Electromagnetic wave scattering by a superconductor

The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in cylindrical coordinates. Numerical results computed up to $\mathcal{O}(77)$ of Bessel functions are presented for different wavelengths showing the appearance of a diffraction pattern.Comment: 3 pages, 3 figure

Bulk and Surface Nanoscale Hole Density Inhomogeneity in HgBa2_2CuO4+δ_{4+\delta} and Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} Cuprates

It is well established that the hole density in the prototypical superconductor La$_{2-x}$Sr$_x$CuO$_4$ is very inhomogeneous due to Sr-dopant induced disorder. On the other hand, until recently it is widely believed that the hole distribution in HgBa$_2$CuO$_{4+\delta}$ and Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ doped by interstitial oxygen is much more uniform. Recent nuclear magnetic resonance measurements indicate, however, that the charge inhomogeneity in HgBa$_2$CuO$_{4+\delta}$ is close to that in La$_{2-x}$Sr$_x$CuO$_4$. Calculations performed in the present paper confirm this observation. We also show that the charge inhomogeneity is most pronounced at the surface layer that can be probed by scanning tunneling microscope. Our simulations demonstrate that, despite having similar amplitudes of charge inhomogeneity, the hole mean free path in HgBa$_2$CuO$_{4+\delta}$ is substantially longer than that in La$_{2-x}$Sr$_x$CuO$_4$. The screening of Coulomb repulsion in HgBa$_2$CuO$_{4+\delta}$ is also stronger. These two reasons might explain the difference in superconducting critical temperatures between these two compounds.Comment: to appear in PRB, extended discussion of hole mean free pat

Numerical Simulation of Multicomponent Ion Beam from Ion Sources

A program library for numerical simulation of a multicomponent charged particle beam from ion sources is presented. The library is aimed for simulation of high current, low energy multicomponent ion beam from ion source through beamline and realized under the Windows user interface for the IBM PC. It is used for simulation and optimization of beam dynamics and based on successive and consistent application of two methods: the momentum method of distribution function (RMS technique) and particle in cell method. The library has been used to simulate and optimize the transportation of tantalum ion beam from the laser ion source (CERN) and calcium ion beam from the ECR ion source (JINR, Dubna)

Electrostatic interaction of a pointlike charge with a wormhole

A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only on the value and location of the charge, while the other, on the contrary, does not change when the charge is quasistatically moved. Correspondingly, the former is interpreted as being generated by the charge, and the latter as being source-free. It is shown that all source-free potentials differ in the flux through the throat (no "multipoles without multipoles"), which enables one to interpret the flux as the "charge" of the wormhole in agreement with Wheeler's concept of "charge without charge". The potential generated by the charge differs from Coulomb's and thus a force (called "self-force") acts on the charge even in the absence of the source-free field. This force is found explicitly in the limit of vanishing throat length. The result differs from that obtained recently by Khusnutdinov and Bakhmatov.Comment: The published version: 1) the regularity is proven 2) the part is rewritten explaining where is the error in Khusnutdinov and Bakhmatov's resul

The Bean model of the critical state in a magnetically shielded superconductor filament

We study the magnetization of a cylindrical type-II superconductor filament covered by a coaxial soft-magnet sheath and exposed to an applied transverse magnetic field. Examining penetration of magnetic flux into the superconductor core of the filament on the basis of the Bean model of the critical state, we find that the presence of a non-hysteretic magnetic sheath can strongly enhance the field of full penetration of magnetic flux. The average magnetization of the superconductor/magnet heterostructure under consideration and hysteresis AC losses in the core of the filament are calculated as well.Comment: 4 pages, 3 figures; Proceedings of the 7th European Conference on Applied Superconductivity, Vienna, Austria, September 11-15, 200

The Bean-Livingston barrier at a superconductor/magnet interface

The Bean-Livingston barrier at the interface of type-II superconductor/soft-magnet heterostructures is studied on the basis of the classical London approach. This shows a characteristic dependence on the geometry of the particular structure and its interface as well as on the relative permeability of the involved magnetic constituent. The modification of the barrier by the presence of the magnet can be significant, as demonstrated for a cylindrical superconducting filament covered with a coaxial magnetic sheath. Using typical values of the relative permeability, the critical field of first penetration of magnetic flux is predicted to be strongly enhanced, whereas the variation of the average critical current density with the external field is strongly depressed, in accord with the observations of recent experiments.Comment: RevTeX 4; revised version; accepted in Journal of Physics: Condensed Matte

