from blue to near-infrared offer the potential to distinguish among different surface conditions. Landsat 7 data for the Baffin Bay region for June 2000 have been analyzed. The analysis shows that different surface conditions, such as wet snow and meltponded areas, have different signatures in the individual Landsat bands. Consistent with in-situ albedo measurements, melt ponds show up as blueish whereas dry and wet ice have a white to gray appearance in the Landsat true-color image. These spectral differences enable the distinction of melt ponds. The melt pond fraction for the scene studied in this paper was 37%.

Markus, Thorsten↗

Simulation Tools Model Icing for Aircraft Design

Here s a simple science experiment to try: Place an unopened bottle of distilled water in your freezer. After 2-3 hours, if the water is pure enough, you will notice that it has not frozen. Carefully pour the water into a bowl with a piece of ice in it. When it strikes the ice, the water will instantly freeze. One of the most basic and commonly known scientific facts is that water freezes at around 32 F. But this is not always the case. Water lacking any impurities for ice crystals to form around can be supercooled to even lower temperatures without freezing. High in the atmosphere, water droplets can achieve this delicate, supercooled state. When a plane flies through clouds containing these droplets, the water can strike the airframe and, like the supercooled water hitting the ice in the experiment above, freeze instantly. The ice buildup alters the aerodynamics of the plane - reducing lift and increasing drag - affecting its performance and presenting a safety issue if the plane can no longer fly effectively. In certain circumstances, ice can form inside aircraft engines, another potential hazard. NASA has long studied ways of detecting and countering atmospheric icing conditions as part of the Agency s efforts to enhance aviation safety. To do this, the Icing Branch at Glenn Research Center utilizes a number of world-class tools, including the Center s Icing Research Tunnel and the NASA 607 icing research aircraft, a "flying laboratory" for studying icing conditions. The branch has also developed a suite of software programs to help aircraft and icing protection system designers understand the behavior of ice accumulation on various surfaces and in various conditions. One of these innovations is the LEWICE ice accretion simulation software. Initially developed in the 1980s (when Glenn was known as Lewis Research Center), LEWICE has become one of the most widely used tools in icing research and aircraft design and certification. LEWICE has been transformed over the years from strictly a research tool to one used routinely by industry and other government agencies. Glenn contractor William Wright has been the architect of this development, supported by a team of researchers investigating icing physics, creating validation data, and ensuring development according to standard software engineering practices. The program provides a virtual simulation environment for determining where water droplets strike an airfoil in flight, what kind of ice would result, and what shape that ice would take. Users can enter geometries for specific, two-dimensional cross sections of an airfoil or other airframe surface and then apply a range of inputs - different droplet sizes, temperatures, airspeeds, and more - to model how ice would build up on the surface in various conditions. The program s versatility, ease of use, and speed - LEWICE can run through complex icing simulations in only a few minutes - have contributed to it becoming a popular resource in the aviation industry.

Source record↗

Characterization of Ice Roughness From Simulated Icing Encounters

Detailed measurements of the size of roughness elements on ice accreted on models in the NASA Lewis Icing Research Tunnel (IRT) were made in a previous study. Only limited data from that study have been published, but included were the roughness element height, diameter and spacing. In the present study, the height and spacing data were found to correlate with the element diameter, and the diameter was found to be a function primarily of the non-dimensional parameters freezing fraction and accumulation parameter. The width of the smooth zone which forms at the leading edge of the model was found to decrease with increasing accumulation parameter. Although preliminary, the success of these correlations suggests that it may be possible to develop simple relationships between ice roughness and icing conditions for use in ice-accretion-prediction codes. These codes now require an ice-roughness estimate to determine convective heat transfer. Studies using a 7.6-cm-diameter cylinder and a 53.3-cm-chord NACA 0012 airfoil were also performed in which a 1/2-min icing spray at an initial set of conditions was followed by a 9-1/2-min spray at a second set of conditions. The resulting ice shape was compared with that from a full 10-min spray at the second set of conditions. The initial ice accumulation appeared to have no effect on the final ice shape. From this result, it would appear the accreting ice is affected very little by the initial roughness or shape features.

Anderson, David N.↗

Piloted Simulation to Evaluate the Utility of a Real Time Envelope Protection System for Mitigating In-Flight Icing Hazards

The utility of the Icing Contamination Envelope Protection (ICEPro) system for mitigating a potentially hazardous icing condition was evaluated by 29 pilots using the NASA Ice Contamination Effects Flight Training Device (ICEFTD). ICEPro provides real time envelope protection cues and alerting messages on pilot displays. The pilots participating in this test were divided into two groups; a control group using baseline displays without ICEPro, and an experimental group using ICEPro driven display cueing. Each group flew identical precision approach and missed approach procedures with a simulated failure case icing condition. Pilot performance, workload, and survey questionnaires were collected for both groups of pilots. Results showed that real time assessment cues were effective in reducing the number of potentially hazardous upset events and in lessening exposure to loss of control following an incipient upset condition. Pilot workload with the added ICEPro displays was not measurably affected, but pilot opinion surveys showed that real time cueing greatly improved their situation awareness of a hazardous aircraft state.

