Transverse Lorentz Force Research Articles

Thermal propagation analysis of 2G HTS stacked wires based on a dimensional coupling method

Stacked structures of high-temperature superconducting (HTS) tapes are usually employed to enhance current-carrying capacity in cable or magnet applications, but their multilayer characteristics may result in local hot spots due to uneven cooling. Besides, the inconsistencies along the length of tapes introduced during manufacturing process and the significant transverse Lorentz forces experienced in magnet operations can lead to weak parts, bringing uncertainties to thermal stability. Finite-element methods are widely used to predict thermal propagations, but 3D models encounter challenges such as distorted mesh elements and convergence issues, particularly when combining electromagnetic and heat transfer modules for long-distance wires. In this work, we have developed a Dimensional Coupling Method (DCM) to assess the thermal impact of weak parts in stacked wires applying coupled 1D and 2D models. The 2D model analyzes the electromagnetic and heat characteristics of stacked surfaces, and provides an initial heat source for the 1D model, which evaluates thermal propagation longitudinally. Simulation results of the 1D module are then transferred back to update the 2D outcomes. Models of distinct dimensions are coupled sequentially in physical steps but simultaneously in the time domain. Our approach is verified by 3D model benchmarks and offers a computational cost reduction of approximately 60 % compared to the benchmarks, making it more suitable for applications with large Iop/Ic ratios. Specially, multi-layer stacked wires under low ratios cases are also been analyzed. What’s more, two influencing factors of heat propagation, the weak-part length and position, are also investigated.

Thermal characterization of Sutterby nanofluid flow under Riga plate: Tiwari and Das model

This investigation uses the Tiwari and Das nanofluid model to enhance the heat transfer rate in Sutterby nanofluid over a Riga plate. The effects of heat source/sink, viscosity dispersion, and mass flow for water-based fluids are also considered in this work. Sutterby fluid has been utilized to investigate the rheological features of nanofluids. The transverse Lorentz force produced by the Riga plate assists in the flow down the plate by producing an electromagnetic field. The main aim of this investigation is to evaluate the presence of two different types of nanoparticles in water, specifically silicon carbide [Formula: see text] and copper [Formula: see text]. Dimensionless variables are first used to convert the mathematical model into a non-dimensional form. The similarity approach is then used to further rewrite the non-dimensional partial differential equations into a set of similarity equations. The bvp4c function in MATLAB software provides a numerical solution to these equations. The effects on temperature and velocity profiles of many physical factors, including the Reynold number, heat source/sink, and Deborah number, have been analyzed and presented. Furthermore, using tables, a detailed analysis of the skin friction coefficient and local Nusselt numbers is conducted. The results show that convective flow is suppressed when solid nanoparticles are added to the base fluid. The velocity distribution improves as Deborah and Reynold’s numbers get a higher value. Also, the temperature field improves by incrementing exponential and thermal heat source/sink parameters.

Experimental research on the influence of HTS tape width and former type on the transverse compression performance of CORC cables

The huge transverse Lorentz force experienced by CORC cable during the operation of fusion projects may cause irreversible degradation of its current-carrying capacity. Therefore, it is particularly important to study the influence of cable parameters on their transverse compression performance, and use these influence laws to adjust cable parameters to improve the critical value of transverse compression load that CORC cables can withstand. Solid copper bar former CORC cables with a former diameter of 5.57 mm are produced using HTS (high temperature superconducting) tapes (manufactured by Shanghai Superconductor) of 4 mm and 5 mm width respectively. The experimental results show that the CORC cable wound with 5 mm wide HTS tape has a greater critical transverse compression load than the cable wound with 4 mm wide HTS tape. This indicates that using wider HTS tapes to wind CORC cables can effectively improve their transverse compression performance. A solid copper bar former CORC cable and a stainless steel spiral tube former CORC cable are also produced. Through transverse compression experiments, it is found that the critical transverse compression load of the solid copper bar former and the stainless steel spiral tube former CORC cable are 130 kN/m and 89 kN/m, respectively. This indicates that the solid copper bar former CORC cable has better transverse compression performance. In addition, we also compared the influences of flat and arc pressure blocks on the transverse compression performance of CORC cables, and this experimental results provided a basis for the selection of the bobbin structure when using CORC cables to make coils.

