Conditions for thermal stabilization of the superconductor’s critical state

Conditions for thermal stabilization of the electrodynamic states of a superconductor are studied. The macroscopic states are simulated in the nonisothermal approximation by numerically solving a set of the Fourier and Maxwell equations with the magnetic flux penetration boundary unknown. Stability criteria for the critical state described by the viscous flow model are formulated. The results are compared with those following from the isothermal theory. It is shown that errors inherent in the isothermal approximation are significant for a thermally insulated superconductor. Therefore, the well-known adiabatic criterion of stability formulated in the isothermal approximation limits the domain of stable states, since a correct determination of conditions for the superconducting-normal state transition must take into account the thermal history of the stable superconducting state formation. On the whole, the error of loss calculation in the isothermal approximation increases when the heat transfer coefficient decreases or an external magnetic field sweep and the size of the superconductor’s cross section increases. On the other hand, nonisothermal stability conditions expand the variety of allowable states, since they include conditions that links the currently developed theory of thermomagnetic instability, the theory of losses, and the theory of a superconductor’s thermal stabilization.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

Magnetization studies in niobium and YBa2Cu3O7 samples

The results of experimental studies on hysteresis in magnetization, thermomagnetic history effects, anomalous variations in magnetic hysteresis curves and the decay rates of magnetization obtained under different thermomagnetic histories in specimens of conventional and high temperature superconductors are presented. The Bean’s critical state model is considered adequate to explain magnetic behaviour in conventional hard superconductors. The similarity in the general features of the results of different experiments on specimens of the two families of superconductors underscores the efficacy of the said model to understand some aspects of the macroscopic magnetic response of high temperature superconductors as well. For instance, the isothermal magnetization hysteresis loop which comprises of magnetization curves along forward (−H _max to +H _max) and reverse (+H _max to −H _max) paths define an envelop within which all isothermal magnetization data along different thermomagnetic histories lie. There exist inequality relationship between various field values identified asH _peak,H _I,H _II etc. in isothermal magnetization hysteresis as well as magnetic relaxation data. The entire field span of an isothermal magnetization hysteresis data set can be considered to comprise of three parts corresponding to (M _rem(H)−M _FC(H)+M _ZFC(H)) being equal to, less than or greater than zero, whereM _rem(H) are the remanent magnetization values obtained on reducing field to zero after having the specimen in different applied field (H) values. There are, however some situations amongst thermomagnetic history effects in specimens which show incomplete flux trapping on field cooling, where the critical state model has been found inadequate.     

Effect of an alternating field on the relaxation of effect of an alternating field on the relaxation of magnetic flux in a Josephson medium

We establish how trapped magnetic flux depends on the frequency and amplitude of an alternating field and how such a field affects the relaxation rate of the flux. We find that the nature of the flux creep changes in the process and that relaxation of the flux stops after the external field is switched off. We examine the dynamics of flux relaxation in a ring in the approximation in which the current density is assumed homogeneous, for various density dependences of the effective vortex activation energy. The critical current density and the vortex activation energy are obtained as functions of the external field strength. Finally, we explain the observed behavior in terms of the different field profiles emerging in the rings. Zh. éksp. Teor. Fiz. 111, 1047–1056 (March 1997)     

High-field magnetoresistance and magnetothermal e.m.f. in many-valley semiconductors with ellipsoidal energy surface

Thermomagnetic coefficients appropriate to a many-valley model of a semiconductor of the n -Germanium type are evaluated in the framework of the density matrix formalism developed earlier. These coefficients are determined for arbitrary values of the magnetic field, within the effective mass approximation. The phonon-drag contribution is not included in this work. An application is made to the four-ellipsoidal model of n-Ge under the conditions where elastic-acoustic phonon scattering is the predominant mechanism of scattering and the high-temperature limit of the phonon distribution is valid. The thermoelectric power (magneto-Seebeck effect) is found to increase with increasing values of the magnetic field except for a small region of low magnetic field values where it decreases in the longitudinal configuration only.     