ЧИСЛЕННЫЕ ОЦЕНКИ ТОКОВ И СИЛ В ЛИНЕЙНЫХ ИНСТРУМЕНТАХ МАГНИТНО-ИМПУЛЬСНОГО ПРИТЯЖЕНИЯ МЕТАЛЛОВ. ЧАСТЬ 2: МЕТАЛЛЫ С ВЫСОКОЙ УДЕЛЬНОЙ ЭЛЕКТРОПРОВОДНОСТЬЮ

Purpose. The purpose of the present work is substantiating workability of the linear tools of the magnetic-pulse attraction of thin-walled sheet metals with high electrical conductance, the principle of which is based on the force interaction of two conductors with unidirectional currents during intensive penetration of the acting electromagnetic fields. Constructively, one of these conductors in the linear tools is the so-called main current lead (an analog of the inductor in EMF) and the second one is the part of the sheet metal which has to be deformed. Methodology. For numerical estimates the analytical dependences are obtained with help of the methods of electromagnetic field theory as well the standard programs from the Wolfram Mathematica package used. Results. The fulfilled calculations illustrate the amplitude-temporal dependences for the excited currents and forces under the demanded decrease of the operating frequencies of the acting electromagnetic fields. The efficiency of the linear magnetic-pulse tools is based on the excitation of the mutual attraction forces of conductors with low-frequency unidirectional currents. Originality. By the example of aluminum, which is the main raw material in modern aviation and automotive industry, it has been found that for processing the metals with high electrical conductance demand a significant decreasing operating frequencies, what is necessary for intensifying the penetration processes of acting fields and, accordingly, for exciting the real attractive forces. Practical value. The results of the work allow formulating the based recommendations for the creation and practical application of the linear magnetic-pulse attraction tools for the progressive technologies of restoring the damaged areas of bodies coatings from the thin-walled sheet metals with the high specific electrical conductivity.Цель. Целью работы является обоснование дееспособности линейных инструментов магнитно-импульсного притяжения тонкостенных листовых металлов с высокой удельной электропроводностью, принцип действия которых основан на силовом взаимодействии проводников с однонаправленными токами при интенсивном проникновении возбуждаемых полей. Методика. Для численных оценок использовались аналитические зависимости, полученные с помощью методов теории электромагнитного поля, и стандартные программы из пакета «Wolfram Mathematica». Результаты. Проведенные вычисления иллюстрируют амплитудно-временные зависимости для возбуждаемых токов и сил при требуемом понижении рабочих частот действующих электромагнитных полей. Обоснована действенность линейных магнитно-импульсных инструментов, основанных на возбуждении сил взаимного притяжения проводников с низкочастотными однонаправленными токами. Научная новизна. На примере с алюминием, который является основным сырьевым материалом в современном авиа- и автомобилестроении, установлено, что для металлов с высокой удельной электропроводностью требуется значительное понижение рабочих частот, что необходимо для интенсификации процессов проникновения действующих полей и, соответственно, для возбуждения реальных сил притяжения. Практическое значение. Результаты работы позволяют сформулировать обоснованные рекомендации по созданию и практическому применению линейных инструментов магнитно-импульсного притяжения в прогрессивных технологиях восстановления повреждённых участков корпусных покрытий из тонкостенных листовых металлов с высокой удельной электропроводностью

Analysis of electromagnetic processes in the system "cylindrical solenoid - massive conductor"

