Influence of AC Loss on Stress and Strain of Superconducting Coils

Estimation of the Electricity Storage Volume Density of Compact SMESs of a New Concept Based on Si Microfabrication Technologies

“…The results of the calculations of ΣB max , w, and S max as a function of R min for two different value settings of m, d, s, and z shown in Figures 16 and 17 are displayed in the same manner as in Figure 14; in Figures S1-S4 in the case of the magnetic flux densitydependent j c of curves (b) and (c) in Figure 4, which is simulated by Equation (11); and in Figures S5-S8 in the case of the magnetic flux density-dependent j c of curve (a) in Figure 4, which is simulated by Equation (12), respectively. The values of w, R min , S max , and ΣB max indicated by the perpendicular dashed-dotted red lines and the perpendicular dashed-two dotted blue lines in Figures S1-S8 are summarized in Table 1.…”

“…Figure 17 schematically summarizes the combinations of the wafer coil design parameters, d, s, z, examined here. Iteration processes using Equation (11) or Equation (12) gave converging values of j c∞. and ΣB max∞ as a function of R min .…”

“…This is essentially an iteration process in which the Σ max decided by the initially set value j c0 reduces j c0 to j c1 , and then j c1 decides the new value of ΣB max1 , which reduces j c1 to j c2 , and so on. For the convenience of calculation, j c was expressed as a function of ΣB max in expression (11) based on curves (b) and (c) in Figure 4.…”

“…The following are available online at https://www.mdpi.com/2312-748 1/7/3/44/s1: Figure S1: R min dependence of w, S max and ΣB max for d = 50 µm, s = 22 µm, m = 600, and (a) z = 30 µm, (b) z = 100 µm based on Equation (11)…”

“…A superconducting current in a coil in the vicinity of the critical superconducting current density (j c ) can induce an intense magnetic field, resulting in a huge electromagnetic force imposed on the superconducting current along the radial direction to enlarge the coil diameter ('hoop stress'). To prevent the coil from breaking under this force, the coil must be protected by specially designed reinforced structures [11][12][13][14][15][16]. The necessity of this reinforced structures is another factor that causes the large volumes of conventional SMES systems.…”