Assume that the waveguide is now tapered as shown. In this case the group
velocity is higher at the wide end than at the narrow end. Thus resolution of the forces
shows F1 is greater than F2, whereas the sidewall force Fs2 is higher than Fs1.
As with the free space example in 2.1.1, the force difference F1-F2 will give rise
to movement of the waveguide, but this will have no effect on the propagation
velocities within the waveguide.
2.5 Propagation in a resonant tapered waveguide
As with any microwave cavity, if the axial path length is a multiple of half the
mean guide wavelength, at the frequency of operation, then the waveguide will form a
resonant cavity. The electrical and magnetic fields at each end plate will add in
phase, to give instantaneous powers equal to Q times the transmitted power. This will
give rise to a force difference equal to Q(F1-F2). Note that in a well designed cavity
the unloaded Q can reach values greater than 50,000. It is this high multiplication of
the small force difference that gives the engine a useful net force.
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