Experimentally, it has been established that negative ions cross the anode‐cathode gap in transmission lines operating at sufficiently high currents that electrons emitted from the cathode would be magnetically insulated (i.e., deflected back to the cathode by the Lorentz force before reaching the anode). In this paper, a one‐dimensional analysis of electron and negative ion emission from a cathode shows that electron emission decreases monotonically to zero as the ion emission increases to the maximum space charge limited value. A second one‐dimensional calculation shows that in high current lines, neglecting electron emission, monopolar emission of ions is inhibited by the self‐magnetic fields in the line, while bipolar emission is enhanced. Finally, a section is devoted to the approximate solution of several two‐dimensional problems using some of the earlier results of this paper, as well as an empirical scaling law derived by other researchers relating the negative ion current densityjnto the current per unit width in a line,J:jn=KJ3. In particular, fractional current loss as a function of distance from a load drawing a fixed current is found. An interesting byproduct of this calculation is the demonstration that the empirical scaling law leads to infinite line currents in a finite distance along a planar line, while such a divergence occurs only for certain parameter ranges on radial disk feed lines.