Advances on permanent high‐T_c superconducting magnets are reported. Materials are tested in the form of small tiles. An accurate phenomenological model of the currents in a magnetized tile predicts that the maximum trapped field B_T,max∝J_cf(d), where J_c is the critical current density, d is the diameter of the single‐grain tile, and f(d) is a function which increases monotonically with d. Results are reported of increasing J_c via chemical additives, and via bombardment by high‐energy light ions and fission fragments. Increases in d via chemical and temperature gradients are also reported. Methods, data, and most recent results are presented. Present values are d=2 cm, and J_c=85 kA/cm², at 77 K. A six tile minimagnet, 1.2×1.2×1.5 cm³, fabricated from earlier tiles with d∼1 cm, J_c∼45 kA/cm², retains 1.52 T at 77 K. It is calculated that the more recent values of J_c and d will result in fields of 3 T at 77 K. B_T,max also increases rapidly with T⁻¹, and approximately doubles at 60 K.

${\mathrm{Bi}}_{\mathrm{2}}{\mathrm{Sr}}_{\mathrm{2}}{\mathrm{Ca}}_{\mathrm{2}}{\mathrm{Cu}}_{\mathrm{3}}{\mathrm{O}}_x$ (Bi-2223) tapes were processed by the standard powder-in-tube technique, but small amounts of ${\mathrm{UO}}_{\mathrm{4}}$ were added prior to processing. Both U-doped and undoped tapes were subsequently exposed to a reactor spectrum of neutrons. Whereas the undoped materials show moderate enhancements of the critical current densities $J_c$ due to the pinning action of the fast-neutron-induced collision cascades, $J_c$ in the U-doped tapes increases by factors of 10–20 due to thermal-neutron-induced fission of ${}^{\mathrm{235}}\mathrm{U}$ and the subsequent formation of fission tracks. Since the enhancements are particularly pronounced, when the magnetic field is applied perpendicular to the tape surface, the characteristic $J_c$ anisotropy is strongly reduced in a certain field range. At the same time, the irreversibility field at 77 K is doubled for both field orientations.

Recent experiments on pulsed-zero field cool magnetization of bulk high J_c YBCO (YBa₂Cu₃O_7-δ) have shown unexpected results. For example, reproducible, non-destructive, rapid, giant field leaps (GFLs) to higher penetrated field are observed. The observations are inconsistent with the critical state model (CSM), in several aspects. Additional experiments have been pursued in an attempt to clarify the physics involved in the observed anomalies. Here, we present experimental results for the J_c dependence of the anomalous features. It is found that the sudden field increase in the GFL is a monotonically increasing function of J_c. The ratio of required pulsed field amplitude, B_A,max, to obtain maximum trappable field, B_T,max, which CSM predicts to be ≥2.0, gradually approaches 1.0 at high J_c. Tests using values of pulsed, applied field B_A,max just below the GFL exhibit two additional anomalies: (i) At high J_c, the highest trapped field is up to ∼6 times lower than predicted by CSM, and (ii) the measured Lorentz force as a function of J_c deviates sharply from CSM predictions. The data rule out heating effects and pinning center geometry as possible physical causes of these anomalies. A speculative cause is considered.