(Color online) (a) Principle of the experiment; (b) rendering of the trochoidal analyzer.
(Color online) 2-D contour plot of the measured velocity distribution function in a single wave at (a) at fixed interaction length increasing wave amplitude with first-order estimates of modulation (lines) and trapping (half parabola) domains; (b) with fixed wave amplitude versus emitting antenna position from the gun end with the second-order estimate of mean test beam velocity (continuous curve).
(Color online) 2-D contour plot of the measured velocity distribution function of a test beam (, ) trapped in a single wave at with a trapping domain (continuous curve) for increasing amplitude and fixed interaction length .
(Color online). Normalized velocity distribution function for a single wave at (curve labeled ), a single wave at (curve labeled ), and two waves at 30 and (curve labeled ). Circles give wave phase velocities; upper horizontal lines indicate trapping regions.
(Color online) Transition to large-scale chaos and experimental “devil’s staircase:” (a) 2-D contour plot of the measured velocity distribution function of a test beam (, ) after interaction over a length with a single wave at for increasing applied signal amplitude; helix mode (respectively, beam mode) trapping domain is indicated by continuous (respectively, dashed) parabola; secondary resonances are indicated at velocities with ; (b) velocity distribution functions showing “devil’s staircase” steps.
(Color online) (a) Normalized beam velocity distribution function at the output of the TWT: test beam (, ) (black peak); with helix and beam modes at (phase velocity and trapping domain of each mode given, respectively, by circles and horizontal bars) (blue curve with large spread); with an additional controlling wave at (phase velocity given by middle circle) (red curve with reduced spread); (b) kinetic coherence versus beam energy.
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