Experimental Observations of Soliton Wave Trains in Electron Beams

The first experimental observation of a Korteweg–de Vries-type soliton wave train in intense electron beams is reported. A narrow, large-amplitude perturbation on a long-pulse beam is observed to steepen and spawn a soliton wave train. The pulse width and amplitude of each peak remain unchanged over a long propagation distance, and the amplitude is inversely proportional to the square of the width. Two such pulses are seen to pass through each other, emerging from the collision unchanged. The experimental results are reproduced by particle-in-cell simulations.

Figure 1

Turn-by-turn plot of 22 mA beam with 25% perturbation propagation at Bergoz and RC10. As the turn increases, the initial pulse starts to develop into a soliton wave train. The perturbation is introduced near the tail of the beam to allow the fast wave to spend a longer time in the flattop portion of the beam. The beam currents are represented by positive values. For better comparison, the beam current is shifted upward by 12 mA on the plot after every turn.

Figure 2

Width and amplitude of the first subpulse at different turns in the ring (both experiment and simulation). The normalized $\mathrm{\text{current}}=\mathrm{\text{perturbation}}$ current/unperturbed beam current.

Figure 3

Plot of soliton ${\mathrm{\text{width}}}^2$ vs 1/amplitude, along with its linear fit, using the data points from the first and second subpulses in the wave train at the fifth, sixth, and seventh turns of 22 mA 25% perturbation experiment and 22 mA 50% perturbation experiment, respectively.

Figure 4

Plot of soliton velocity vs amplitude, along with its linear fit, using the same data points with Fig. 3.

Figure 5

Comparison of two-perturbation experiment and one-perturbation experiment (30 mA, 50%). The fast wave of the right perturbation interacts with the slow wave of the left perturbation (red; gray) and is compared with the fast wave propagation of the one perturbation experiment (black).

Figure 6

Current profile comparison between experiment (red) and simulation (blue) at WCM for different turns. Reasonable agreement is achieved on the soliton wave train profile, current loss, sound speed, and beam edge erosion rate. Beam current is shifted upward by 10 mA every two turns for better comparison.