Ranaudo, Richard J.↗

Impact Ice Adhesion at NASA Glenn: Current Experimental Methods and Supporting Measurements

When examining the literature on the adhesion strength of impact ice, there have been a wide range of methodologies tried to measure the required stresses to induce interfacial delamination. Utilizing the Icing Research Tunnel at the NASA Glenn Research Center to generate the impact ice required for this work, several different mechanical tests have been and are being developed to determine the stresses along the interface between ice and coupon. This set of tests includes the technical mature modified lap joint test which has been used to conduct ice adhesion studies through a wide sweep of icing conditions. To conduct in situ ice adhesion measurements inside of the Icing Research Tunnel, several new experiments are currently being developed to make ice adhesion measurements during and immediately after ice accretion. In addition to these experimental methods, several supporting measurement techniques have been developed to allow for a better understanding on the influence of icing cloud conditions on the mechanical behavior of impact ice. Digital image correlation has been successfully implemented to augment the data generated by the modified lap joint test with full field surface displacement and strain measurements which allow for insight into the deformation processes present during a test. Both optical microscopy of impact ice samples along with ice replication techniques have been used to study the grain structure of the impact ice. This has led to a deeper understanding of the results from the modified lap joint method and how the structure of impact ice changes as it is accreted during an icing spray. The freezing process of impact ice generated by supercooled liquid water is not a volume conserving process, which leads to the presence of residual strains along the interface between ice and substrate. These strains have been observed using both a simplified flat geometry and a representative airfoil. The data gathered by these experimental adhesion methods and supporting measurements allows for a comprehensive understanding on the behavior of impact ice which will be critical to the development of future ice shedding models.

Ice Adhesion↗

Impact Ice Adhesion at NASA Glenn: Current Experimental Methods and Supporting Measurements

When examining the literature on the adhesion strength of impact ice, there have been a wide range of methodologies tried to measure the required stresses to induce interfacial delamination. Utilizing the Icing Research Tunnel at the NASA Glenn Research Center to generate the impact ice required for this work, several different mechanical tests have been and are being developed to determine the stresses along the interface between ice and coupon. This set of tests includes the technical mature modified lap joint test which has been used to conduct ice adhesion studies through a wide sweep of icing conditions. To conduct in situ ice adhesion measurements inside of the Icing Research Tunnel, several new experiments are currently being developed to make ice adhesion measurements during and immediately after ice accretion. In addition to these experimental methods, several supporting measurement techniques have been developed to allow for a better understanding on the influence of icing cloud conditions on the mechanical behavior of impact ice. Digital image correlation has been successfully implemented to augment the data generated by the modified lap joint test with full field surface displacement and strain measurements which allow for insight into the deformation processes present during a test. Both optical microscopy of impact ice samples along with ice replication techniques have been used to study the grain structure of the impact ice. This has led to a deeper understanding of the results from the modified lap join method and how the structure of impact ice changes as it is accreted during an icing spray. The freezing process of impact ice generated by supercooled liquid water is not a volume conserving process, which leads to the presence of residual strains along the interface between ice and substrate. These strains have been observed using both a simplified flat geometry and a representative airfoil. The data gathered by these experimental adhesion methods and supporting measurements allows for a compressive understanding on the behavior of impact ice which will be critical to the development of future ice shedding models.

Ice Adhesion↗

Methods for Scaling Icing Test Conditions

This report presents the results of tests at NASA Lewis to evaluate several methods to establish suitable alternative test conditions when the test facility limits the model size or operating conditions. The first method was proposed by Olsen. It can be applied when full-size models are tested and all the desired test conditions except liquid-water content can be obtained in the facility. The other two methods discussed are: a modification of the French scaling law and the AEDC scaling method. Icing tests were made with cylinders at both reference and scaled conditions representing mixed and glaze ice in the NASA Lewis Icing Research Tunnel. Reference and scale ice shapes were compared to evaluate each method. The Olsen method was tested with liquid-water content varying from 1.3 to .8 g/m(exp3). Over this range, ice shapes produced using the Olsen method were unchanged. The modified French and AEDC methods produced scaled ice shapes which approximated the reference shapes when model size was reduced to half the reference size for the glaze-ice cases tested.

