Using a generalized coupled-mode model, the paper shows that in an inhomogeneous accelerating section the beam-excited counter-propagating field component is not a simple left-travelling wave and contributes a non-negligible correction to the total field.
Masunov, The current loading and nonlinear beam dynamics in linac, Proceedings of EPAC 2000, pp.1315 -
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Description of electromagnetic fields in inhomogeneous accelerating sections. III Beam loading
Using a generalized coupled-mode model, the paper shows that in an inhomogeneous accelerating section the beam-excited counter-propagating field component is not a simple left-travelling wave and contributes a non-negligible correction to the total field.