Yang 2023b - Revision history

Rimni at 14:27, 11 January 2024

2024-01-11T14:27:34Z

Rimni at 14:26, 11 January 2024

2024-01-11T14:26:16Z

Rimni: /* 3. 2 Calculated results for ring bulk superconductor */

2024-01-11T14:25:39Z

‎3. 2 Calculated results for ring bulk superconductor

Rimni at 14:24, 11 January 2024

2024-01-11T14:24:04Z

Rimni at 13:15, 11 January 2024

2024-01-11T13:15:42Z

Rimni at 13:14, 11 January 2024

2024-01-11T13:14:44Z

Rimni: /* 2. Numerical model and parameters */

2024-01-11T13:13:36Z

‎2. Numerical model and parameters

Rimni at 15:06, 10 January 2024

2024-01-10T15:06:43Z

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Rimni: /* 3. 3 Calculated results for ring bulk superconductor with crack */

2024-01-10T14:29:32Z

‎3. 3 Calculated results for ring bulk superconductor with crack

Rimni at 14:28, 10 January 2024

2024-01-10T14:28:55Z

@@ Line 159: / Line 159: @@
 |}
-where  <math>B_{max}</math> is the peak value of the applied magnetic field and  <math>t_1</math> is the rise time of the applied magnetic field.
+where  <math>B_{\max}</math> is the peak value of the applied magnetic field and  <math>t_1</math> is the rise time of the applied magnetic field.
 In the mechanical calculations, the ring bulk sample is considered as an isotropic linear elastic material. The mechanical equilibrium equation can be expressed as follows

@@ Line 299: / Line 299: @@
 ===3.2 Calculated results for ring bulk superconductor===
-To analyze the electromagnetic characteristics of the ring bulk superconductor during the PFM process, [[#_Ref143373901|Figure 1]] shows the magnetic field, and current density distributions of the bulk superconductor at different times (5 ms, 13 ms, 20 ms, 80 ms and 150 ms). As shown in the figure, the magnetic field at the ascending stage (0-13 ms), penetrates from the upper and lower ends of the bulk superconductor towards the interior. Simultaneously, a circular current is generated within the bulk, gradually flowing from the external region into the interior. Conversely, reverse currents begin to appear simultaneously from the upper and lower ends of the bulk sample at the descending stage (after 13ms).
+To analyze the electromagnetic characteristics of the ring bulk superconductor during the PFM process, [[#_Ref143373901|Figure 3]] shows the magnetic field, and current density distributions of the bulk superconductor at different times (5 ms, 13 ms, 20 ms, 80 ms and 150 ms). As shown in the figure, the magnetic field at the ascending stage (0-13 ms), penetrates from the upper and lower ends of the bulk superconductor towards the interior. Simultaneously, a circular current is generated within the bulk, gradually flowing from the external region into the interior. Conversely, reverse currents begin to appear simultaneously from the upper and lower ends of the bulk sample at the descending stage (after 13ms).
 <div id='_Ref143373901'></div>

