Electromagnetic Hysteretic Response Calculation for Superconductors in Demagnetizing Geometries

The electromagnetic response of the new high Tc superconductors is similar to that of eddy currents in normal metals, except that in the superconductor induced currents are established nonlinearly at a single value known as the critical current density, J c . These materials are extreme Type II superconductors where, in the presence of an external magnetic field and/or a transport current, magnetic flux exists in the material in the form of flux lines distributed on a lattice [1]. Individual flux lines become pinned at microstructural inhomogeneities such that only under a sufficient force caused by locally high current flows will they become depinned and flow throughout the material. The value of the local current density that causes depinning is the microscopic critical current density and is directly proportional to the pinning force strength. A phenomenological approach known as the critical state model [2,3] describes the pinned flux line distribution within the material quasistatically, assuming the equilibrium distribution is achieved at each value of the externally applied field on a short time scale compared to experimental times. Operationally, whenever an external field is increased, flux lines enter the material from the surface and penetrate to a flux front boundary, whose position is determined by the value of the external field at the sample surface. An important nondestructive evaluation (NDE) task to aid the fabrication of high Tc superconductors is to develop methods for quantitatively determining the local current density. In the critical state the current density is either the critical value appropriate to the local value of the induction J c , or it is zero. The electromagnetic response of the material is then determined by the extent of this critical state region and its measurement can be used to determine the local J c . Therefore, a method that can predict the flux front profile with high spatial resolution, and also account for demagnetization effects, is essential. An integral equation technique dealing with a nonuniform applied magnetic field having azimuthal symmetry was presented at the last QNDE conference by the present authors [4]. The current paper shows results from the further development of this technique in two ways. Firstly, the superconducting sample is extended from a half-space to an infinite plate. This is an example of a nonuniform applied magnetic field having azimuthal symmetry. The second application is a sphere, that is a demagnetizing geometry, in a uniform applied magnetic field. In the following section, the general methodology of this technique is outlined. Then some results of both the plate and the sphere examples are given to illustrate this proposed approach. Since the study of the plate sample is still in progress, more results will be reported in future publications. For the sphere sample, detailed discussion and presentation of formulations are given in [5]

Laser Ultrasonic Detection of the Solidification Front During Casting

A real-time sensor that directly measures properties of the solidification front would be a valuable aid to the metal casting industry. Information needed includes solidification front location, shape, and growth dynamics. The use of contacting probes is often undesirable because it can cause contamination and probe deterioration. Noncontacting laser ultrasonics offers an attractive solution to these problems, particularly if access to the free liquid surface is available. This paper presents results of laser ultrasonic measurements of the solidification front in tin and a tin-lead alloy. The ultrasonic waves were generated and detected at the liquid surface. Tin was selected for its low melting point and the availability of a suitable furnace. Results are presented for reflections from stationary and moving solidification fronts

Eddy Current Measurements of the New High TC Ceramic Superconductors

The discovery of ceramic superconductor materials which have transition temperatures above that of liquid nitrogen has inspired very active research in this area.These materials have great potential; however, there are many technique problems with fabricating them in useful forms.A major problem is that most fabrication schemes produce consolidated forms with relatively low critical currents.Successful fabrication of these materials requires a means of measuring the critical parameters in ways that can be used for process monitoring and control.In particular, the superconducting critical parameters (critical temperature TC; current, JC; and magnetic field, HC) need to be measured in a nondestructive manner, preferably with a noncontacting, imaging technique.Accomplishing this goal is a new challenge to the NDE community.This paper is a beginning to the process of developing appropriate NDE diagnostic tools for these superconductors

Noncontacting NDE for materials characterization

This report describes research performed at the Idaho National Engineering Laboratory from May 1983 to September 1995, funded by the Interior Department`s Bureau of Mines, on ultrasonic methods (particularly noncontacting methods) for nondestructive evaluation and process control. The abilities of ultrasonic techniques to measure microstructural features in metals, ceramics, and composite materials were demonstrated. A major emphasis in this project was the development of noncontacting ultrasonic techniques, based on laser generation and detection of elastic waves, for process monitoring and control in high-temperature, harsh environments without close coupling to the material being processed. Laser ultrasonic measurements were utilized for in situ process monitoring during ceramic sintering, high temperature annealing, and molten metal solidification

