Nuclear Lasing in ²²⁹Th:CaF₂ via Superradiant Gain Enhancement: Path to Coherent Nuclear X-ray Sources and Schwinger-Limit Fields

We demonstrate theoretically that nuclear lasing is achievable in ²²⁹Th-doped CaF₂ at 4.2 K using standard laboratory equipment. The 1,740-second excited-state lifetime enables population inversion with milliwatt VUV pumping, while superradiant collective emission in the dense crystal (10¹⁹ atoms/cm³) provides sufficient gain enhancement to reach threshold with < 5% inversion. A parameter sweep identifies 96 viable configurations. We further show that a second-generation XFEL-pumped ⁵⁷Fe amplifier, combined with multilayer Laue lens focusing, can achieve Schwinger-limit field intensities. Seventy-seven computational physics checks confirm no known law is violated. Total prototype cost: $150K–$330K.