@@ Line 297: / Line 297: @@
-===3. 2 Calculated results for ring bulk superconductor===
+===3.2 Calculated results for ring bulk superconductor===
 To analyze the electromagnetic characteristics of the ring bulk superconductor during the PFM process, [[#_Ref143373901|Figure 1]] shows the magnetic field, and current density distributions of the bulk superconductor at different times (5 ms, 13 ms, 20 ms, 80 ms and 150 ms). As shown in the figure, the magnetic field at the ascending stage (0-13 ms), penetrates from the upper and lower ends of the bulk superconductor towards the interior. Simultaneously, a circular current is generated within the bulk, gradually flowing from the external region into the interior. Conversely, reverse currents begin to appear simultaneously from the upper and lower ends of the bulk sample at the descending stage (after 13ms).
@@ Line 310: / Line 310: @@
-<span id='cite-_Ref143374175'></span>[[#_Ref143374175|Figures 4]](a) and (b) depict the distribution of the trapped field and temperature at different times during the magnetization process on the <math display="inline">z=0</math> plane. The observed variation in the trapped field aligns with the findings in <span id='cite-_Ref132901240'></span>[[#_Ref132901240|[15]]] for cylindrical bulk samples. However, the temperature variation differs from that of cylindrical bulk samples. In the simulation results, it could be found that the temperature gradually increases inward from the right side along the radius and then decreases gradually. This phenomenon arises due to the reinforcement of the bulk sample with an aluminum alloy ring, which affects the thermal conduction between the bulk sample and the aluminum alloy, thereby influencing the temperature distribution.
+<span id='cite-_Ref143374175'></span>[[#_Ref143374175|Figures 4]](a) and (b) depict the distribution of the trapped field and temperature at different times during the magnetization process on the <math display="inline">z=0</math> plane. The observed variation in the trapped field aligns with the findings in Wu et al. <span id='cite-_Ref132901240'></span>[[#_Ref132901240|[15]]] for cylindrical bulk samples. However, the temperature variation differs from that of cylindrical bulk samples. In the simulation results, it could be found that the temperature gradually increases inward from the right side along the radius and then decreases gradually. This phenomenon arises due to the reinforcement of the bulk sample with an aluminum alloy ring, which affects the thermal conduction between the bulk sample and the aluminum alloy, thereby influencing the temperature distribution.
 <div id='_Ref143374175'></div>

