Möbius Magnetic Topology Theory (MMT): A Unified Framework for Field-Line Closure, Linking Invariants, and 4π Orbits in a Bi-Conical Plasma Cavity

This is the English version of MMT-I Abstract This paper establishes a global topological theory of vector field lines in a biconical Möbius plasma cavity, termed Möbius Magnetic Topology (MMT). The core structure of this cavity is a Möbius closed coil, with two driving modes (pulsed electron beam drive and magnetic flux drive) separated in time. The waist "torus" is redefined as a Möbius tube surface woven by field line families themselves—a non-trivial S¹ fiber bundle. The complete theory consists of seven main propositions and one corollary: Theorem A (allowed modes determined by the congruence condition 2p≡q (mod 2)), P1 Closure Theorem (closure winding number satisfies k(p+2q)≡0 (mod 2p)), P2 Mutual Linking Invariant (field line pairs classified into co-directional mutual linking, counter-directional zero linking, and cross self-linking), P3 Cross Structure (linking number and self-linking number are two essentially different topological quantities), P4 Induced Association (E-M nested mutual linking topological transmission), P5 Composite Structure (four field lines exhibit Whitehead-type signature), P6 4π Orbit Unification (under integer pitch ratio, two "field lines" are actually two loops of the same 4π orbit), and P6-corollary (induced dual field manifold equation, stable 4π closure when q/p=2). Numerical scanning further yields the quantitative relationship between cone angle and field line pitch ratio: q/p≈0.0097tan²α+0.978tanα-0.098, and reveals that the symmetry breaking relative deviation δ(α)/tanα monotonically decreases with cone angle. This work provides a theoretical foundation for plasma diagnostics, topological electromagnetic structure design, and magnetic island early warning in magnetically confined fusion.