The superheating field of the Meissner state is thought to determine the theoretical field-limit of superconducting accelerator cavities. We investigate of semi-infinite superconductors and layered structures in the diffusive limit using the well-established quasiclassical Green’s function formalism of the BCS theory. The coupled Maxwell–Usadel equations are self-consistently solved to obtain the spatial distributions of the magnetic field, screening current density, penetration depth, pair potential, and . For a semi-infinite superconductor in the diffusive limit, we obtain at the temperature . Here, is the thermodynamic critical-field at the zero temperature. By laminating a superconducting film (S) with the thickness on a semi-infinite superconductor (Σ), we can engineer of the layered structure. When is the optimum thickness , can be larger than that of the simple semi-infinite superconductors made from the S and Σ materials: . The present study addresses the calculation of of the dirty heterostructure using the microscopic theory from beginning to end for the first time, which contributes to the microscopic understanding of the surface engineering for pushing up the accelerating gradient of superconducting cavities for particle accelerators.

据认为，迈斯纳状态的过热场决定了超导加速器腔的理论场极限。我们使用已建立的BCS理论的准古典格林函数形式主义，研究扩散极限中的半无限超导体和层状结构。可以自洽地求解耦合的Maxwell-Usadel方程，以获得磁场的空间分布，筛选电流密度，穿透深度，线对电势和。对于扩散极限中的半无限超导体，我们在温度下获得。此处是零温度下的热力学临界场。通过层压具有一定厚度的超导膜（S）在半无限超导体（Σ）上，我们可以设计分层结构。当为最佳厚度时，可以大于由S和Σ材料制成的简单的半无限超导体的厚度：。本研究首次使用微观理论从头到尾解决了脏异质结构的计算问题，这有助于对表面工程的微观理解，从而推动了粒子加速器超导腔的加速梯度。