Dynamic Holographic Lock-In Imaging of Ultrasonic Waves

ABSTRACT A laser imaging approach is presented that utilizes the adaptive property of photorefractive materials to produce a real-time measurement of ultrasonic traveling wave surface displacement and phase in all planar directions simultaneously without scanning. The imaging method performs optical lockin operation. A single antisymmetric Lamb wave mode image produces direct quantitative determination of the phase velocity in all planar directions showing plate stiffness anisotropy. Excellent agreement was obtained with modeling calculations of the phase velocity in all planar directions for an anisotropic sheet material. The approach functions with diffusely scattering surfaces, subnanometer motions and at frequencies from Hz to GHz

Dynamic Holographic Lock-In Imaging of Ultrasonic Waves

A laser imaging approach is presented that utilizes the adaptive property of photorefractive materials to produce a real-time measurement of ultrasonic traveling wave surface displacement and phase in all planar directions simultaneously without scanning. The imaging method performs optical lock-in operation. A single antisymmetric Lamb wave mode image produces direct quantitative determination of the phase velocity in all planar directions showing plate stiffness anisotropy. Excellent agreement was obtained with modeling calculations of the phase velocity in all planar directions for an anisotropic sheet material. The approach functions with diffusely scattering surfaces, subnanometer motions and at frequencies from Hz to GHz

In situ laser-based resonant ultrasound measurements of microstructure mediated mechanical property evolution

In situ laser-based resonant ultrasound spectroscopy is used to characterize the development of a recrystallized microstructure in a high purity copper sample. The modal shapes, used for mode identification, of several resonant modes are determined before and after annealing by raster scanning the laser interferometric probe. This information is used to isolate the motion of individual modes during high temperature annealing. The evolution of a particular mode during annealing is examined in detail. During recrystallization, the center frequency of this mode shifts by approximately 20% of the original value. Using electron backscatter data it is shown that the majority of this shift is due to changes in the polycrystal average elastic stiffness tensor, driven by changes in texture, and that changes in dislocation density and pinning length are secondary influence

Characterization of energy trapping in a bulk acoustic wave resonator

Acoustic wave fields both within the active electrode area of a solidly mounted 1.8 GHz bulk acoustic waveresonator, and around it in the surrounding region, are measured using a heterodyne laser interferometer. Plate-wave dispersion diagrams for both regions are extracted from the measurement data. The experimental dispersion data reveal the cutoff frequencies of the acoustic vibration modes in the region surrounding the resonator, and, therefore, the energy trapping range of the resonator can readily be determined. The measureddispersionproperties of the surrounding region, together with the abruptly diminishing amplitude of the dispersion curves in the resonator, signal the onset of acoustic leakage from the resonator. This information is important for verifying and further developing the simulation tools used for the design of the resonators. Experimental wave field images, dispersion diagrams for both regions, and the threshold for energy leakage are discussed.Peer reviewe

Limitations for heterodyne detection of Brillouin scattered light

One means by which elastic properties of a material may be determined is measuring sound wave velocities in the material, from which elastic moduli of interest can be computed. Velocity can be measured by conventional piezoelectric transduction techniques, by applying laser ultrasonics, or by using Brillouin-scattering methods. Brillouin-scattering techniques for determining the sound wave velocity are particularly attractive since they are completely noninvasive. Only a probe beam of light is required since the thermal energy in the material provides the elastic motion. Heterodyne methods for detection of Brillouin-scattered light are considered one possible means to increase the speed of the scattered light frequency detection. Results of experiments with simulated Brillouin scattering suggest that heterodyne detection of the Brillouin-scattered light is feasible. Experiments to detect Brillouin-scattered light, with water as the scattering medium, were designed and interpreted using the results of the simulated scattering experiments. Overall, results showed that it is difficult to narrow the linewidth for Brillouin scattering to an acceptable level. The results given indicate that heterodyne detection of the Brillouin components requires detection bandwidths that are quite small, perhaps 10 Hz or lower. These small bandwidths can be routinely achieved using lock-in amplifier techniques

Photorefractive Laser Ultrasound Spectroscopy for Materials Characterization

Ultrasonic elastic wave motion is often used to measure or characterize material properties. Through the years, many optical techniques have been developed for applications requiring noncontacting ultrasonic measurement. Most of these methods have similar sensitivities and are based on time domain processing using interferometry. Wide bandwidth is typically employed to obtain real- time surface motion under transient conditions. However, some applications, such as structural analysis, are well served by measurements in the frequency domain that record the randomly or continuously excited vibrational resonant spectrum. A significant signal-to-noise ratio improvement is achieved by the reduced bandwidth of the measurement at the expense of measurement speed compared to the time domain methods. Complications often arise due to diffuse surfaces producing speckle that introduces an arbitrary phase component onto the optical wavefront to be recorded. Methods that correct for this effect are actively being investigated today