{"knowledge_schema": {"broad_category": "Mathematics \u2192 Functional Analysis \u2192 Spectral Series Expansion", "refinement": "This category involves techniques used to represent functions in terms of orthogonal basis functions, particularly in the context of solving partial differential equations in toroidal geometries.", "specific_scope": "The focus is on identifying the appropriate spectral series expansion technique that is specifically adapted for poloidal dependence in toroidal systems, which often arise in plasma physics and magnetically confined fusion devices.", "goal": "Select the correct spectral series expansion technique that effectively captures the poloidal variation in toroidal systems."}, "summary": "In the context of toroidal systems, particularly in plasma physics, the appropriate spectral series expansion technique adapted for poloidal dependence is typically the use of Fourier series. This method allows for the representation of functions with periodic properties, which is essential in capturing the behavior of poloidal variations in toroidal geometries."}