The term “impedance” is well established in particle accelerator physics. It was however, introduced by early circuit theorists, like Campbell, Wagner, Heaviside in the early 1900’s and then taken from there into particle physics by Sessler, Zotter, Hofman, Chin and others. Without making too much a point of it, one has to accept that “impedance” existed before particle acceleration.
Longitudinal impedance is usually defined by the ratio of the beam E-field, integrated over a short distance in beam direction and the beam current (Wiedemann, p. 739-743). A warning on the over-use of the impedance concept was voiced by early microwave pioneers for good reasons:
There is a high probability for such a warning being justified in the field of particle acceleration as well.