Dynamic magnetic susceptibility of a superconductor with a relaxing magnetic moment

Within the framework of the diffusion approximation for the dynamic magnetic flux, a model is constructed for the dynamic magnetic susceptibility of a superconductor with a nonuniform and time-dependent magnetic field distribution in the sample. The possibility of appearance of peaks in the temperature (or frequency) dependence of χ″ in a structurally homogeneous superconducting sample in the presence of a magnetic-field-induced nonuniformity of the diffusion parameter is demonstrated. The character of the temporal evolution of the magnetic susceptibility during relaxation of the magnetic moment of the sample is predicted and its properties are investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 811–815 (May 1997)     

Distribution of the electric field and current in a turbulent conducting fluid for small magnetic Reynolds numbers

Various aspects of the influence of an external magnetic field on turbulent flow of a conducting fluid are investigated. The distributions of electric variables are determined for weak magnetic fields (both the electric field and the current have nonzero values in this case). For very strong magnetic fields it is shown that turbulent motion acquires a two-dimensional character. The emergence of an electric current component perpendicular to the flow and to the magnetic field is described in the case of a temperature-stratified medium in the presence of turbulent heat flux. Zh. éksp. Teor. Fiz. 111, 528–535 (February 1997)     

Oscillator strengths of optical transitions of a cylindrical shell: Crossed static electric and magnetic fields

The single-electron eigenstates of a cylindrical shell are determined as functions of the applied crossed electric and magnetic fields in the effective-mass approximation. The system considered consists of donor charges taken to be uniformly distributed within an inner core of infinitely long length. The core is concentrically enveloped by a semiconducting material of finite thickness; which is essentially the host material. This configuration of the donor charges sets up a spatially varying electric field nonetheless with only the radial component. In addition, a uniform magnetic field is applied parallel to the axis of symmetry of the inner core. As is well known, the axial applied magnetic field lifts the double degeneracies of the electron’s subbands characterized by the same azimuthal quantum numbers which differ only in sign. The main effect of increasing the external electric field is to elevate the various energy subbands, more or less to the same extent, to higher values. Further, evaluations of the oscillator strengths of optical transitions of the cylindrical shell are carried out within the dipole approximation. The radiation field is taken to be that of circularly polarized light incident along the axis of the core. The oscillator strengths of optical transitions are found to increase with an increase of the applied magnetic field, particularly in the regime of small magnetic fields. In contrast, the oscillator strengths of these optical interactions become suppressed as the donor charge density is increased.     

Influence of isothermal approximation on the phase-field simulation of directional growth in undercooled melt

By using the phase-field approach,we have simulated the directional growth of alloys in undercooled moten states under the isothermal and nonisothermal conditions.The influences of the isothermal approximation on simulation results are discussed.We found that for undercooling greater than 25K,the isothermal approximation overestimates the interface growth velocity and reduces a critical velocity for an absolute stable planar interface,thus in this simulation,the uinterface morphology shows the plane-cell-plane transition with increasing initial undercooling of the mele,and the planar interface obtained under a large undercooling is absolutely stable.Whereas in the nonisothermal simulation,only plane-cell transition occures in the same range of the initial undercoolings of the melt,and the planar interface tends to be destabilized and evolve into cells.     

“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell

We have analyzed the spectrum of gapless excitations emerging upon the perturbation of the Abrikosov lattice with a single flux quantum in the unit cell. Superconductors with Ginzburg–Landau parameter κ close to unity are of special interest. We have determined the spectrum of gapless excitations close to zeroth shear modes for an arbitrary angle ? between the unit cell vectors. Analysis of the excitation spectra of triangular and square lattices with a single flux quantum in the unit cell has shown that solutions with a number of flux quanta greater than one exist at least in the range of parameters κ close to unity (κ > 1) and give smaller values of the free energy as compared to its values for a triangular lattice with a single flux quantum. For small values of momentum k (in the k ² approximation), the excitation spectrum of the “transverse” mode in the triangular lattice is independent of the direction of the momentum lying in the plane perpendicular to the magnetic field. For the square lattice (? = π/2), the transverse mode is anisotropic in the k ² approximation also.     