Quantitative proton radiography and shadowgraphy for arbitrary intensities

Charged-particle radiography and shadowgraphy data can be directly inverted to obtain a line-integrated transverse Lorentz force or a line-integrated transverse refractive index gradient if intensity modulations due to scattering and absorption are negligible, and angular deflections are small. We develop a new direct-inversion algorithm based on plasma physics and compare it to a new Monge–Ampère code and an existing power diagram code (Kasim et al., 2017). The measured or source intensity is represented by electrons subject to drag, and the other intensity by fixed ions. The decrease in kinetic plus electrostatic energy determines convergence. The displacement of the electrons from their initial to their equilibrium positions determines the line-integrated force or refractive index gradient. We have implemented two approaches: PIC (particle in cell) and Lagrangian fluid, in 1-D and 2-D. The PIC code works for arbitrary intensities, can work efficiently in parallel, and can make use of existing codes. The Lagrangian code requires less memory and is faster than the PIC code without massively parallel processing, but fails in 2-D for large intensity modulations. The Monge–Ampère code is by far the fastest in 2-D, without massively parallel processing, but fails for intensities with large voids, high contrast ratios and large deflections across the boundaries, and could not obtain the degree of convergence possible with the PIC code. The power diagram code was by far the slowest and most memory intensive, and failed for large peaks in the measured intensity.

Cattaneo-Christov Double Diffusion (CCDD) on Sutterby Nanofluid with Irreversibility Analysis and Motile Microbes Due to a RIGA Plate.

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This Riga plate creates an electric and magnetic field, where a transverse Lorentz force is generated that contributes to the flow along the plate. A new study field has been created by Sutterby nanofluid flows down the Riga plate, which is crucial to the creation of several industrial advancements, including thermal nuclear reactors, flow metres, and nuclear reactor design. This article addresses the second law analysis of MHD Sutter by nanofluid over a stretching sheet with the Riga plate. The Cattaneo–Christov Double Diffusion heat and mass flux have been created to examine the behaviour of relaxation time. The bioconvection of motile microorganisms and chemical reactions are taken into consideration. Similarity transformations are used to make the governing equations non-dimensional ordinary differential equations (ODE’s) that are subsequently solved through an efficient and powerful analytic technique, the homotopy analysis method (HAM). The effect of pertained variables on velocity, temperature, concentration, and motile microorganism distributions are elaborated through the plot in detail. Further, the velocity distribution enhances and reduces for greater value Deborah number and Reynold number for the two cases of pseudoplastic and dilatant flow. Microorganism distribution decreases with the augmented magnitude of Peclet number , Bioconvection Lewis number , and microorganism concentration difference number . The entropy production distribution is increased for the greater estimations of the Reynolds number and Brinkman parameter . Two sets of graphical outputs are presented for the Sutterby fluid parameter. Finally, for the justification of these outcomes, tables of comparison are made with various variables.

Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon

Using lattice QCD, we calculate the twist-2 contribution $a_2$ to the third Mellin moment of the spin structure functions $g_1$ and $g_2$ in the nucleon. In addition we evaluate the twist-3 contribution $d_2$. Our computations make use of $N_f=2+1$ gauge field ensembles generated by the Coordinated Lattice Simulations (CLS) effort. Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given in Eqs. (58) and (59). While the $a_2$ results have been converted to the $\overline{\mathrm{MS}}$ scheme using three-loop perturbation theory, the numbers for $d_2$ are given in the regularization independent momentum subtraction (RI$^\prime$-MOM) scheme, i.e., the conversion has been performed only in tree-level perturbation theory. The $d_2$ results can be interpreted as corresponding to a transverse color Lorentz force on a quark in a transversely polarized proton of size $F^{(u)} = 116(61)$ MeV/fm and $F^{(d)} = -38(66)$ MeV/fm for $u$ and $d$ quarks, respectively. The error estimates quoted include statistical and systematic uncertainties added in quadrature.

Width-bending characteristic of REBCO HTS tape and flat-tape Rutherford-type cabling

