Electromagnetic momenta for wave-particle systems in vacuum waveguides

Whenever light is slowed down, for any cause, two different formulas give its momentum. The coexistence of those momenta was the heart of the century-old Abraham-Minkowski dilemma, recently resolved for dielectrics. We demonstrate that this framework extends to momentum exchange in wave-particle interaction; in particular to vacuum waveguides of electron tubes (dispersive metallic slow-wave structures). In waveguides, the dilemma can be easily investigated since energy and force are well established through the use of Maxwell equations in vacuum, and since waveguides can have a strong refractive index. Our theory is assessed with simulations validated against measurements from a traveling-wave tube. In addition, we show that the dilemma resolution is not limited to discriminating between kinematic and canonical momenta but also involves a non-negligible flowing momentum from Maxwell’s electromagnetic stress. The existence of two momenta for diverse systems like materials, plasmas and waveguides, for which light velocity modification has entirely different origin, points to the universality of the Abraham-Minkowski dilemma. Graphical abstract