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Turbulence-Driven Corrugation of Collisionless Fast-Magnetosonic Shocks

Collisionless fast-magnetosonic shocks are often treated as smooth, planar boundaries, yet observations point to organized corrugation of the shock surface. A plausible driver is upstream turbulence. Broadband fluctuations arriving at the front can continually wrinkle it, changing the local shock geometry and, in turn, conditions for particle injection and radiation. We develop a linear-MHD formulation that treats the shock as a moving interface rather than a fixed boundary. In this approach the shock response can be summarized by an effective impedance determined by the Rankine-Hugoniot base state and the shock geometry, while the upstream turbulence enters only through its statistics. This provides a practical mapping from an assumed incident spectrum to the corrugation amplitude, its drift along the surface, and a coherence scale set by weak damping or leakage. The response is largest when the transmitted downstream fast mode propagates nearly parallel to the shock in the shock frame, which produces a Lorentzian-type enhancement controlled by the downstream normal group speed. We examine how compression, plasma $β$, and obliquity affect these corrugation properties and discuss implications for fine structure in heliospheric and supernova-remnant shock emission.