Pinning by twin boundaries and peak effect in YBaCuO high-T c superconductors

Measurements of the imaginary part of the ac magnetic susceptibility of single crystals and melt-textured samples of YBa₂Cu₃O_x (YBCO) at T=77 K in a magnetic field ranging between 1 and 20 kOe are reported. If the dc magnetic field H _dc is rotated in the ab plane of the sample, the magnetic susceptibility and critical current density j _c have peaks corresponding to the magnetic field aligned with twin boundaries. Peaks in the curve of j _c versus magnetic field are observed at angles corresponding to these peaks, where AH _dc in a wide range of magnetic fields. The results have been interpreted in terms of the theory describing twin boundaries as a system of quasi-planar pinning sites. The pinning is strong if the elastic displacements of flux lines are of the order of the vortex lattice constant d _f. These displacements decrease with the magnetic field because of the decrease in d _f, and the contribution of the elastic energy to the Gibbs potential is reduced accordingly, which is the cause of the peak effect. Zh. éksp. Teor. Fiz. 111, 2158–2174 (June 1997)     

Whistler detrapping from a density crest duct

A theory of whistler wave leakage from a magnetic field aligned duct with enhanced plasma density is presented. The energy flux from the duct and the corresponding wave attenuation rate are calculated in the WKB approximation. Possible experimental confirmations of the theory are indicated.     

Magnetic moment of quantum cylinders

The magnetic response of a two-dimensional layer rolled into a cylinder and located in a longitudinal magnetic field is examined. The magnetic moment of the degenerate electron gas is studied as a function of the magnetic flux. The shape of the fluctuation maxima is analyzed in detail. It is shown that at zero temperature there are breaks in each period of the change in the magnetic moment. Over this period, a plot of the magnetic moment depends strongly on the ratio of the Fermi energy to the size-confinement energy. In particular, there are no breaks for integral or semi-integral values of the square root of this ratio. Fiz. Tverd. Tela (St. Petersburg) 41, 856–858 (May 1999)     

Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field

An analytic solution is given for classical magnetohydrodynamic (MHD) problem of almost rigid-body rotation of a viscous, conducting spherical layer of liquid in an axisymmetric potential magnetic field. Large-scale flows bounded by rigid spheres are described for the first time in a new approximation. Two problems are solved: (1) in which both spheres are insulators and (2) in which the outer sphere is an insulator and the inner sphere a conductor. Axially symmetric flows and azimuthal magnetic fields are maintained by a slightly faster rotation of the inner sphere. The primary regeneration takes place in the boundary and shear MHD layers. The shear layers, described here for the first time, smooth out the large gradients at the boundaries of the MHD structures encompassed by them. There is essentially no azimuthal magnetic field inside these original structures, which are bounded by potential contours tangent to the spheres. An applied constant magnetic field creates a rigid MHD structure outside an axial cylinder tangent to the inner sphere. Inside the cylinder the rotation is faster and the meridional flux depends on height. A magnetic dipole forms a structure tangent to the outer equator. Outside the structure, the rotation is also rigid-body when both spheres are insulators. When a conducting sphere is present, the liquid rotates differentially everywhere, while near the axis and inside the MHD structure, it rotates even faster than the inner sphere. The last example of a general solution is a quadrupole magnetic field. In this case, two equatorially symmetric MHD structures are formed which rotate together with the inner sphere. Outside the structures, as in the most general case, the rotation is differential, the azimuthal magnetic field falls off as the first power of the applied field, and the meridional flux falls off as the square of the field in the first problem, and as the cube in the second. Zh. éksp. Teor. Fiz. 112, 2056–2078 (December 1997)     

Stabilization of Drift Instabilities of an Inhomogeneous Plasma by Means of an RF Electric Field

The possibility of stabilizing effects that an rf electric field imposes on drift instabilities in an inhomogeneous plasma is investigated. A two-species, nonisothermal plasma, situated in an externally applied static magnetic field is considered with the rf electric field applied in the same direction as the dc magnetic field. The plasma is "mildly" inhomogeneous in density, with a density gradient perpendicular to the confining magnetic field. Using a hydrodynamic model for the plasma it is found that under certain conditions an increase in the frequency of the drift oscillations is obtained as the result of the application of the rf electric field. The increase in the frequency of the drift oscillations results in an increase in the magnitude of the stabilizing term associated with Landau damping which in turn yields a smaller growth rate for the drift instability. Discussions of the state of the plasma for different values of the frequency of the applied electric field are presented and the feasible ranges of values of the above quantity required for stabilization are determined. It is concluded that the resulting stabilization is significant only in a very narrow rf band. Therefore, the application of this technique appears to be a difficult experimental undertaking.     