The width-bending behaviors for a rare earth barium copper oxide (REBCO) high-temperature superconducting (HTS) tape have been investigated. It has been found experimentally that the width-bending strain of a Yttrium Barium Copper Oxide (YBCO) tape does not degrade the critical current as much as is expected from the axial strain. The critical current is not directly affected by the width-bending strain but by the axial strain, which the width-bending strain generates by the Poisson effect. Since Poisson’s ratio is about 0.3, the axial strain effective on the critical current is about 30% of the width-bending strain. Therefore, the width-bending strain of even 1.5% degrades the critical current by only 15% if the REBCO layer side is bent inward. However, the critical current degraded by more than 70% when the REBCO layer is outward. The width-bending effects on the critical current have been further examined, considering Poisson’s ratio changes and the neutral plane shift of the REBCO tape substrate. Those changes would occur when the material yields due to severe width-bending. Based on the width-bending of REBCO tapes, flat-tape Rutherford-type cabling is discussed. A REBCO Rutherford-type cable can provide various advantages, especially for narrow-tape cabling. The flat-tape Rutherford-type cable has better characteristics against an electromagnetic transverse Lorentz force. Furthermore, the tape length of the cable can be approximately the same as the cable length allowing for excellent tape usage. REBCO Rutherford-type cabling will be a promising high-current, high-field cabling method using thin substrate REBCO tapes. It will be useful for AC ramp-field and pulse-field applications with low AC losses and low shield currents. It notes that the filaments in the cable are symmetrically distributed in parallel. Therefore, each filament’s inductance is uniform, and a uniform current distribution among the filaments can be obtained.

Micropolar Fluid Flow Along with an Inclined Riga Plate Through a Porous Medium

This study presents the one-dimensional unsteady micropolar fluid flow set in a porous medium along with an inclined infinite Riga plate. This Riga plate is created an electric and magnetic field, where a transverse Lorentz force is generated that contributes a flow along with the plate. The explicit finite difference method is used to find the solution of the non-dimensional form of the governing equations and estimated results are analyzed in terms of Microrotation parameter, Suction parameter, thermal Grashof number, mass Grashof number, Permeability parameter, Hartmann number, Dufour number, Soret number, Schmidt number. Also, the effects of the pertinent parameters on the local and average shear stress, Nusselt number, and Sherwood number are reported numerically as well as graphically.

Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields

Due to the increasing usage of nanostructures in nanotechnology and nanodevice, the following article aims to investigate the free vibration and buckling behaviours of a Timoshenko functionally graded nanobeam under to thermal and magnetic environment. The nanoscale and microstructure effects of FG nanobeam are included to classical mechanics using nonlocal strain gradient theory. The gradation of material properties throughout the beam thickness is described by power-law function. The material properties are assumed to be temperature dependent. Considering the thermal and Lorentz forces, the equations of motion of the functionally graded Timoshenko nanobeam are obtained using the strain gradient and nonlocal elasticity theories. The transverse Lorentz force induced by the horizontal magnetic field vector is derived using Maxwell’s equations. External compressive axial and transverse point loads are included in the formulation and the motion equations are solved using a Navier-type approach. The effects nonlocal size scale, and strain gradient microstructure influence, thermal loadings and magnetic field intensities on the free vibration, transverse bending and buckling behaviours of the functionally graded nanobeam are presented. The following model can be used as benchmark to analyse the nanobeam structure under thermomagnetic field using a finite element or any other numerical method.

Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment

A mathematical model is developed, though this article, to investigate a vibrational behaviour of functionally graded (FG) cracked microbeam rested on elastic foundation and exposed to thermal and magnetic fields. The model includes a size scale effect and temperature dependent material properties, for the first time. The crack is modelled as a rotating spring, that is connecting the two parts of the microbeam at the crack’s position. The equation of motion of the FG microbeam is obtained by using the Euler-Bernoulli beam theory for kinematic assumption and nonlocal elasticity theory for size-dependency effects. The transverse Lorentz force induced from the magnetic field is derived using Maxwell's equations. By adding the effects of thermal loading and foundation parameters on the cracked micro beam, the motion equation of the entire system is obtained using the Hamilton’s principle and then solved with a Navier type solution method. Eight constraints equations are used to derived the frequency equation, which are boundary conditions at the end points and the displacement, slope, bending moment and transverse force continuity in the section where the crack is located. The resulting system of equations is solved sequentially, and natural frequencies and vibration modes of the cracked microbeam are obtained. The model is verified with previous published work. Numerical results are presented to illustrate influences of temperature, material composition, foundation parameters and magnetic field on the dynamics of the cracked FG microbeam.

