A symmetry property of space-charge waves in accelerated electron beams

A symmetry property is deduced for an electron beam modulated and demodulated by gaps of cavities. This property results from a combination of the theory of space-charge wave propagation in an accelerated beam and of the theory of gaps. It states that in a region bounded by two cavities, the power detected by the second cavity is unaltered by an interchange of potentials on the two cavities, provided the widths of the gaps are small. Experimental results are given for both linear and nonlinear acceleration and deceleration regions. In all cases, this property is found to be true. Most of the experimental results are also tested vs theoretical solutions of the electronic equation for regions of acceleration. The reduction factor is included in the theory.