Dynamical phase transition of a driven vortex lattice with disordered pinning

We have numerically solved the overdamped equation of vortex motion in a two-dimensional driven vortex lattice with disordered pinning, in which the driving Lorentz force, the pinning force due to point defects, the intervortex interacting force, and the thermal fluctuation force are taken into account. It is found that the vortex density and pinning strength are two important factors of affecting the melting transition of a vortex lattice. At low magnetic fields, there exist hysteresis loops of the average vortex velocity and the average pinning force vs. the driving force, from which the feature of a first-order melting transition of the vortex motion can be clearly seen. As the magnetic field is increased beyond a critical value, the hysteresis loops disappear and the melting transition is replaced by a second-order glass transition. We have also studied the influence of intervortex interactions on the vortex melting transition by comparing several forms of repulsive forces between the vortices.     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

Determination of the critical current density and the flux pinning force in single crystals YBa2Cu3O7-δ from the magnetization hysteresis cycles

In this study, the magnetization measurements have been performed on high-temperature superconductor's single crystals YBa₂Cu₃O_7-δ at large ranges of temperature T (15-85 K) and in magnetic fields up to 6T at different values of the angle θ between the applied magnetic field and c-axis. The critical current density Jc deduced from the magnetic hysteresis loops by the Bean formula for H parallel to the c-axis (θ=0°), our results have shown that the critical current density Jc was strongly dependent on the applied magnetic field. The pinning force Fp=Jc×μ₀H was determined from magnetization for H//c, however, a plot of the normalized pinning force density fp= Fp/Fpmax as a function of the reduced magnetic field h= H/Hirr at different temperatures have shown good scaling with the form fp ~h^p(1-h)^q, where p and q are scaling parameters. We also found that the point pinning is more dominant than surface pinning under high temperatures.     

感生电场与动生电场的等效性探究

本文认为在感生电场的情况下,磁场的强弱变化可以引起磁场自身的横向运动,使得线圈中电子相对于磁场发生运动,从而等效为一个动生电场,受到洛伦兹力的作用.借助磁感线模拟磁场的运动方式,得到圆形回路中任意一点与磁场相对运动速度的表达式,进而推得该＂等效动生电场＂中的洛伦兹力.以螺线管为例,验证该方法可以解释感生电场所满足的规律.将感生电场与动生电场的产生原因统一为导体中电子与磁场的相对运动,相应电动势的非静电力统一为洛伦兹力.     

Critical current density behaviors across a grain boundary inclined to current with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions

The critical current density behaviors across a bicrystal grain boundary(GB) inclined to the current direction with different angles in YBa_2Cu_3O_(7-δ) bicrystal junctions in magnetic fields are investigated.There are two main reasons for the difference in critical current density in junctions at different GB inclined angles in the same magnetic field:(i) the GB plane area determines the current carrying cross section;(ii) the vortex motion dynamics at the GB affects the critical current value when the vortex starts to move along the GB by Lorentz force.Furthermore,the vortex motion in a bicrystal GB is studied by investigating transverse(Hall) and longitudinal current–voltage characteristics(I–V_(xx) and I–V_(xy)).It is found that the I–V_(xx) curve diverges from linearity at a high driving current,while the I–V_(xy) curve keeps nearly linear,which indicates the vortices inside the GB break out of the GB by Lorentz force.     

Commensurability effects in the critical forces of a superconducting film with Kagomé pinning array at submatching fields

Using molecular dynamics simulations, we find the commensurability force peaks in a two-dimensional superconducting thin-film with a Kagomé pinning array. A transport force is applied in two mutually perpendicular directions, and the magnetic field is increased up to the first matching field. Usually the condition to have pronounced force peaks in systems with periodic pinning is associated to the rate between the applied magnetic field and the first matching field, it must be an integer or a rational fraction. Here, we show that another condition must be satisfied, the vortex ground state must be ordered. Our calculations show that the pinning size and strength may dramatically change the vortex ground state. Small pinning radius and high values of pinning strength may lead to disordered vortex configurations, which fade the critical force peaks. The critical forces show anisotropic behavior, but the same dependence on pinning strength and radius is observed for both driven force directions. Different to cases where the applied magnetic field is higher than the first matching field, here the depinning process begins with vortices weakly trapped on top of a pinning site and not with interstitial vortices. Our results are in good agreement with recent experimental results.     

Force law in material media,hidden momentum and quantum phases

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.     