Defining the key parameters of the inductor geometry, as a long multi-turn solenoid, that influence on the current amplitude induced excited in a massive conductor with a flat boundary surface. Performing a mathematical analysis of the electrodynamic problem solution for an area with variable structure by integrating Maxwell's equation within the given boundary and initial conditions and also physical assumptions simplifying the process of solving but not distorting the result and carrying out an experiment that confirms not only the correctly construction considered but also the acceptability of the chosen assumption the opacity applying of the metal blank for these operating fields frequencies. Functional dependencies of the current induced parameters on the metal surface of the heating object have been obtained, along which numerical estimates of the electrodynamic process have been performed, and key parameters influencing the heating efficiency have been determined. The correctness of the solutions obtained was confirmed experimentally. The final form of the solution function of the physical-mathematical problem was shown to be acceptable for performing further engineering and research calculations. The functional connection of the measured values of the induced surface current and the parameters of the measuring system is determined, the experimental confirmation of which indicates the satisfactory calculation model of the induction heating system and the entire solution as a whole. Based on the calculations performed, working samples of inductive systems for induction heating that meet the specified heating rate and area requirements can be constructed. The obtained analytical expressions were transformed and simplified for their further using for engineering calculations with a minimum error value.Определение ключевых параметров геометрии индуктора, как длинного многовиткового соленоида, влияющих на амплитуду индуцированного тока возбуждаемого в массивном проводнике с плоской граничной поверхностью. Выполнение математического анализа решения электродинамической задачи для среды с переменной структурой путем интегрирования уравнений Максвелла в рамках заданных граничных и начальных условий, а также физических допущений, которые упрощают процесс решения, но не искажают его результат; а также проведение эксперимента подтверждающего не только правильно выполненное построение, но и допустимость применения выбранного допущения о непрозрачности металлической заготовки для данных частот действующих полей. Получены функциональные зависимости искомых параметров индуцированного тока на поверхности металла объекта нагрева, по которым были выполнены численные оценки электродинамического процесса, определены ключевые параметры, влияющие на эффективность нагрева. Правильность полученных решений была подтверждена экспериментально. Окончательный вид функции решения физико-математической задачи был приведен к приемлемому для выполнения дальнейших инженерных и исследовательских расчётов. Определена функциональная связь измеряемых величин индуцированного поверхностного тока и параметров измерительной системы, экспериментальное подтверждение которой свидетельствует об удовлетворительности расчетной модели системы индукционного нагрева и всего решения в целом. На основании проведенных расчетов могут быть сконструированы рабочие образцы индуктивных систем для индукционного нагрева, отвечающие заданным требованиям скорости нагрева и его площади. Полученные аналитические выражения были преобразованы и упрощены с целью их дальнейшего использования для инженерных расчётов с минимальной величиной погрешност

ЭКСПЕРИМЕНТАЛЬНЫЕ ИССЛЕДОВАНИЯ РАСПРЕДЕЛЕНИЯ ТОКА НА ПОВЕРХНОСТИ ЛИСТОВОЙ ЗАГОТОВКИ В ЛИНЕЙНЫХ ИНСТРУМЕНТАХ МАГНИТНО-ИМПУЛЬСНОГО ПРИТЯЖЕНИЯ

Purpose. The purpose of the present work consists in the characteristics experimental determination of the pulsed current transverse distribution on the surface of a sheet non-magnetic metal between the point contacts of the power source with different geometry of their connection under operating frequencies variation. Methodology. The measurements were carried out using methods based on the known positions of electromagnetism. The simulating low-voltage equipment was used, as well as high-voltage power sources with a high level of the stored energy. Numerical processing of the measurement results was carried out using standard programs from the «Wolfram Mathematica» package. Results. The space-temporal shapes of the pulsed current density transverse distribution on the surface of the sheet blank were obtained and analyzed. It is established that the degree of transverse current concentration in sheet metal relative to the center of the system in the operating frequency range of ~ 1.8…22 kHz depends very little on its temporal characteristics. It was found that the level of the transverse current concentration in the conditionally allocated band connecting the contacts of connection depends significantly on the ratio of the width of this band and the transverse dimensions of the contact connection. Moreover, the smallest current is concentrated in a strip whose width is much less than the distance between the contacts (£ 11…16 %). Originality. For the first time, the numerical estimates degree of the current transverse concentration are obtained and the dependence of this parameter on the temporal characteristics of the current, as well as on the method of connecting the power source contacts, is established. Practical value. The research results will allow creating the new more efficient linear tools of magnetic-pulsed attraction of sheet metals, based on the force interaction of conductors with unidirectional currents. Целью работы является экспериментальное определение характеристик поперечного распределения плотности импульсных токов разной частоты на поверхности листового немагнитного металла между точечными контактами источника мощности при различной геометрии их подключения. Методика. Измерения проводились с помощью методов, основанных на известных положениях электромагнетизма. Использовалось модельное низковольтное оборудование, а также высоковольтные источники мощности с высоким уровнем запасаемой энергии. Численная обработка результатов измерений проводилась с помощью стандартных программ из пакета «Wolfram Mathematica». Результаты. Получены и проанализированы пространственно-временные формы поперечного распределения плотности импульсного тока на поверхности листовой заготовки. Научная новизна. Впервые получены численные оценки степени поперечной концентрации тока и установлена зависимость данного параметра от временных характеристик тока, а также от способа подключения контактов источника мощности. Практическое значение. Результаты исследований позволяют создавать новые более эффективные линейные инструменты магнитно-импульсного притяжения листовых металлов, основанные на силовом взаимодействии проводников с однонаправленными токами