A simple analysis of the subband energies in quantum-confined non-parabolic semiconductors in the presence of a parallel magnetic field

Summary We study the subband energies in quantum wells and quantum wires in the presence of a parallel magnetic field in non-parabolic semiconductors, on the basis of a generalized dispersion relation considering all types of anisotropies of the energy-band parameters within the framework ofk·p formalism, by formulating the respective electron energy spectra. It is found, by takingn-Cd₃As₂ as an example, that the subband energies are greater for quantum wires and smaller for quantum wells, respectively. The magnetic field diminishes the above values and the corresponding well-known results for quantum-confined parabolic semiconductors have also been obtained from our generalized expressions under certain limiting conditions.     

Neutrino magnetic moment solution for the solar neutrino problem and the SNO experiment

The motivations for the magnetic moment solution to the solar neutrino problem are briefly reviewed and the expected values for a number of observables to be measured by the SNO experiment are calculated assuming three different solar magnetic field profiles. The observables examined are the charged current event rate, the ratio of the neutral current to the charged current event rates and the charged current electron spectrum as well as their first and second moments. The dependence of results on the hep neutrino flux is also analysed and a comparison is made with the corresponding oscillation results.     

Vortex structure in superconductors with a many-component order parameter

Abstract

The phenomenological theory of superconductors with a many-component order parameter (OP) is developed. On the basis of a generalized Ginzburg-Landau functional, equations for a two-component-OP superconductor are derived. It is shown that such a superconductor is specified by three length dimensionality parameters—penetration depth λ, correlation length ζ, and width d of the boundary between two superconducting-phase domains. With λ ? d ? ζ, the equations for the OP of a superconductor in a magnetic field can be explored analytically. The transition from the superconducting to the mixed phase may occur not only by the formation of ordinary Abrikosov vortices, but also owing to vortices that have two cores, each transferring a half-integral flux quantum. The total flux transferred by a vortex certainly constitutes an integral quantum. The cores of such a dimer are interconnected by two domain walls, which exercise confinement within the dimer. The distance between the cores in the dimer is of the order of d. Within a domain wall that separates two superconducting-phase domains, a dimer may fall apart into two vortices with a half-integral flux quantum.

For many-component-OP superconductors in a magnetic field, vortex structures of a more complicated nature than a dimer may occur. An individual core may transfer a fractional flux quantum, but the structure as a whole transfers an integral flux quantum. Confinement of individual cores occurs owing to a complicated system of domain walls determined by the topological charges of these vortices.

Under certain conditions, on attaining field H _c1, vortices may arise first in the domain walls, carrying a fractional flux quantum, and then within the superconducting domains.     

Thermal activation in the quantum regime and macroscopic quantum tunnelling in the thermal regime in a metabistable system consisting of a superconducting ring interrupted by a weak junction : Part II: Thermal activation in the quantum regime (continuation)

In this short contribution we present a commentary on the interpretation of our thermal activation data obtained in the quantum regime of a SQUID, as discussed in part I [Bol et al., Physica B 133 (1985) 196]. Under certain circumstances a superconducting ring containing a weak superconducting junction, a SQUID, has two metastable magnetic flux states separated by a potential energy barrier ΔV. In this metabistable system stochastic magnetic flux transitions were observed due to intrinsic thermal activation. It was found that the transition rate was strongly reduced compared with the predictions of the classical thermal activation theory of Kramers or with the modern thermal activation theory of Grabert and Weiss which is an extension to the quantum regime where kT ω₀ (ω₀ being the free oscillation frequency corresponding to the metastable potential well). In these theories the transition rate is proportional to exp(-ΔV/kT), in which V is treated as a temperature independence potential just as in the case in microscopic activated processes. In fact, however, from the thermodynamic point of view the relevant quantity in the exponent is the magnetic availability of the system with respect to the surroundings fixed by the temperature of the heat bath and the external magnetic field. Only when the system is completely isothermal can the potential V be identified with the Gibbs function. But in general when a flux transition takes place between the metastable potential wells, some energy will be dissipated possibly causing a temporary temperature rise due to self-heating. In principle, therefore, the system behaves neither perfectly isothermal nor adiabatic.     

Dynamical correlations in the one-dimensional electron gas with short-range interactions

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj?lander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction . There is a corresponding local-field factor for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of and , and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations. Received 11 December 1998 and Received in final form 25 April 1999