Flux quanta, magnetic field lines, merging – some sub-microscale relations of interest in space plasma physics

Abstract. We clarify the notion of magnetic field lines in plasma by referring to sub-microscale (quantum mechanical) particle dynamics. It is demonstrated that magnetic field lines in a field of strength B carry single magnetic flux quanta Φ₀=h/e. The radius of a field line in the given magnetic field B is calculated. It is shown that such field lines can merge and annihilate only over the length ℓ_∥ of their strictly anti-parallel sections, for which case we estimate the power generated. The length ℓ_∥ becomes a function of the inclination angle θ of the two merging magnetic flux tubes (field lines). Merging is possible only in the interval 12πθ≤π. This provides a sub-microscopic basis for "component reconnection" in classical macro-scale reconnection. We also find that the magnetic diffusion coefficient in plasma appears in quanta D₀^m=eΦ₀/m_e=h/m_e. This lets us conclude that the bulk perpendicular plasma resistivity is limited and cannot be less than η_0⊥=μ₀eΦ₀/m_e=μ₀h/m_e~10⁻⁹ Ohm m. This resistance is an invariant.