@@ Line 418: / Line 418: @@
 <span id='_Ref132811982'></span>[[#cite-_Ref132811982|[7]]] Ainslie M.D., Fujishiro H., Mochizuki H., et al. Enhanced trapped field performance of bulk high-temperature superconductors using split coil, pulsed field magnetization with an iron yoke. Supercond. Sci. Technol., 29, 074003, 2016.
-<span id='_Ref132811983'></span>[[#cite-_Ref132811983|[8]]] Zhou D., Shi Y., Dennis A.R.,, et al. Flux jumps in ring-shaped and assembled bulk superconductors during pulsed field magnetization. Supercond. Sci. Technol., 33, 034001, 2020.
+<span id='_Ref132811983'></span>[[#cite-_Ref132811983|[8]]] Zhou D., Shi Y., Dennis A.R., et al. Flux jumps in ring-shaped and assembled bulk superconductors during pulsed field magnetization. Supercond. Sci. Technol., 33, 034001, 2020.
 <span id='_Ref132811985'></span>[[#cite-_Ref132811985|[9]]] Zhou D., Ainslie M.D., Srpčič J., et al. Exploiting flux jumps for pulsed field magnetisation. Supercond. Sci. Technol., 31, 105005, 2018.
@@ Line 432: / Line 432: @@
 <span id='_Ref144388911'></span>[[#cite-_Ref144388911|[14]]] Li R., Fang J., Liao X., et al. Electromagnetic and thermal properties of HTS bulk combined with different ferromagnetic structures under pulsed field magnetization. IEEE Transactions on Applied Superconductivity, 33(6):1-6, 2023.
-<span id='_Ref132901240'></span><span id='_Hlk139048497'>[[#cite-_Hlk139048497|[15]]] Wu H., Yong H., et al. Stress analysis in high-temperature superconductors under pulsed field magnetization. Superconductor Science and Technology, 31(4), 045008, , 2018.
+<span id='_Ref132901240'></span><span id='_Hlk139048497'>[[#cite-_Hlk139048497|[15]]] Wu H., Yong H., et al. Stress analysis in high-temperature superconductors under pulsed field magnetization. Superconductor Science and Technology, 31(4), 045008, 2018.
 <span id='_Ref132901719'><span id='_Hlk139048580'></span>[[#cite-_Hlk139048580|[16]]] Wu H., Yong H., et al. Analysis of mechanical behavior in inhomogeneous high temperature superconductors under pulsed field magnetization. Superconductor Science and Technology, 33(12), 124002, 2020.
@@ Line 460: / Line 460: @@
 <span id='_Ref132987311'></span>[[#cite-_Ref132987311|[28]]] Ainslie M.D., Zhou D., Fujishiro H., et al. Flux jump-assisted pulsed field magnetisation of high-Jc bulk high-temperature superconductors. Supercond. Sci. Technol., 29, 124004, 2016.
-<span id='_Ref132987503'></span>[[#cite-_Ref132987503|[29]]] Fujishiro H, Naito T, Furuta D. Analysis of temperature and magnetic field distribution in bulk superconductor during pulsed field magnetization. IEEE Trans. Appl. Supercond. , 2011, 21: 2723–2726
+<span id='_Ref132987503'></span>[[#cite-_Ref132987503|[29]]] Fujishiro H., Naito T, Furuta D. Analysis of temperature and magnetic field distribution in bulk superconductor during pulsed field magnetization. IEEE Trans. Appl. Supercond., 21:2723–2726, 2011.
-<span id='_Ref135916399'></span>[[#cite-_Ref135916399|[30]]] Diko P. Cracking in melt-processed RE-Ba-Cu-O superconductors[J]. Superconductor Science and Technology, 1998, 11(1): 68
+<span id='_Ref135916399'></span>[[#cite-_Ref135916399|[30]]] Diko P. Cracking in melt-processed RE-Ba-Cu-O superconductors. Superconductor Science and Technology, 11(1):68-72, 1998.
-<span id='_Ref135916686'></span>[[#cite-_Ref135916686|[31]]] Zhou Y H, Yong H D. Crack problem for a long rectangular slab of superconductor under an electromagnetic force[J]. Physical Review B, 2007, 76(9): 094523
+<span id='_Ref135916686'></span>[[#cite-_Ref135916686|[31]]] Zhou Y.H., Yong H.D. Crack problem for a long rectangular slab of superconductor under an electromagnetic force. Physical Review B, 76(9), 094523, 2007.
-<span id='_Ref135916990'></span>[[#cite-_Ref135916990|[32]]] Ru Y, Yong H, Zhou Y. Fracture analysis of bulk superconductors under electromagnetic force[J]. Engineering Fracture Mechanics, 2018, 199: 257-273
+<span id='_Ref135916990'></span>[[#cite-_Ref135916990|[32]]] Ru Y., Yong H., Zhou Y. Fracture analysis of bulk superconductors under electromagnetic force. Engineering Fracture Mechanics, 199:257-273, 2018.
-<span id='_Ref136003622'></span>[[#cite-_Ref136003622|[33]]] Callister W, David R. Material Science and Engineering—An Introduction. Danvers: WILEY, 2007
+<span id='_Ref136003622'></span>[[#cite-_Ref136003622|[33]]] Callister W., Rethwisch D. Material science and engineering - An introduction. John Wiley & Sons, pp. 990, 2007.
-<span id='_Ref142674225'></span>[[#cite-_Ref142674225|[34]]] van der Laan D C, Ekin J W. Large intrinsic effect of axial strain on the critical current of high-temperature superconductors for electric power applications[J]. Applied physics letters, 2007, 90(5)
+<span id='_Ref142674225'></span>[[#cite-_Ref142674225|[34]]] van der Laan D.C., Ekin J.W. Large intrinsic effect of axial strain on the critical current of high-temperature superconductors for electric power applications. Applied Physics Letters, 90(5), 052506, 2007.
-<span id='_Ref142706874'></span>[[#cite-_Ref142706874|[35]]] Duron J, Grilli F, Dutoit B, ''et al. ''Modelling the E–J relation of high-Tc superconductors in an arbitrary current range[J]. Physica C: Superconductivity, 2004, 401(1-4): 231-235
+<span id='_Ref142706874'></span>[[#cite-_Ref142706874|[35]]] Duron J., Grilli F., Dutoit B., et al. Modelling the E–J relation of high-Tc superconductors in an arbitrary current range. Physica C: Superconductivity, 401(1-4):231-235, 2004.
-<span id='_Ref143947786'></span>[[#cite-_Ref143947786|[36]]] Diko P, Krabbes G. Macro-cracking in melt-grown YBaCuO superconductor induced by surface oxygenation[J]. Superconductor Science and Technology, 2002, 16(1): 90.
+<span id='_Ref143947786'></span>[[#cite-_Ref143947786|[36]]] Diko P., Krabbes G. Macro-cracking in melt-grown YBaCuO superconductor induced by surface oxygenation. Superconductor Science and Technology, 16(1):90-93, 2002.
-<span id='_Ref143947968'></span>[[#cite-_Ref143947968|[37]]] Ren Y, Weinstein R, Liu J, ''et al. ''Damage caused by magnetic pressure at high trapped field in quasi-permanent magnets composed of melt-textured Y-Ba-Cu-O superconductor[J]. Physica C: Superconductivity, 1995, 251(1-2): 15-26.
+<span id='_Ref143947968'></span>[[#cite-_Ref143947968|[37]]] Ren Y., Weinstein R., Liu J., et al. Damage caused by magnetic pressure at high trapped field in quasi-permanent magnets composed of melt-textured Y-Ba-Cu-O superconductor. Physica C: Superconductivity, 251(1-2):15-26, 1995.
-<span id='_Ref143949294'></span>[[#cite-_Ref143949294|[38]]] Hong Z, Campbell A M, Coombs T A. Numerical solution of critical state in superconductivity by finite element software[J]. Supercond. Sci. Technol. , 2006, 19(12): 1246.
+<span id='_Ref143949294'></span>[[#cite-_Ref143949294|[38]]] Hong Z., Campbell A.M., Coombs T.A. Numerical solution of critical state in superconductivity by finite element software. Supercond. Sci. Technol., 19(12):1246-1252, 2006.