Absence of correlated flux pinning by columnar defects in irradiated epitaxial Bi2Sr2CaCu2O8 thin films

Using heavy-ion irradiation, we produced columnar defects of different density and orientation in epitaxial Bi₂Sr₂CaCu₂O₈ thin films. Although this increases the normal state resistivity and the critical temperature is reduced proportionally to the volume fraction of damaged material, pinning-related quantities like critical current density, activation energy and depinning field are enhanced in external magnetic fields. Transport measurements in dependence of the magnetic field and its orientation consistently indicate two-dimensional pinning of pancake vortices at the columnar defects. We observe the absence of correlated flux pinning by columnar defects and compare to heavy-ion-irradiated single crystals and tapes, where line-like correlations have been observed.     

ANISOTROPY OF CRITICAL CURRENT DENSITY IN c-AXIS ORIENTED EPITAXIAL YBa2Cu3O7-δ FILMS

The dependence of critical current density J_c on the angle α between the directions of the applied magnetic field H (which was rotated in the c-axis-I plane) and the in-plane current I was measured on a c-axis oriented epitaxial YBa₂Cu₃O_7-δ films at 81 K, with the magnetic field strength up to 6T, Analysis of the experimental results on the basis of the classical scaling law of pinning force shows that there exist simultaneously planar-pinning and volume-pinning mechanisms, and the contribution of volume pinning increases wish decreasing while that of the planar pinning decreases, We propose that the decrease of Lorentz-force-independent critical current density with increasing H for H∥I results from the suppression of superconductivity by the magnetic field, The fact that the contribution of volume pinning increases with decreasing α also arises from the suppression of superconductivity in CuO₂ plane by the magnetic field.     

Electric field and Lorentz force contribution to atmospheric vortex phenomena

The physics that initiate and sustain tornados and dust devils is still under investigation. Forces that operate throughout a wide range of scales and could contribute to atmospheric vortex phenomena are the Lorentz force and the force of electric fields. The Lorentz force results in a circular motion of charged particles in a magnetic field. An electric field will pull or repel a charged particle in the direction of the field. This paper will demonstrate that the Lorentz force and the force of electric fields, acting on charged particles that exist in atmospheric vortex phenomena, plausibly contribute to the set of physics that will explain tornados and other atmospheric vortex phenomena.     

高T_c超导体YBCO磁通钉扎的计算机模拟研究

临界电流密度Jc是影响高温超导体在强电领域应用的一个重要参数,在实际应用中,特别在外加磁场下,临界电流密度与超导材料的磁通钉扎性质密切相关.因此,磁通钉扎一直是高温超导体研究中的一个重要领域.由于高温超导体磁通钉扎力密度Fp的标度律存在,本文根据D.Dew-Hughes总结的钉扎力函数,主要存在两种主要作用类型(正常相和△K).我们将D.Dew-HugBes给出的钉扎力密度Fp标度函数改进为一个简化的具有物理意义的函数表达式.结合文献中已有的实验数据,我们对YBcO进行了计算机模拟,确定了它的磁通钉扎类型,模拟的研究结果与实际情况比较吻合.     

Existence of double-pinning force maxima for a single pinning mechanism

Critical current measurements on a cold rolled Pb₆₀In₄₀ foil show two pinning maxima, one close to H_c2 in the neighborhood of h = 0.95, and the other at low fields around h = 0.15. The high field pinning force maximum shifts to lower fields, and the low field maximum shifts to higher fields with increasing pinning strength. The data is explained in terms of Kramer's pinning force model incorporating Brandt's expression for C>₆₆.     

Suppression of magnetic relaxation by a transverse alternating magnetic field

The evolution of the spatial distribution of the magnetic induction in a superconductor after the action of the alternating magnetic field perpendicular to the trapped magnetic flux has been analyzed. The observed stabilization of the magnetic induction profile is attributed to the increase in the pinning force, so that the screening current density becomes subcritical. The last statement is corroborated by direct measurements.     

高速飞行器磁控阻力特性

采用低磁雷诺数磁流体数学模型,对外加磁场下的高超声速半球体流场进行数值模拟.选取三种简单理想磁场(轴向、径向、周向均布磁场),分析了不同磁场类型对流场结构、气动阻力与洛伦兹阻力的影响及作用机理.研究发现,轴向磁场径向"挤压"效应使得激波外形凸出,且壁面静压存在"饱和现象";径向磁场存在轴向"外推"效应,较大的磁场强度会导致肩部形成高温区;周向磁场下感应电场的存在导致增阻效果很差.进而对比了两种相同驻点磁感应强度特殊分布磁场(偶极子磁场、螺线管磁场)下的流场,发现了不同于理想磁场的径向"扩张"效应.按增阻效果从大到小依次为径向磁场、螺线管磁场、轴向磁场、偶极子磁场、周向磁场.     

