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Residual gas within the envelope of an electron tube forms positive ions by electron collision. Ordinarily these ions are quickly lost to the cathode; however, if they can be held within the beam space, the spreading due to the space charge of the beam might be considerably reduced. A "trapping" electrode, with an appropriate positive potential, placed at the cathode end of the drift tube was believed sufficient to affect trapping. Since this simple method was first proposed, attempts to make the scheme work yielded inexplicable results. A detailed study of the phenomenon reveals that the trapping process is more complex than was originally believed. A qualitative theory is advanced which is consistent with experiment and leads to suggestions for an improved performance. By a proper design of the trapping electrode, transmission through a drift space was improved from twelve per cent to eighty per cent.