Anderson, David N.↗

Improving the Simulation of Sea Ice Lead Conditions and Turbulent Fluxes Using RGPS Products and Merged RADARSAT, AVHRR and MODIS Data

The importance of sea ice leads in the ice-ocean-atmosphere system lies in the fact that each of the boxes in the 'surface processes' interface in this diagram is closely linked to lead conditions. For example, heat, moisture and salt exchange between the Ocean and atmosphere within the ice pack occur nearly entirely through leads. The shear, divergence and convergence associated with lead formation and closure alter surface and basal roughness and topography, which in turn affects momentum transfer in the atmosphere and ocean boundary layers, and modifies the accumulation of snow on the ice surface, which then affects heat conduction and summertime albedo. In addition to providing openings for loss of heat and moisture fluxes to the atmosphere, leads absorb solar energy, which is used to melt ice and is transmitting to the underlying ocean. Given that leads dominate the ice-ocean interface in this manner, then it stands to reason that focusing on lead treatments within models can identify performance limitations of models and yield routes for significant improvements.

Maslanik, James A.↗

Measured Interfacial Residual Strains Produced by In-Flight Ice

The formation of ice on aircraft is a highly dynamic process during which ice will expand and contract upon freezing and undergoing changes in temperature. Finite Element Analysis (FEA) simulations were performed investigating the stress build up in a simplified case with uniform temperature changes between an idealized ice sample and acrylic substrate. These results were used to place strain gages on custom-built acrylic and aluminum specimens; these specimens were then placed in icing conditions such that ice was grown on top of the specimen. Tee rosettes were placed in two configurations adjacent to thermocouple sensors. It was hypothesized that the ice would expand on freezing and contract as the temperature of the interface returned to the equilibrium conditions. While results from the aluminum specimens matched this hypothesis, results from the acrylic specimens show a short period of contraction followed by a much larger expansion at the interface, indicating more complex ice growth thermodynamics than anticipated. Samples were observed to delaminate, and the data suggests that the residual strain is significant to the shedding of ice for in-flight applications.

residual strain↗

Understanding the Transport Properties of Methane–Hydrogen Mixtures under the Interior Conditions of Ice Giants

Inaccuracy in our knowledge of the transport properties of relevant mixtures under planetary interior conditions is a roadblock in predicting the observable properties of planets in our solar system and beyond. In this work, we investigate methane–hydrogen mixtures using data sets obtained from density functional theory calculations for the electronic structure, combined with molecular dynamics simulations for the ions for a wide range of pressure and temperature. Hydrogen concentration significantly affects the equation of state (EOS) but has little influence on transport properties. We provide an analytical expression to model thermal EOS and transport properties as a function of hydrogen content, with the maximum deviation observed at low P–T conditions. These insights are particularly relevant to improve the planetary models and enhance our ability to predict the properties of “ice” giants and beyond.

Methane↗

Icing Physics Studies Using the 3D SIDRM Test Article: Aerodynamic and Supercooled Liquid Icing Analysis

In-flight icing is an important safety issue and is a factor that affects aircraft design and performance. Newer regulations are driving a need for improvements in airframe and engine icing simulation capability. Experimental data is required for development of icing physics models and simulation validation. To that end, this paper presents the analysis of the supercooled liquid icing data subset from tests conducted in 2022 at the NASA Icing Research Tunnel that studied both supercooled water and ice-crystal icing. The test article that was utilized replicated 3D geometrical features of an inter-compressor duct and strut region of a turbofan engine. The surfaces of the Simulated Inter-compressor Duct Research Model (SIDRM) can be heated to simulate the warm surfaces of the turbofan inter-compressor duct. The test article is instrumented with pressure taps, heaters, heat flux gauges, and thermocouples, while a 3D laser scanner, cameras, and a scale to measure ice mass were utilized to characterize the icing behavior. The aim of these tests was to generate ice accretions on the SIDRM test article under well-characterized supercooled liquid icing and ice crystal icing conditions. This paper discusses measurements related to aerodynamic testing and supercooled liquid icing tests that were conducted. Aerodynamic measurements were analyzed and compared to computational simulations and were found to be in good agreement for the range of airspeeds (50 to 230 knots) and angles of attack (0 to 4°) tested. Various parametric sweeps were conducted during the supercooled liquid icing portion of the test entry (cloud median volumetric diameter ranged from 15 to 90 µm, total air temperature from -3 to -17 °C, angle of attack from 0 to 4°, and accretion time from 5 to 20 min). These sweeps were performed to measure that parameter’s impact on ice accretion size, location (icing extent), characteristics (such as glaze/rime ice and shedding behavior), and test article surface temperature. Analysis of the test data showed that clouds composed of larger drops, colder air temperatures, smaller angles of attack, and longer spray times were the primary parameters that resulted in accretions with greater ice mass. Test article angle of attack and cloud droplet size influenced the location of ice accretion as these two parameters directly impact collection efficiency. With respect to icing characteristics, total air temperature dictated icing type, and smaller cloud drop size along with warmer air temperatures resulted in greater amounts of ice shedding. Surface temperature increased during ice accretion from the release of latent (fusion) heat, where total air temperature and cloud drop size impacted the amount of surface temperature change. The icing measurements collected during the SIDRM tests will be used to develop and validate 3D computational engine icing tools, such as GlennICE, that predictively assesses the onset and growth of ice. One of the goals of the sponsoring NASA project is to develop simulation models and tools that can assist in the design and certification of engines for flight in icing conditions in a cost effective way.

