Home Journals Article. Energy Losses in Superconductors. Charles Dean , Milind N. DOI: Abstract Absence of macroscopic resistance is the most essential trait of superconductors for their practical applications.
Share and Cite:. Dean, C. Journal of Power and Energy Engineering , 4 , Received 22 March ; accepted 22 May ; published 25 May 1. Introduction The transport of electrical current and levitation are two of the most important areas of practical importance for the application of superconductors.
Dimensional Enhancement of the Lower Critical Field The most straightforward vortex free state arises when the applied B is less than the lower critical field. Under these conditions B c 1 becomes greatly enhanced with respect to its usual bulk value and was shown by Abrikosov to be [1] : its usual bulk value and was shown by Abrikosov to be [1] : 1 2.
Dimensional Destruction of the Mixed State Another vortex excluding condition occurs when the cross section of the sample parallel to the applied B becomes too small. This process was studied theoretically by Likharev and he found the critical cross-sectional dimension to be [2] : 2 2.
High Viscous Coefficient Due to Delocalization of Vortex Electric Fields A third novel low-dissipative condition arises in a two-band superconductor when vortex electric fields become delocalized and one of the bands becomes normal but with a high normal conductivity at high B. Experimental Techniques Transport measurements were conducted in a Cryomech pulsed-tube closed-cycle refrigerator with the magnetic field supplied by a GMW water-cooled electromagnet.
Results and Discussion We show here one example each for the two sets of special conditions: the vortex-explosion scenario and the two-band mixed state with delocalized electric fields.
This is consistent with our observations for the B a b Figure 1. Conflicts of Interest The authors declare no conflicts of interest. References [ 1 ] Abrikosov, A. Journals Menu. Contact us. All Rights Reserved. Abrikosov, A. Likharev, K. Tinkham, M. Larkin, A. Subsequent research has produced new compounds with related structures that are superconducting at temperatures as high as K. The superconducting phase is thus a nonstoichiometric compound, with a fixed ratio of metal atoms but a variable oxygen content.
The overall equation for the synthesis of this material is as follows:. As shown in Figure The chains of Cu atoms are crucial to the formation of the superconducting state.
Table Engineers have learned how to process the brittle polycrystalline and related compounds into wires, tapes, and films that can carry enormous electrical currents. Commercial applications include their use in infrared sensors and in analog signal processing and microwave devices. How do you expect its structure to differ from those shown in Figure Given: stoichiometry.
Asked for: average oxidation state and structure. A Based on the oxidation states of the other component atoms, calculate the average oxidation state of Cu that would make an electrically neutral compound. B Compare the stoichiometry of the structures shown in Figure A The net negative charge from oxygen is 7.
Superconductors are solids that at low temperatures exhibit zero resistance to the flow of electrical current, a phenomenon known as superconductivity. The temperature at which the electrical resistance of a substance drops to zero is its superconducting transition temperature T c.
Superconductors also expel a magnetic field from their interior, a phenomenon known as the Meissner effect. The more efficient high-voltage transmission lines are used for moving electricity long distances.
At substations, the high voltage electricity is stepped down so that it can be distributed on lower voltage power lines. These less efficient distribution lines result in higher electricity losses.
However, market and policy restraints make some solutions more practical than others. Superconducting materials can conduct electricity with little to no resistance, but require cooling to nearly absolute zero.
These cooling requirements typically make superconducting materials too expensive to be considered for transmission lines. However, advances in higher temperature superconducting technology have reduced cooling requirements, also reducing their cost of operation. The city of Essen, Germany, installed a liquid nitrogen-cooled 0. However, the adopted superconductors have to experience time-varying currents or magnetic fields in many applications, e.
In this case, power dissipation is generated, which is defined by the term Alternating Current AC loss. In fact, the external field penetrates Type-II superconductors in the form of magnetic vortices pinned to the superconductor material. Variation of the transport current or external magnetic field as in an AC cycle can lead to the movement of vortices inside the superconductor, which induces currents in the normal conducting regions associated with the core of each vortex where AC power dissipation is thus produced [ 1 ].
