arXiv subjects

Leonid Prigozhin

Publications and source records attributed to Leonid Prigozhin.

At least 19 recordsLinked to original sources

arXiv2026

T-E formulation-based modeling of thin HTS shell magnetization

Numerical methods for modeling thin-film magnetization are primarily focused on computing the current density distribution. The highly nonlinear current-voltage characteristic of type-II superconductors significantly complicates the accurate computation of the electric field. The T-E formulation-based mixed finite element method, previously derived for flat superconducting films, enables the simultaneous, accurate determination of both variables. Another advantage of this method is that the computational domain is limited to the film itself: no meshing of the surrounding space is required. The thin-shell approximation reduces the problem to a two-dimensional one. This work extends the T-E formulation and numerical method to non-flat superconducting shells with a metal substrate. We validate the method with several test examples, including modeling the magnetization of a sphere. The method is then applied to a realistic model of a cylindrical magnetic dynamo pump, and the generated open-circuit voltage is computed.

cond-mat.supr-con↗

arXiv2026

Spectral solution of axisymmetric magnetization problems for thin superconducting shells

Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving non-flat films. The method is based on the integral thin-shell current-density formulation of the problem, employs Chebyshev polynomial expansions for spatial discretization, and uses the method of lines for time integration. It applies to both open and closed axisymmetric shells and is so accurate that the solutions obtained can serve as benchmarks for numerical methods for general, not necessarily axisymmetric, thin-shell magnetization problems. As one of the examples, we consider magnetic shielding by a superconducting sphere.

cond-mat.supr-con↗

arXiv2025

Electromagnetic analysis of coated conductors with ferromagnetic substrates: Novel insights

Ferromagnetic substrates can significantly influence the electromagnetic response of a coated conductor to an external magnetic field and transport current. This study analyzes this response theoretically using the thin shell integrodifferential model. First, assuming the substrate is strongly magnetic and the superconductor is in the Meissner state, we present the analytical solution in a convenient explicit form. This helps us to analyze the superconducting current density distributions, highlighting their differences from those in conductors with non-magnetic substrates. Secondly, for a superconducting layer characterized by a nonlinear current-voltage relation and a substrate with a finite field-independent magnetic permeability, we use an effective spectral numerical method to study the unique features of this hybrid superconductor/ferromagnet system, such as magnetization in a parallel external field and the peculiar nonmonotonic variation of loss observed when alternating transport current and parallel field are applied simultaneously. Dynamic losses for the case of a direct transport current and an alternating parallel field are also investigated. It is shown that tuning the phase and amplitude of the applied parallel field relative to those of the transport current can minimize AC losses.

cond-mat.supr-con↗

arXiv2024

Magnetization of Flat Superconducting Films on Ferromagnetic Substrates

Ferromagnetic substrate influences the electromagnetic response of a type-II superconducting film to the applied magnetic field. We present a two-dimensional integrodifferential model for the magnetization of a flat superconductor/ferromagnet bilayer of an arbitrary shape using a thin shell quasistatic model for the ferromagnetic substrate and an infinitely thin approximation for the superconducting layer. An efficient numerical method is developed and used to investigate the effect of a ferromagnetic substrate. In particular, we simulate the thin bilayer magnetization in a parallel field and, for a high field, the critical-state distributions of the superconducting current density. These critical-state distributions are different from those known for a normal external field.

cond-mat.supr-con↗

arXiv2023

HTS Dynamo Flux Pump: The Impact of a Ferromagnetic Stator Substrate

HTS dynamo magnetic flux pumps are perspective devices for contactless charging the superconductor magnets and coils. In this work, we investigate the influence of a ferromagnetic substrate of a coated conductor used as the pump stator. We use the thin shell model of a coated conductor with a ferromagnetic substrate and show that such a conductor increases the pump-generated voltage if the superconducting layer is between the rotor and the substrate. Chebyshev spectral method is employed for numerical solution. Using simulation results for problems with a given transport current we also derive a simple analytical description for feeding a current to a coil.

