On the Concept of Fictitious Surface Charges of an Electron Beam

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Abstract
The electrodynamical phenomena in the boundary strip of a sharply focused electron beam are extremely complicated. This difficulty is usually resolved by postulating a layer of surface current on the boundary of the unperturbed beam while considering the troublesome boundary strip as nonexistent. A critical examination is made of this technique with the result that, if the calculated rf power is to be the same as in the actual beam, a layer of electric dipoles must also be postulated. The discussion begins with the Jacobian and Taylor's expansion, with particular emphasis on the applicability of the latter to the boundary strip, then proceeds to the formulation of a modified problem on an equal‐power basis and the specification of the surface conditions which are to be satisfied. Second‐order quantities are included in all equations, so that the small‐signal beam kinetic quantities can be reliably calculated.