It is a common practice related to experiments to categorize AC loss based on the AC source. Therefore, AC loss can be classified into transport current loss and magnetization loss. Magnetization loss describes the dissipation due to purely external magnetic fields without transport current, and transport current loss is caused by the carried current inside the superconductor in the absence of external magnetic fields [ 2 ].
Magnetization loss consists of eddy current loss, hysteresis loss, and coupling loss. Hysteresis loss is generated by flux pinning and the loss per cycle is proportional to the area of the hysteresis loop. Coupling loss occurs due to the flowing of eddy current induced by external magnetic fields between filaments in multifilamentary conductors.
Therefore, coupling loss can also be a problem for striated superconducting tapes. Eddy current loss is the ohmic power dissipation generated by the eddy current in the metal matrix. Transport current loss includes hysteresis loss and flux flow loss. Hysteresis loss occurs because the carried time-varying current provides the self-field. Flux flow loss happens due to more and more vortices moving in the superconductor with the increase of the transport current or the load proportion between the transport current and the self-field critical current.
Particularly, when a superconductor carries a DC and experiences simultaneously a time-varying magnetic field, the interaction between the DC transport current and the moving vortices leads to a time-averaged potential drop along the superconductor [ 3 ]. Dynamic resistance and dynamic loss are thus proposed to characterize the resistance and power dissipation generated in this specific case. Let us consider a thin high temperature superconducting HTS film of a coated conductor CC with the width of 2 w and the thickness of h , having I c0 as the self-field critical current.
Equation 1 shows that the magnetization power loss is in a positive correlation with the amplitude of the external field and the square of the film width. It can be found that the transport power loss increases positively with the load ratio. Actually, it can increase even more rapidly due to flux-flow dissipation. At sufficiently high load ratios, some of the current will flow in the normal conducting parts of the HTS CC leading to a resistive contribution [ 1 ].
It should be noted that in Equation 3 n is even. When n is odd, the upper bound of summation has to be changed correspondingly [ 7 ]. According to Equation 3 , it can be seen that the dynamic power loss is in positive correlation with the width of the film, the load ratio, as well as the external field.
When the HTS film with a low load ratio experiences a low external field, its dynamic loss is mainly determined by the first term in 3 and varies almost linearly with the external field. However, at both high load ratios and high external fields, the dynamic loss is dominated by the second term in 3 and varies rapidly in a non-linear way with the external field, putting the CC in danger of a quench.
More analytical formulae for calculating the AC loss of distinct HTS geometries can be found in the review article [ 12 ]. According to Equations 1 - 3 , it is intuitively understood that the magnetization power loss, transport power loss, and dynamic power loss all increase linearly with frequency.
However, at sufficiently high frequencies, the transport current and magnetic flux will be driven towards the normal conducting regions of the CC under the skin effect [ 13 ] [ 14 ].
Besides, analytical loss calculations are imperfect in that the formulae have been derived based on some fundamental assumptions, e. Additionally, the analytical equations are normally limited to simple structures, e. Therefore, numerical models and experimental measurements appear to be indispensable tools to quantify the AC loss of complex geometries in a complicated electromagnetic environment.
The first step for numerically calculating AC loss is to build a geometric model 1D, 2D, or 3D for the studied object based on its physical properties, e. Afterwards, one has to choose a numerical method and a formulation. The FEM-based numerical models can be incorporated into commercial software, e. Once the electromagnetic state variables in the chosen formulation are obtained, the AC loss can be calculated according to the methods presented in Section II-C in [ 15 ].
It can be seen that the modelled total AC loss of the whole CC based on the H -formulation is in good agreement with the measured data. Through numerical modelling, we can access quantities not available from measurements, e. In this case, the analytical formulae, e. Figure 1. Experimental data are taken from [ 16 ]. To overcome the limitations of the full models and decrease the modelling complexity, e. There exist three main approaches for measuring AC loss of superconductors, namely electric, magnetic, and calorimetric methods.
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