1. JARED GINSBERG WITH BRIAN BEAUDOIN Modeling and Characterization of Soliton Trains in an Electron Beam

2. “…The mass of water in the channel… accumulated round the prow of the vessel… then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation… Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon..” - John Scott Russell The earliest observed solitons were found as water waves Video credit goes to youtube user Christophe FINOT

3. Nonlinear and Dispersive Effects The initial wave steepens due to nonlinearity. The wave also widens and separates due to dispersion. When balanced these two effects can exactly cancel, yielding a soliton. Image courtesy of Yichao Mo

4. Experimental Setup for Launching Velocity Perturbations Perturbations from Induction Cell 30 cm initial perturbation width Beam Velocity = 5.85 x 10 7 m/s (.2c) Machine Circumference = 11.52 m Circulation Time = 197 ns UMER Perturbation at beam tail Beam head

5. The Math and The Model What’s so great about a model? Confirm your choice of equation (KdV!) Direct control over more parameters Faster and more portable Red: computer modeled Blue: experimental data Determining ε is a major challenge Korteweg de-Vries (KdV) nonlinearity dispersion μ dictates the dispersion strength

6. Agreement Between Model and Experiment ε = 5.85 x 10 7 = beam velocity μ = +42 t = 9 x 197 ns Position (meters) Current (amps) Data with minimal current loss Data with considerable current loss Positive Dispersion

7. Agreement Between Model and Experiment ε = 5.85 x 10 7 = beam velocity μ = - 42 t = 9 x 197 ns Position (meters) Current (amps) Negative Dispersion Data with minimal current loss A negative dispersion in the model can then be used to model negative perturbations to the beam that are done in the experiment.

8. Sub-Pulse Spacing (Future Work) Sub-pulse Spacing vs. Dispersive Coefficient Dispersive Coefficient Peak-to-peak Space in meters Sub-pulse Spacing vs. Dispersive Coefficient Dispersive Coefficient Peak-to-peak Space in meters

9. Acknowledgements Brian Beaudoin Kathryn Tracey, Michelle Girvan, Thomas Murphy, Sonali Shukla and the rest of TREND National Science Foundation