Abstract
This paper described first an extension to the method of synthesis of electrodes for MIG's, which allows electrodes to be generated correctly even when trajectories of electrons from different parts of the cathode cross one another. Secondly, it is shown that electron beams of low velocity spread can be produced even when the cathode current is limited by space-charge. Trajectories calculated by a separate tracing program show that synthesis with allowance for space charge generates electrodes which are correctly shaped so as to counter the diverging force due to space-charge. The orbital velocity produced by given electrodes with space-charge-controlled emission is initially smaller than for the same electrodes with a temperature-limited cathode, but may be increased beyond the first anode by a non-adiabatic change in radial electric field.