Bean Critical State Research Articles

IMPACT OF NANO-Mo ADDITION/SUBSTITUTION ON THE PHASE FORMATION AND SUPERCONDUCTIVITY OF Mg1-xMoxB2 (x=0.0to 0.50)

Bulk polycrystalline samples of nano- Mo doped MgB 2 were synthesized by Fe tube encapsulation at ambient pressure under argon annealing (850°C). Mo substitution takes place successfully at the Mg site in Mg 1-x Mo x B 2 only till x=0.2. For higher (x>0.2) Mo content the same did not enter the MgB 2 lattice but rather forms an isomorphic lattice in the host with decreased c but an increased a-parameter. The ρ(T) measurements showed superconducting transition temperature (T c ) of around 36 K for all the samples till x=0.3 and slightly decreased values of 35 and 34 K for x=0.4 and 0.5 samples, respectively. Resistivity under magnetic field [R(T)H] experiments showed distinct single peaks in dρ/dT for all applied fields up to 8 Tesla. The estimated upper critical field H c2 is 8 Tesla for pristine and x=0.2 samples at 15.6 and 19 K, respectively. Thus H c2 increases up to x=0.20 samples and decreases afterwards. Magnetic susceptibility measurements exhibited sharp transition to superconducting state with a sizeable diamagnetic signal at 38 K (T c ) in zero field-cooled measurements. Commendable current density (J c ) of up to 105 A/cm2 in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements invoking the Bean's critical state model for pristine samples. For higher fields above 2.5 Tesla the J c (H) characteristics of x=0.1 and 0.2 samples were found to be slightly superior to that for pristine samples with enhanced H irr (irreversibility field).

Numerical Evaluation of AC Loss Property in Bi-2223 Tapes Affected by Multifilament Structure

This paper describes the numerical results of AC losses in various types of non-twisted multifilamentary tapes that actual Bi-2223 Ag-sheathed wires are idealized. The penetration process of magnetic flux into the superconductor filaments subject to Bean's critical state model is simulated for the application of an external transverse magnetic field perpendicular to the broadest face of tape wire by means of energy minimization. The AC losses under cyclic fields are calculated from the distribution of a vector potential in an initial state. The influences of arrangements and shapes of the filaments on the losses are investigated as compared with those for a wire that the entire filamentary region is regarded as a homogeneous superconductor.

Influence of Oxygen Partial Pressure on the Microstructures and Critical Current Densities of PMP-Processed YBCO Bulks with Submicron Y<sub>2</sub>BaCuO<sub>5</sub> Particles

YBCO bulks with submicron Y2BaCuO5 particles have been prepared under oxygen partial pressures of 0.21atm and 1atm, respectively, by the powder melting process (PMP). The microstructures, oxygen contents and critical current densities of the samples have been investigated. The results showed that the sample grown under P(O2) = 1 atm contained Y2BaCuO5 particles with a little bigger average size and had a slightly higher density of stacking faults than the one prepared under P(O2) = 0.21 atm. Oxygen content measurements indicated that the as-grown sample under P(O2) = 1 atm had a higher oxygen content. After post-annealing in flowing oxygen, the oxygen content of the P(O2) = 1 atm sample was still higher than that of the P(O2) = 0.21 atm sample. They were examined to be 6.94 and 6.88 with X-ray diffraction for the two oxygenated samples, respectively. Magnetization measurements have been performed on the two types of oxygenated samples and critical current densities (Jc) have been calculated based on the extended Bean critical state model. The P(O2) = 0.21 atm sample exhibits Jc values of 5.47×105 A/cm2 and 2.22×104 A/cm2 in 1 T magnetic field at 20K and 77K, respectively. The P(O2) = 1 atm sample, meanwhile, has Jc values of 9.46×105 A/cm2 and 1.47×104 A/cm2 in 1 T magnetic field at 20K and 77K, respectively. Moreover, at 20K, the Jc of the P(O2) = 1 atm sample is higher than that of the P(O2) = 0.21 atm sample in an applied magnetic field up to 5 T. At 77K, however, the Jc of the P(O2) = 1 atm sample drops more quickly than that of the P(O2) = 0.21 atm sample. The mechanisms of the different microstructures, oxygen contents and magnetic field dependence behaviors of Jc for the two kinds of samples have been discussed.

