Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and indeterminacy field-lines at a magnetic null. Electron inertia changes implications both features. Magnetic field lines are distinguishable only when their distance closest approach exceeds $\Delta_d$. ensures $\Delta_d\gtrsim c/\omega_{pe}$. that lie within flux tube radius $\Delta_d$ place where strength $B$ strongest fundamentally indistinguishable. If tube, somewhere along its length, encloses point $B=0$,vanishes, then come no closer null than $\approx (a^2c/\omega_{pe})^{1/3}$, $a$ characteristic spatial scale field. behavior presence studied for dipole embedded spatially constant In addition distinguishability, constraint on obtained, time required thin sheets arise derived.