Response of a micro-capillary system exposed to a moving mass in magnetic field using nonlocal strain gradient theory

In this study, the dynamic behaviour of the micro dimensional Timoshenko beam (micro capillary system) exposed to a moving mass in a magnetic field is modelled using the non-local strain gradient theory. The motion equations of the Timoshenko micro-beam, which interacts with the moving mass, are obtained by considering the effects of strain gradient elasticity that provides stiffening and non-local elasticity that provide softening. The transverse Lorentz force acting on the beam in the magnetic field is obtained by Maxwell's equations and combined with the motion equations of the beam. These equations are converted into a weak form finite element equation by applying the exact shape functions of the two-node Timoshenko beam element in the Galerkin's method. Along with the effects of the magnetic field, the effects of the amount of different non-local parameters and the mass ratio and speed of the moving mass on the dynamics of the micro beam are presented. Experimental and theoretical studies have shown that the dynamic behaviour of the capillary structural systems is negatively affected by the effect of moving mass except for the non-local properties. Depending on the velocity and quantity of the mass and the nonlocal elasticity, the natural frequencies of the system drop excessively. When the mass ratio (moving mass/mass of the beam) is around 0.5, the frequencies have been observed to drop by as much as 60%, and the non-local elasticity and velocity of the mass are also effective in this. It has been shown that these disadvantages can be eliminated by the effect of the force obtained using the directed magnetic field. In fact, a desired system stiffness can be obtained by adjusting the magnitude of the magnetic field at the level required by the application.

Transverse force tomography

While twist-2 GPDs allow for a determination of the distribution of partons on the transverse plane, twist-3 GPDs contain quark-gluon correlations that provide information about the average transverse color Lorentz force acting on quarks. We demonstrate how twist-3 GPDs can be used to provide transverse position information about that force.

Overview of verification tests on AC loss, contact resistance and mechanical properties of ITER conductors with transverse loading up to 30 000 cycles

The ITER magnet system uses cable-in-conduit conductor (CICC) technology with individual strands twisted in several stages resulting in a rope-type cable, which is inserted into a stainless steel conduit. The combination of high current (up to 68 kA) and background magnetic field (up to 13 T) results in large transverse Lorentz forces exerted on the conductors during magnet system operation. The high transverse forces, accompanied with the cyclic nature of the load, have a strong influence on the conductor properties. The Twente Cryogenic Cable Press is used to simulate the effect of the Lorentz forces on a conductor comparable to the ITER magnet operating conditions. An overview is presented of the AC coupling and hysteresis loss, mechanical deformation characteristics and inter-strand contact resistance measurement results obtained on full-size ITER CICCs measured in the Twente Cryogenic Cable Press. The aim of this work is to characterize conductors’ electromagnetic and mechanical properties during cycling of the load up to 30 000 cycles. The evolution of the magnetization (AC coupling loss time constant nτ), mechanical properties and inter-strand resistance Rc between selected strands is presented along with loading history. The Rc between first triplet strands is also measured as a function of applied load. It is shown that transverse load cycling has a strong influence on the CICC properties. An overview of the results for eight toroidal field conductors, two central solenoid conductors, three poloidal field conductors of different types (PF1&6, PF4, PF5), one main bus-bar and one correction coil conductor is presented.

Electro-mechanical behavior of single twisted high-temperature superconducting tape under transverse Lorentz force

In recent years, several cabling methods of high temperature superconducting (HTS) cable have been proposed; e.g., the conductor on a round core cable (CORC), the Roebel assembled coated conductor cable, the helical twisted stacking-tape cable (TSTC) and the twisted-stack slotted core HTS cable (TSSC). These cabling methods allow the high temperature superconducting tapes widely used in the high-field magnets. The single superconducting tape performance under applied loads directly relates to the transport performance of the cable and the choice of the cabling method. In this paper, we investigate the effect of twisting morphology on the electro-mechanical properties of HTS tapes. Particular attention is given to the transverse Lorentz force of a pre-twisted HTS tape. The analytical solution of the deflection of the HTS tape under transverse Lorentz force is derived. Then, the current distribution and AC loss of the tape are calculated by using H-formulation. The effects of twist angle and loading conditions are examined for different HTS tape lengths. The results show that the stiffness resistance ability to Lorentz force of the HTS tape can be increased in several ranges by increasing the twist angle. The twisting structure can also reduce current degradation and AC loss, and thus enhance the transport capacity of HTS tape. This study helps understand the electro-mechanical properties of pre-twisted HTS tapes and provides theoretical reference for the design of novel HTS cable structures.

Transverse optical forces for manipulating nanoparticles

We study optical forces acting on a subwavelength particle with anisotropic polarizability and discover an optomechanical effect that resembles the Hall effect for electrons. While in the classical Hall effect the transverse Lorentz force and the transverse voltage appear due to the static magnetic field which induces the nondiagonal components of the electric conductivity tensor; in our case the imaginary parts of the nondiagonal elements of the polarizability tensor are responsible for the transverse scattering force. We calculate this force for the examples of the ellipsoidal plasmonic nanoparticles and the spherical particle with gyromagnetic properties, and show that the transverse force depends on the physical origin of the anisotropy of the polarizability, and on the electromagnetic wave structure around the particle. Moreover, this force primarily occurs in the inhomogeneous field only.