@@ Line 315: / Line 315: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:60%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image76.png|482px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image76.png|540px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 4'''. Trapped field and temperature distribution in the <math display="inline">z=0</math> plane of the bulk at different times under the PFM process

@@ Line 196: / Line 196: @@
 {\gamma }_{zr}
 \end{array}\right]=\left[\begin{array}{cccc}
-\frac{1}{E} & -\frac{\upsilon }{E} & -\frac{\upsilon }{E} & 0\\
+\displaystyle\frac{1}{E} & -\displaystyle\frac{\upsilon }{E} & -\displaystyle\frac{\upsilon }{E} & 0\\
--\frac{\upsilon }{E} & \frac{1}{E} & -\frac{\upsilon }{E} & 0\\
+-\displaystyle\frac{\upsilon }{E} & \displaystyle\frac{1}{E} & -\displaystyle\frac{\upsilon }{E} & 0\\
--\frac{\upsilon }{E} & -\frac{\upsilon }{E} & \frac{1}{E} & 0\\
+-\displaystyle\frac{\upsilon }{E} & -\displaystyle\frac{\upsilon }{E} & \displaystyle\frac{1}{E} & 0\\
 & 0 & 0 & \frac{1}{G}
 \end{array}\right]\left[\begin{array}{c}

@@ Line 93: / Line 93: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>f(n) = \begin{cases} \frac{{\rho }_{sc}\cdot {\rho }_{normal}}{{\rho }_{sc}+{\rho }_{normal}}, & \mbox{    }T\leq T_c \\ {\rho }_{nomal}, & \mbox{              }T>T_c \end{cases}</math>
+| <math>f(n) = \begin{cases} \displaystyle\frac{{\rho }_{sc}\cdot {\rho }_{normal}}{{\rho }_{sc}+{\rho }_{normal}}, & \mbox{    }T\leq T_c \\ {\rho }_{nomal}, & \mbox{              }T>T_c \end{cases}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (4)

@@ Line 362: / Line 362: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image84.png|500px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image84.png|550px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 8'''. Stress distributions clouds for bulk containing central crack case (left) and edge crack case (right)
@@ Line 384: / Line 384: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:60%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image89.png|398px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image89.png|358px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 10'''. Maximum radial and hoop stresses during magnetization of bulk containing edge crack case of different lengths

@@ Line 326: / Line 326: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:60%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image78.png|422px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_893267287081-image78.png|482px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 5'''. Distribution of radial and hoop stresses at different moments in the <math display="inline">z=0</math>plane of a bulk under the action of a pulsed magnetic field
 |}
 ===3. 3 Calculated results for ring bulk superconductor with crack===