physics.app-ph↗

arXiv2023

Thin shell model of a coated conductor with a ferromagnetic substrate

Coated conductors with magnetic substrates are thin multilayer structures; their high aspect ratio and nonlinear material properties present significant difficulties for numerical simulation. Using the high width-to-thickness ratio of coated conductors we derive an integral formulation for a model based on an infinitely thin approximation for the superconducting layer and a quasistatic thin shell approximation for the magnetic substrate. The proposed model describes electromagnetic response of a coated conductor with a magnetic substrate and is much simpler than the existing models. A single dimensionless parameter characterizes the substrate having a finite magnetic permeability and a finite thickness. An accurate and efficient Chebyshev spectral method is derived for numerical solution. The influence of a magnetic substrate on the superconducting current and AC losses is investigated. In the limiting cases our model solution tends to the known analytical solutions.

cond-mat.supr-con↗

arXiv2021

Hermite-Chebyshev pseudospectral method for inhomogeneous superconducting strip problems and magnetic flux pump modeling

Numerical simulation of superconducting devices is a powerful tool for understanding the principles of their work and improving their design. We present a new pseudospectral method for two-dimensional magnetization and transport current superconducting strip problems with an arbitrary current-voltage relation, spatially inhomogeneous strips, and strips in a nonuniform applied field. The method is based on the bivariate expansions in Chebyshev polynomials and Hermite functions. It can be used for numerical modeling magnetic flux pumps of different types and investigating AC losses in coated conductors with local defects. Using a realistic two-dimensional version of the superconducting dynamo benchmark problem as an example, we showed that our new method is a competitive alternative to finite element methods.

cond-mat.supr-con↗

arXiv2021

Fast solution of the superconducting dynamo benchmark problem

A model of high temperature superconducting dynamo, a promising type of flux pumps capable of wireless injection of a large DC current into a superconducting circuit, has recently been chosen as an applied superconductivity benchmark problem and solved using ten different numerical methods (Ainslie et al 2020 Supercond. Sci. Technol. 33 105009). Using expansions in Chebyshev polynomials for approximation in space and the method of lines for integration in time we derive a simple and accurate numerical method which is much faster. The proposed numerical method was applied also to problems with transport current and a field-dependent sheet critical current density.

physics.comp-ph↗

arXiv2021

Two-dimensional model of a high-Tc superconducting dynamo

High temperature superconducting dynamos are capable of low loss contactless pumping large dc currents into superconducting magnet coils. We present a model of such devices and use efficient numerical methods for computing the two-dimensional loop currents and electric fields induced in the thin superconducting stator strip by a dynamo rotor mounted permanent magnet. We find also the voltages generated in the stator under the open circuit conditions. It is shown that if the length of a permanent magnet is comparable to or smaller than the strip width, the one-dimensional model employed in the previous works can be inaccurate.

cond-mat.supr-con↗

arXiv2019

Optically Tailored Trapping Geometries for Ultracold Atoms on a Type-II Superconducting Chip

Superconducting atom chips have very significant advantages in realizing trapping structures for ultracold atoms compared to conventional atom chips. We extend these advantages further by developing the ability to dynamically tailor the superconducting trap architecture. Heating the chosen parts of a superconducting film by transferring optical images onto its surface we are able to modify the current density distribution and create desired trapping potentials. This method enables us to change the shape and structure of magnetic traps, enabling versatile applications in atomtronics.

physics.atom-ph↗

arXiv2018

Solution of 3D magnetization problems for superconducting film stacks

A stack of coated conductors is a perspective configuration for various applications of high temperature superconductors. We present an efficient fast Fourier transform-based numerical method for magnetization problems for a stack of flat films of the same (arbitrary) shape and compare it with the recently proposed finite element methods. For stacks containing a large number of densely packed films an accurate solution can be obtained as a properly rescaled solution for a stack of only several films. For an infinite stack the problem simplifies and becomes similar to that for a single film.

cond-mat.supr-con↗

arXiv2018

3D Simulation of Superconducting Magnetic Shields and Lenses using the Fast Fourier Transform