Temperature- and field-dependent characterization of a conductor on round core cable

The conductor on round core (CORC) cable is one of the major high temperature superconductor cable concepts combining scalability, flexibility, mechanical strength, ease of fabrication and high current density; making it a possible candidate as conductor for large, high field magnets. To simulate the boundary conditions of such magnets as well as the temperature dependence of CORC cables a 1.16 m long sample consisting of 15, 4 mm wide SuperPower REBCO tapes was characterized using the ‘FBI’ (force—field—current) superconductor test facility of the Institute for Technical Physics of the Karlsruhe Institute of Technology. In a five step investigation, the CORC cable’s performance was determined at different transverse mechanical loads, magnetic background fields and temperatures as well as its response to swift current changes. In the first step, the sample’s 77 K, self-field current was measured in a liquid nitrogen bath. In the second step, the temperature dependence was measured at self-field condition and compared with extrapolated single tape data. In the third step, the magnetic background field was repeatedly cycled while measuring the current carrying capabilities to determine the impact of transverse Lorentz forces on the CORC cable sample’s performance. In the fourth step, the sample’s current carrying capabilities were measured at different background fields (2–12 T) and surface temperatures (4.2–51.5 K). Through finite element method simulations, the surface temperatures are converted into average sample temperatures and the gained field- and temperature dependence is compared with extrapolated single tape data. In the fifth step, the response of the CORC cable sample to rapid current changes (8.3 kA s−1) was observed with a fast data acquisition system. During these tests, the sample performance remains constant, no degradation is observed. The sample’s measured current carrying capabilities correlate to those of single tapes assuming field- and temperature dependence as published by the manufacturer.

Rf Wien filter in an electric dipole moment storage ring: The “partially frozen spin” effect

An rf Wien filter (WF) can be used in a storage ring to measure a particle's electric dipole moment (EDM). If the WF frequency equals the spin precession frequency without WF, and the oscillating WF fields are chosen so that the corresponding transverse Lorentz force equals zero, then a large source of systematic errors is canceled but the EDM signal is not. This effect, discovered by simulation, can be called the ``partially frozen spin'' effect.

Turbulent drag reduction via a transverse wave traveling along streamwise direction induced by Lorentz force

Lorentz force can be used to induce motion in the electrically conducting fluids which might then lead to turbulence suppression and drag reduction. In this paper, drag reduction in turbulent channel flow via a transverse wave traveling along streamwise direction induced by Lorentz force is investigated numerically by direct numerical simulation. It is found that the intrinsic and induced flows are modified each other due to the two-way coupling when the transverse wavy Lorentz force is utilized to modulate the near-wall turbulent flow. There is an optimal wave number kx in flow control, in which the influence of the intrinsic flow on the induced flow is weakest, and on the contrary, the intrinsic turbulent flow is modified strongly by the induced flow. The variable-interval space averaging detective technique (a spatial version of the VITA technique) and conditionally sampled and ensemble averaging method are used to obtain the frequency and intensity of the turbulent bursts which mainly contribute to the turbulent skin-friction drag. The results show that the frequency and intensity vary with kx in the contradictious tendencies. Therefore, the turbulent skin-friction reduction can be optimized with kx. It is also shown that the maximum drag reduction is affected by the oscillation parameters.

$I_{\rm c}$ Measurements on ${\rm Nb}_{3}{\rm Sn}$ Strands Extracted From ITER CICC Prototypes

The unexpectedly low critical current performance of some ITER prototype cable-in-conduit conductors (CICC) measured in the SULTAN test facility during the last two years led to the question whether it arises from a transverse strain in the strands caused by the transverse Lorentz force or from a damage of filaments in the strands. Since the former process is in principle a reversible effect while the latter is not, measurements of the critical current of ~8 cm long strand sections extracted systematically from prototype samples were performed to see if and by how much the critical current dropped relative to the one of the witness sample. Strand witness samples had been mounted on ITER reference barrels, heat treated together with the conductor samples for the SULTAN tests and their I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> measured. Although the short sample lengths caused experimental difficulties and the number of measured strands permitted only a limited statistical analysis, the general trend of the conductor performance in SULTAN samples-high and stable (i.e. without cyclic load degradation) T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cs</sub> or not-is reflected in the I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> measurements on extracted strands.

Entropy production of Brownian macromolecules with inertia.

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.