A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh

A conservative formulation of the Lorentz force is given here for magnetohydrodynamic (MHD) flows at a low magnetic Reynolds number with the current density calculated based on Ohm’s law and the electrical potential formula. This conservative formula shows that the total momentum contributed from the Lorentz force is conservative when the applied magnetic field is constant. For the case with a non-constant applied magnetic field, the Lorentz force has been divided into two parts: a strong globally conservative part and a weak locally conservative part.The conservative formula has been employed to develop a conservative scheme for the calculation of the Lorentz force on an unstructured collocated mesh. Only the current density fluxes on the cell faces, which are calculated using a consistent scheme with good conservation, are needed for the calculation of the Lorentz force. Meanwhile, a conservative interpolation technique is designed to get the current density at the cell center from the current density fluxes on the cell faces. This conservative interpolation can keep the current density at the cell center conservative, which can be used to calculate the Lorentz force at the cell center with good accuracy. The Lorentz force calculated from the conservative current at the cell center is equivalent to the Lorentz force from the conservative formula when the applied magnetic field is constant, which can conserve the total momentum. We will further prove that the simple interpolation scheme used in the Part I [M.-J. Ni, R. Munipalli, N.B. Morley, P.Y. Huang, M. Abdou, A current density conservative scheme for MHD flows at a low magnetic Reynolds number. Part I. On a rectangular collocated grid system, Journal of Computational Physics, in press, doi:10.1016/j.jcp.2007.07.025] of this series of papers is conservative on a rectangular grid and can keep the total momentum conservative in a rectangular grid.     

INFLUENCE OF PINNING CENTRE DISTRIBUTION ON THE DYNAMICS OF TWO-DIMENSIONAL VORTEX SYSTEM

Numerical study of the influence of the distribution of pinning centres on the dynamics of a two-dimensional vortex system is performed. The superconductor sample has a periodic structure with a pinned region of length L_p and an unpinned region of length L_x-L_p along the direction of driving force (Lorentz force). Results show that, at zero temperature, the critical force F_c increases with the increase of L_p, indicating that the homogeneity of pinning centres helps to enhance the critical electric current of the superconductor. At large driving forces, vortex static channels form in the pinned region even for L_px.     

Vortex dynamics in Pb-doped Hg-1234 superconductor by AC susceptibility response

The general equation that describes the AC magnetic susceptibility response of the superconducting system due to the change of varying AC field has been reviewed. By using the AC susceptibility measurements, the temperature, magnetic field and current density dependence of the effective pinning potential U(T, H, J) for our Pb-doped Hg-1234 superconductor has been determined. It is found that the fast drop of the effective pinning potential with current density is due to the large value of the characteristic exponent μ which depends on the existing types of non-superconducting phases that form the intergrowth structures with the dominant matrix. The characteristic curve of electric field E(J) against the current density J has been obtained from the AC susceptibility technique. For consideration of current relaxation due to the presence of giant flux creep, we have studied and determined the temperature dependence of the critical current density J_c for our specimen.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

Reciprocity and equivalence in reciprocal and non-reciprocal media through reflection transformations of the current distributions

The electromagnetic wave fields generated by arbitrary electric and equivalent magnetic current distributions are expressed by means of a Maxwell operator in anisotropic, gyrotropic or bianisotropic media. Provided that the constitutive tensorK(r), (which relates the wave-field vectorsD andB toE andH), has in each case the appropriate symmetry in its spatial variation, Lorentz-type reciprocity relations are obtained connecting the given current distributions and their wave fields with a transformed (reflected) set of current distributions and their fields. Reflections are with respect to a plane, a line or a point, depending on the symmetry structure of the constitutive tensor. Modified Lorentz reciprocity appears as a special case of the reflection transformations. A related set of reflection transformations yields equivalence (rather than reciprocity) relationships, in which mirrored current distributions generate mirrored wave fields. Various applications are discussed.     

Bi_2Sr_2CaCu_2O_(8+δ)单晶的钉扎力标度和磁通钉扎机制

测量了 Bi2 Sr2 Ca Cu2 O8+δ单晶不同温度下的磁化曲线。根据 Bean临界态模型得到了不同温度下的钉扎力密度 FP 对磁场的依赖关系 ,发现在不同温度下的钉扎力密度可以标度在同一条曲线上。标度函数和最大钉扎力所对应的磁场与不可逆场 Hirr的比值都表明 Si2 Sr2 Ca Cu2 O8+δ单晶在磁通玻璃态的钉扎机制主要是正常相面钉扎。