Shielding sensitive scientific and medical devices from the magnetic field environment is one of the promising applications of superconductors. Magnetic field concentration by superconducting magnetic lenses is the opposite phenomenon based, however, on the same properties of superconductors: their ideal conductivity and ability to expel the magnetic field. Full-dimensional numerical simulations are necessary for designing magnetic lenses and for estimating the quality of magnetic shielding under arbitrary varying external fields. Using the recently proposed Fast Fourier Transform based three-dimensional numerical method [Prigozhin and Sokolovsky, ArXiv 1801.04869] we model performance of two such devices made of a bulk type-II superconductor: a magnetic shield and a magnetic lens. The method is efficient and can be easier to implement than the alternative approaches based on the finite element methods.

physics.comp-ph↗

arXiv2018

FFT-based solution of 2D and 3D magnetization problems in type-II superconductivity

We consider the Fast Fourier Transform (FFT) based numerical method for thin film magnetization problems [Vestgården and Johansen, SuST, 25 (2012) 104001], compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current-voltage relation; its efficiency is illustrated by numerical simulations.

physics.comp-ph↗

arXiv2016

On the Energy-Based Variational Model for Vector Magnetic Hysteresis

We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation which can be inaccurate in the vectorial case. The parameters of this model for a nonoriented steel are identified using a set of first order reversal curves. Finally, the model is incorporated as a local constitutive relation into a 2D finite element simulation accounting for both the magnetic hysteresis and the eddy current.

cond-mat.other↗

arXiv2014

3D modeling of magnetic atom traps on type-II superconductor chips

Magnetic traps for cold atoms have become a powerful tool of cold atom physics and condense matter research. The traps on superconducting chips allow one to increase the trapped atom life- and coherence time by decreasing the thermal noise by several orders of magnitude compared to that of the typical normal-metal conductors. A thin superconducting film in the mixed state is, usually, the main element of such a chip. Using a finite element method to analyze thin film magnetization and transport current in type-II superconductivity, we study magnetic traps recently employed in experiments. The proposed approach allows us to predict important characteristics of the magnetic traps (their depth, shape, distance from the chip surface, etc.) necessary when designing magnetic traps in cold atom experiments.

cond-mat.supr-con↗

arXiv2013

Sandpiles and Superconductors: Nonconforming Linear Finite Element Approximations for Mixed Formulations of Quasi-Variational Inequalities

Similar evolutionary variational and quasi-variational inequalities with gradient constraints arise in the modeling of growing sandpiles and type-II superconductors. Recently, mixed formulations of these inequalities were used for establishing existence results in the quasi-variational inequality case. Such formulations, and this is an additional advantage, made it possible to determine numerically not only the primal variables, e.g. the evolving sand surface and the magnetic field for sandpiles and superconductors, respectively, but also the dual variables, the sand flux and the electric field. Numerical approximations of these mixed formulations in previous works employed the Raviart--Thomas element of the lowest order. Here we introduce simpler numerical approximations of these mixed formulations based on the nonconforming linear finite element. We prove (subsequence) convergence of these approximations, and illustrate their effectiveness by numerical experiments.

math.NA↗

arXiv2013

Transport current and magnetization problems for thin type-II superconducting films

Thin film magnetization problems in type-II superconductivity are usually formulated in terms of the magnetization function alone, which allows one to compute the sheet current density and the magnetic field but often inhibits computing the electric field in the film. Accounting for the current leads presents an additional difficulty encountered in thin film transport current problems. We generalize, to the presence of a transport current, the two-variable variational formulation proposed recently for thin film magnetization problems. The formulation, written in terms of the magnetization function and the electric field, is used as a basis for a new numerical approximation enabling us to solve the magnetization and transport current problems for flat films of arbitrary shapes, including multiply connected films. The advantage of this approach is in its ability to compute accurately all variables of interest, including the electric field, for any value of the power in the power law current-voltage relation characterizing the superconducting material. In the high power limit the critical state model solution is obtained.

cond-mat.supr-con↗

arXiv2012

Electric field formulation for thin film magnetization problems

We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes it possible to accurately compute all variables of interest, including the electric field, for any value of the power in the power law current-voltage relation characterizing the superconducting material. For high power values we obtain a good approximation to the critical state model solution. Numerical simulation results are presented for simply and multiply connected films, and also for an inhomogeneous film.

cond-mat.supr-con↗