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We consider an infinite three-dimensional waveguide that far from thecoordinate origin coincides with a cylinder. The waveguide has two narrows ofdiameter $\varepsilon$. The narrows play the role of effective potentialbarriers for the longitudinal electron motion. The part of waveguide betweenthe narrows becomes a "resonator"\, and there can arise conditions for electronresonant tunneling. A magnetic field in the resonator can change the basiccharacteristics of this phenomenon. In the presence of a magnetic field, thetunneling phenomenon is feasible for producing spin-polarized electron flowsconsisting of electrons with spins of the same direction.  We assume that the whole domain occupied by a magnetic field is in theresonator. An electron wave function satisfies the Pauli equation in thewaveguide and vanishes at its boundary. Taking $\varepsilon$ as a smallparameter, we derive asymptotics for the probability $T(E)$ of an electron withenergy $E$ to pass through the resonator, for the "resonant energy"\,$E_{res}$,where $T(E)$ takes its maximal value, and for some other resonant tunnelingcharacteristics.

Effect of magnetic field on resonant tunneling in 3D waveguides of variable cross-section