AC susceptibility study of Bi 1.66Pb 0.34Sr 2Ca 2− xMg xCu 3O y ( x = 0, 0.2 and 0.4) superconductor systems

A systematic study of the intergranular properties of Bi 1.66Pb 0.34Sr 2Ca 2− x Mg x Cu 3O y ( x = 0, 0.2 and 0.4) samples has been done, using the AC susceptibility technique. The samples were prepared by conventional solid state reaction method. It was found that Mg substitution in place of Ca reduces the intergranular coupling of Bi-2223 system. Analysis of the temperature dependence of the AC susceptibility near the transition temperature ( T c) has been done employing Bean's Critical State Model. The observed variation of intergranular critical current densities ( J c) with temperature indicates that the critical current density decreases by increasing the amount of Mg. The higher electronegativity of Mg in the unit cell promotes more intake of oxygen in the material, and the grain boundaries are in more over-doped regime. These over-doped regions reduce the intergranular coupling and increases weak link behavior of Mg doped samples.

Low field AC-susceptibility study on γ -irradiated Bi1.2Pb0.33Sr1.54Ca2.06Cu3O10+δ superconductor

We report here, the effect of γ-irradiation on low field AC susceptibility as a function of temperature on the grown polycrystalline Bi1.2Pb0.33Sr1.54Ca2.06Cu3O10+δ sample. The sample was irradiated with γ-ray dose of 100 MR and 300 MR. The temperature dependent AC susceptibility measurements have been carried out with varying AC field amplitude H ac (0.5 to 9.0 Oe) at frequency 131.1 Hz on both un-irradiated and irradiated samples. AC susceptibility measurements as a function of temperature at AC field amplitude H ac = 2.0 Oe have also been carried out with varying frequency (31.1 Hz to 1131.1 Hz). The temperature dependence of AC susceptibility with varying amplitude has been analyzed using well defined Bean's critical state model. The critical current density (J c) is calculated as a function of both AC field amplitude (H ac) and temperature. An increase in J c with the increase of γ-dose has been found.

Demagnetization of Trapped Field in High $T_{C}$ Superconductors Using Pulsed Field Methods

This paper examines the demagnetization of a trapped magnetic field in a high TC superconducting (HTS) monolith using a single, short, high-amplitude field pulse. With a single optimized pulse, the peak trapped field can be reduced to one-third of the maximum saturated value. Alternatively, the spatial average of the trapped field could be fixed very close to zero. After demagnetization, the trapped field has both positive and negative values at various locations in the HTS monolith. Transient responses of the HTS to pulsed fields with different amplitudes are also reported and discussed. It does not appear that the residual trapped field can be reduced to zero throughout the monolith using pulsed field demagnetization methods in a fixed sample/coil geometry. Bean's critical state model is used to explain the measured equilibrium field distributions. Transient response of the HTS to an externally applied field is qualitatively explained by magnetic diffusion. Drive circuit characteristics and design feasibility issues are also addressed

Detecting and describing the inhomogeneity of critical current in practical long HTS tapes using contact-free method

The nondestructive and contact-free apparatus for measuring local critical current of long high temperature superconducting (HTS) tapes is presented. The local critical current of tape is acquired by using Hall probe array sensor to measure the remanent field after exposed to dc external magnetic field since the critical current is proportional to remanent field based on Bean critical state model. A detailed experiment on multifilamentary Bi2223/Ag tape is made to validate reproducibility, reliability, resolution, nondestructiveness and usefulness for manufacturer and user of tapes. The parameter COV (coefficient of critical current variation) is suggested for quantitatively describing the inhomogeneity and quality of practical long HTS tape based on Gaussian statistical analysis. The developed apparatus can detect HTS tape at velocity of 100 m/h with resolution smaller than 3 mm in liquid nitrogen.

Crossover from intravalley to intervalley vortex motion in type-II superconductors with a periodic pinning array

We have determined the transition from intravalley vortex motion (Campbell regime) to intervalley motion (critical state regime) in Pb thin films with and without a square array of holes (antidots) by means of ac susceptibility $\ensuremath{\chi}(T,H)$ measurements. The Campbell regime is characterized by a maximum dissipation ${\ensuremath{\chi}}_{\mathrm{max}}^{\ensuremath{''}}$ dependent on the ac excitation $h$ but nearly temperature independent. In contrast, in the critical state regime, the height of the dissipation peak remains constant, whereas its position shifts to lower temperatures with increasing $h$. We introduce an alternative way for determining the temperature dependence of the ac onset of the Bean critical state by analyzing the critical current density $J(T)$ extracted from the ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$ data at several $h$. We demonstrate that the presence of a periodic pinning array strongly affects the extension of the crossover area in the $h\ensuremath{-}T$ diagram between these regimes. We show that this effect can be ascribed to the lower dispersion of the pinning energy together with the higher topological order for the antidot sample.

