  We report a detailed theoretical model of recently-demonstrated magnetic trap
system based on a pair of magnetic tips. The model takes into account key
parameters such as tip diameter, facet angle and gap separation. It yields
quantitative descriptions consistent with experiments such as the vertical and
radial frequency, equilibrium position and the optimum facet angle that
produces the strongest confinement. We arrive at striking conclusions that a
maximum confinement enhancement can be achieved at an optimum facet angle
$\theta_{max}=\arccos{\sqrt{2/3}}$ and a critical gap exists beyond which this
enhancement effect no longer applies. This magnetic trap and its theoretical
model serves as a new and interesting example of a simple and elementary
magnetic trap in physics.
