The beam-loading admittance of gridless klystron gaps

Expressions for the beam-loading conductance for an electron beam have been derived in Branch and Vlasov. This paper shows that the beam-loading susceptance is the Hilbert transform of the conductance. The expressions for the admittance of the ideal gridded gap and the gridless gap are then derived. In particular, curves of G/G
0
and B/G
0
are presented for gridless gaps with different gap lengths and with different beam sizes.