Orbital Stability and Formation Flying Control of a Superconducting-Loop Solar Sail Under Combined Solar Radiation Pressure and Solar Wind Forces

Continuous stationkeeping near Sun–Earth collinear libration points requires thrusts of several mm/s², which exhausts propellant-based propulsion and bounds mission lifetime. Building on the superconducting-loop solar sail configuration originally proposed by Kezerashvili and Kezerashvili, this paper investigates a propellant-free sailcraft (superconducting-loop solar sail, SCLSS) where a single superconducting loop deploys a reflective membrane and provides a magnetic sail thrust channel via solar wind interaction. A dual-channel thrust model with a ±11.38° cone angle limit is embedded in the circular restricted three-body problem. The existence regions of artificial equilibrium points (AEPs) are derived, and linear stability is reduced to a cubic characteristic equation. NSGA-II optimization yields a compromise design, (β_s, β_m) = (0.0941, 0.0795), with a thrust index of 0.0956, identified as a theoretical envelope; a self-consistent baseline, m_total ≈ 1060 kg, confirms deployment and thrust capability. Artificial Halo orbits exist near Sub-L1 for 0 < β < β_D = 0.07602. For a five-spacecraft formation, a fixed-time disturbance-observer-based nonlinear backstepping controller converges position errors within about 1.1 days, compared to about 1.3 days for a benchmark PID, while reducing the steady-state position error from the 0.3 m level to below 0.1 m. Sensitivity analysis with an alternative thrust scaling confirms the robustness of these conclusions. This study provides a stability-oriented design methodology and control framework for SCLSS missions.