Influence of the surface magnetic field of a cylindrical permanent magnet on the maximum levitation forcein high-Tc superconductors

In this paper we present the dependence of the maximum levitation force(FzMax) of ahigh-Tc superconductor on the surface magnetic field(Bs) of acylindrical permanent magnet, based on the Bean critical state model and Ampère’s law. A transition point ofBs is found at whichthe relation between FzMax and Bs changes: while the surface magnetic field is less than the transition point thedependence is subjected to a nonlinear function, otherwise it is a linear one. Thetwo different relations are estimated to correspond to partial penetration of theshielding currents in the interior of the superconductor below the transition pointand complete penetration above it, respectively. Furthermore, the influenceof the geometrical properties of superconductors on the transition point ofBs is discussed, which shows a quadratic polynomial function between the transition points and theradii and the thickness of superconductors. Some optimum contours of the transition point ofBs are presented in order to achieve large levitation forces.

Effective pinning energy in Li-dopedMTG-YBa2Cu3Oy crystals

Li-doped YBa2Cu3Oy crystals were fabricated by a typical top seed melt textured growth (MTG) method.The measured dc magnetization loops indicate that there is a very pronouncedsecond peak in the field dependence of the critical current density for -axis. The complex ac susceptibility has been measured as a function of temperature atvarious dc fields, and frequencies, respectively. The irreversibility line shifts to lowertemperature with increasing ac and dc fields, and with decreasing frequency. Based onthe nonlinear flux diffusion theory and the Bean critical state, we analysed themeasured ac susceptibility curves. The temperature, dc field and current densitydependence of the effective pinning barrier follows the form of , where μ = 0.13 is consistent with the theoretical predictions indicating that a vortex-glass phase is possiblein the sample.

Discrete model analysis of the critical current-density measurements in superconducting thin films by a single-coil inductive method

The critical current density of a superconducting film can be easily determined by an inductive and contactless method. Driving a sinusoidal current in a single coil placed in front of a superconducting sample, a nonzero third-harmonic voltage V3 is induced in it when the sample goes beyond the Bean critical state. The onset of V3 marks the value of current beyond which the sample response to the magnetic induction is no more linear. To take into account, in a realistic way, the magnetic coupling between the film and the coil, we have developed a discrete model of the inducing and induced currents distribution. In the framework of this model the magnetic-field profile on the sample surface and the coefficient linking the current flowing in the coil and the critical current density JC of superconducting thin films are evaluated. The numerical results are checked by measuring JC of several thin films of YBa2Cu3O7−δ of known superconducting properties, used as a control material.

The effect of sintering temperature on the intergranular properties of Bi2223 superconductors

A systematic study of the intergranular properties of (Bi,Pb) 2Sr 2Ca 2Cu 3O y (Bi2223) polycrystalline samples has been done using the electrical resistivity and Ac susceptibility techniques. In this project, we have prepared a series of Bi2223 samples with different sintering temperature. The XRD results show that by increasing sintering temperature up to 865 °C the Bi2212 phase fraction decrease. It was found that the Bi2212 phase on the grain boundaries is likely to play the role of weak links and consequently reduces the intergranular critical current densities. Analysis of the temperature dependence of the Ac susceptibility near the transition temperature ( T c) has been done employing Bean's Critical State Model. The observed variation of intergranular critical current densities ( J c) with temperature indicates that the weak links are changed from superconductor–normal metal–superconductor (SNS) for well-coupled sample to superconductor–insulator–superconductor (SIS) type of junctions for the sample with high Bi2212 phase fraction.

Estimation of Apparent AC Transport Losses for Cylindrical Conductors Composed of Superconductor Tapes

The distributions of resistive electric field under alternating current transmission and the apparent AC transport losses have been investigated on cylindrically assembled conductors with superconductor tapes through the numerical calculations. Several superconductor tapes with a rectangular cross section of various sizes were arranged on a cylindrical former, in a parallel way to the conductor axis. Numerical calculation of the resistive electric field distributions and the apparent AC transport losses were performed, by taking account of the geometry and the arrangements of tape strands under Bean's critical state model. The influence of the form and arrangement of tape strands on the electric field distributions and the apparent losses is discussed.

