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Introduction to Superconducting Devices
Published in Raja Sekhar Dondapati, High-Temperature Superconducting Devices for Energy Applications, 2020
Superconductors lose their superconductivity when the magnetic field strength exceeds a certain value in the external magnetic field. The magnetic field strength which causes a superconductor to lose its superconductivity is called critical field strength and is denoted by Hc. When the temperature is below Tc, Hc is a function of temperature and continuously increases with a decrease in temperature. With a similar behavior as Tc, there is also a field transition width when the superconductors transfer from a normal state to a superconducting state. For a practical superconductor, there are usually two critical fields, namely, lower critical field Hc1 and upper critical field Hc2. When the external field is less than Hc1, the superconductor is in Meissner state; however, when the external field is larger than Hc2, the superconductor is in normal state. While the field is between Hc1 and Hc2, the superconductor is in mixed state (more details provided in Section 1.5).
Fundamentals of Superconductors
Published in A. G. Mamalis, D. E. Manolakos, A. Szalay, G. Pantazopoulos, Processing of High-Temperature Superconductors at High Strain Rates, 2019
A. G. Mamalis, D. E. Manolakos, A. Szalay, G. Pantazopoulos
In this class of superconductors two different values of the critical magnetic field, a lower critical field Hc1 and an upper critical field Hc2, are present. When the applied field H < Hc1, then the diamagnetic effect (exclusion of magnetic field lines from the interior of the material) is observed. In the case of Hc1 < H < Hc2, progressive penetration of the magnetic field begins forming an intermediate or mixed or vortex state. Finally, when H exceeds Hc2, the magnetic field totally penetrates into the interior of the material, destroying, therefore, the superconducting state in the interior of the material that remains in a surface superconducting state for Hc2 < Hc < Hc3, see Figure 2.3(b). Type II superconductors are all the alloys (including Nb), intermetallic components and ceramic oxides.
Magnesium Diboride
Published in David A. Cardwell, David C. Larbalestier, I. Braginski Aleksander, Handbook of Superconductivity, 2023
The upper critical field Hc2 is a very important property in a superconducting material in view of potential high-field applications. In a conventional BCS superconductor, Hc2 is determined by the relation μ0Hc2=ϕ0/2πξ2, where ϕ0 is the quantum flux, and ξ is the coherence length, and the Hc2 anisotropy, γ, is substantially temperature independent. In the clean limit, the coherence length depends on the Fermi velocity and the gap amplitude by ξ0=ℏvF/πΔ(0). In the dirty limit, i.e. when the mean free path is l < ξ0, the upper critical field at zero temperature is determined by the Werthamer–Helfand–Hohenberg (WHH) relation (Werthamer et al., 1966): Hc2(0)=0.69TcdHc2dTTc
Investigations of arsenic substitution on the physical, electrical and magnetic properties of Bi-2212 superconductors
Published in Phase Transitions, 2020
W. Labban, W. Malaeb, K. Habanjar, M.S. Hassan, R. Sakagami, Y. Kamihara, R. Awad
For the magnetism study, half magnetic-hysteresis loops are shown in Figure 5(a) and (b) up to 50 kOe field, at 5 and 30 K, respectively. Apparently, the magnitude of magnetization effectively depends on As content. It is obvious that sample As2 with 0.2 arsenic content has the largest hysteresis loop with the toughest diamagnetic behaviour at both applied temperatures. Thus, arsenic probably acts as an effective flux pinning centre in Bi-2212 superconductors. As the temperature increased, in Figure 5(b), a decrease in the area and in the maximum magnetization is observed. This is attributed to the decrease in the number of Cooper pairs as the temperature increases, as well as the motion of the pinning centres. This is a general characteristic feature of HTSC materials with granular structure and weak link between the grains. Moreover, at high field values, the separation vanishes as the upper and lower curves of the loops converge into a straight ‘irreversibility’ line. This line’s extrapolation intercepts with the x-axis at the temperature dependent upper critical field Hc2(T) (see the inset) [45]. These calculated values of Hc2, listed in Table 4, follow the same trend of Tc, with As1 having the highest Hc2. This is because the upper critical field is a superconducting parameter, which does not, unlike Jc, depend on the transport quality of the bulk. This can be remarked at the high field values, where the As2 line starts to approach the x-axis faster than the As1 line, as As1 possesses the highest Tc and hence the most stable superconducting state. The coherence length ξ values, listed in Table 4, were calculated using the Ginzburg-Landau theory by: where Φ0 is the magnetic flux quantum which has a value of 2.0678 × 10−15 T.m2 [46].