supercooled liquid icing↗

Icing Physics Studies Using the 3D SIDRM Test Article: Aerodynamic and Supercooled Liquid Icing Analysis

In-flight icing is an important safety issue and is a factor that affects aircraft design and performance. Newer regulations are driving a need for improvements in airframe and engine icing simulation capability. Experimental data is required for development of icing physics models and simulation validation. To that end, this paper discusses analyzed data from icing tests conducted with a 3D test article in 2022 at the NASA Icing Research Tunnel. The test article, whose geometry is representative of an inter-compressor duct and strut region of a turbofan engine, has been designed and constructed to study the physics of supercooled water icing and ice crystal icing. The surfaces of the Simulated Inter-compressor Duct Research Model (SIDRM) can be heated to simulate the warm surfaces of the turbofan inter-compressor duct. The test article is instrumented with pressure taps, heaters, heat flux gauges, and thermocouples, while a 3D laser scanner, cameras, and a scale to measure ice mass were utilized to characterize the icing behavior. The aim of these tests was to generate ice accretions on the SIDRM test article under well-characterized supercooled liquid icing and ice crystal icing conditions. This paper discusses measurements related to aerodynamic tests and supercooled liquid icing tests that were conducted. Aerodynamic measurements were analyzed and compared to computational simulations and were found to be in good agreement for the range of airspeeds (50 to 230 knots) and angles of attack (0 to 4°) tested. Various parametric sweeps were conducted during the supercooled liquid icing portion of the test entry (cloud median volumetric diameter ranged from 15 to 90 µm, total air temperature from -3 to -17 °C, angle of attack from 0 to 4°, and accretion time from 5 to 20 min). These sweeps were performed to measure that parameter’s impact on ice accretion size, location, characteristics (such as glaze/rime ice and shedding behavior), and test article surface temperature. Analysis of the test data showed that clouds composed of larger drops, colder air temperatures, smaller angles of attack, and longer spray times were the primary parameters that resulted in accretions with greater ice mass. Test article angle of attack and cloud droplet size influenced the location of ice accretion as these two parameters directly impact collection efficiency. With respect to icing characteristics, total air temperature dictated icing type, and smaller cloud drop size along with warmer air temperatures resulted in greater amounts of ice shedding. Surface temperature increased during ice accretion from the release of latent (fusion) heat, where total air temperature and cloud drop size impacted the amount of surface temperature change. The icing measurements collected during the SIDRM tests will be used to develop and validate 3D computational engine icing tools, such as GlennICE, that predictively assesses the onset and growth of ice. One of the goals of the sponsoring NASA project is to develop simulation models and tools that can assist in the design and certification of engines for flight in icing conditions in a cost‑effective way.

supercooled liquid icing↗

Dynamic compression of water to conditions in ice giant interiors

Abstract Recent discoveries of water-rich Neptune-like exoplanets require a more detailed understanding of the phase diagram of H 2 O at pressure–temperature conditions relevant to their planetary interiors. The unusual non-dipolar magnetic fields of ice giant planets, produced by convecting liquid ionic water, are influenced by exotic high-pressure states of H 2 O—yet the structure of ice in this state is challenging to determine experimentally. Here we present X-ray diffraction evidence of a body-centered cubic (BCC) structured H 2 O ice at 200 GPa and ~ 5000 K, deemed ice XIX, using the X-ray Free Electron Laser of the Linac Coherent Light Source to probe the structure of the oxygen sub-lattice during dynamic compression. Although several cubic or orthorhombic structures have been predicted to be the stable structure at these conditions, we show this BCC ice phase is stable to multi-Mbar pressures and temperatures near the melt boundary. This suggests variable and increased electrical conductivity to greater depths in ice giant planets that may promote the generation of multipolar magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