Numerical Evaluation of Anisotropy of Magnetization Losses in Superconducting Wires With Elliptic Cross Section

AC losses are numerically estimated in straight superconductors with an elliptic cross section exposed to a transverse magnetic field. It is assumed that the distribution of magnetic field in the superconductors is determined by Bean's critical state model, in which the critical current density is independent of the magnitude of local magnetic field. The penetration process of magnetic flux into the superconductors approximated as a group of fine rectangular bars is evaluated by means of the minimization of magnetic energy for the application of the external magnetic fields with arbitrary angles to their broadest face. By using the obtained penetration process, the AC losses are also calculated from the distribution of magnetic vector potential inside the superconductors. Furthermore, the compensation for the numerical results of AC losses enables us to obtain a universal loss property that is scarcely affected by the aspect ratio of cross section and the angle of external field.

Modeling of Current Density Distributions in Critical State by Commercial FE Codes

The method of minimum magnetic energy variation has proved its merit in modeling the magnetic field interaction with hard type-II superconductors. Its main advantage is that the front of flux penetration is calculated starting from a physical principle equivalent to the Bean's critical state model. We have developed a procedure that adapts the above-mentioned method to the environment of the commercial finite element code ANSYS. As a step forward with respect to existing works, this allows to include magnetic materials into simulations. The case of a superconducting strip covered by a ferromagnetic sheath is reported.

Magneto-Optical Imaging Studies of Flux Propagation in Ultra-Pure and Carbon-Doped<tex>$rm MgB_2$</tex>Thin Films

The mixed state in c-axis oriented ultra-pure MgB/sub 2/ thin films and carbon-doped MgB/sub 2/ thin films produced by hybrid physical-chemical vapor deposition was studied using magneto-optical imaging (MOI) technique. In the ultra-pure MgB/sub 2/ films, a regular magnetic flux penetration pattern was observed, as expected from the Bean critical state model. This is in striking contrast to earlier MOI observations of MgB/sub 2/ films made by pulse laser deposition, where dentritic flux jumps were usually abundant at temperature below 10 K. In our carbon-doped MgB/sub 2/ thin films, similar dentritic flux jumps were also observed at low temperature and low applied magnetic field. It is evident that the dendritic flux jumps or stability of the film is strongly influenced by the material parameters of the films, rather than inherent in all MgB/sub 2/ thin films.

Fast Algorithms for the Bean Critical-State Model for Superconductivity

ABSTRACT The Bean critical-state model describes the penetration of magnetic field into type-II superconductors. Mathematically, it is a free boundary problem, and fast algorithms for its solution are needed in applied superconductivity. Existence and uniqueness of solution, parallel algorithms, stability, and error estimation for this model are discussed.

Critical state in type-II superconductors of arbitrary shape

The well-known Bean critical state equations in general are not sufficient to describe the critical state of type-II superconductors when the sample shape is not symmetric. We show how one can find the critical state in superconductors of arbitrary shapes. Analyzing a simple example of nonsymmetry, we demonstrate that in the general case, a perturbation of the current distribution in the critical state propagates into the sample smoothly in a diffusive way. This is in contrast to the usual Bean critical state where the current distribution changes abruptly at a narrow front.

AC susceptibility study of fluorine-doped Bi-2212 ceramics

Two superconducting ceramics of Bi 2Sr 2CaCu 2O yF x ( x=0, 0.4) were elaborated by solid state reaction. Their temperature dependence of AC susceptibility under different magnetic fields were measured on rectangular bar-shaped samples. The study shows that fluorine doping improves the intergrain connectivity and increases the effective superconducting volume fraction f g of the grains. f g increases linearly with the applied magnetic field in the doped sample while it saturates at high fields in the undoped one. For each sample, the maximum of the extracted matrix susceptibility differs slightly from the predicted theoretical values of Bean's critical state model. The deduced intergranular critical current density J c( T) was observed to increase with fluorine doping. At 5 K, the estimated value of the critical field H c w of the weak links is higher in the doped sample.

Temperature dependence of vortex flux pinning in polycrystalline YBa 2Cu 4O 8

Magnetization measurements versus the magnetic field were done on a polycrystalline YBa 2Cu 4O 8 sample over temperature range from 4.2 K up to T C = 80 K. Within the applicability of the Bean critical state model, the magnetization remanence Δ M R represents the pinning forces at H = 0. We found that Δ M R decreases sharply with the temperature T for T/ T C < 0.4 and for T/ T C > 0.4 square root behavior exists. We found that Δ M R scales according to the empirical formula Δ M R (emu/cm 3) = 13(1 − T/ T C) 6 + 2(1 − T/ T C) 1/2. The two distinct behavior of Δ M R with T implies an existence of different pinning mechanisms.