K-dV type solitary waves in intense electron beams. Jayakar Charles Tobin Thangaraj Patrick O Shea Rami Kishek Don Feldman Irving Haber

Transcription

1 K-dV type solitary waves in intense electron beams Jayakar Charles Tobin Thangaraj Patrick O Shea Rami Kishek Don Feldman Irving Haber

2 Outline of the talk Introduction Basic theory of solitons Previous work on soliton transport Experiments and Recent results from UMER Conclusion and Proposal

3 What is a Soliton? A wave that can hold it s shape is called a soliton A soliton is a localized wave solution of a nonlinear PDE One PDE that has such a solution is the Korteweg-deVries (KdV) equation:

4 KdV equation u t 6 uu + u = 0 x xxx uxt (, ) = f( x ct) Solution: c 2 1 uxt (, ) = sec h[ cx ( ct)] 2 2

5 Basic properties a KdV soliton Its amplitude increases with its velocity The width of the solitary wave is inversely proportional to the square root of its velocity width 2 * amplitude = constant

6 Classic works on solitons before 1900 I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. --- Scott Russell 1834 In 1895 by D.J. Korteweg and G. de Vries developed the KdV equation to model water waves in a shallow canal.

7 Resurrection of solitons:

8 Zabusky and Kruskal (1965) any localized initial profile allowed to evolve according to the KdV equation eventually consisted Final of a finite set of localized travelling waves similar to the original solitary waves 1895 Initial They named it as solitons

9 Solitons in plasmas

10 Solitons in beams Bisognano, Haber (1981) A simulation study of nonlinear and dispersive effects. Conclusion: Large amplitude perturbation significantly influences the longitudinal beam dynamics H.Suk (1996) - proposed a possible experiment to transport solitary wave Other relevant works are in [i] high energy coasting beams GSI Phys. Rev. Lett(1999). [ii] solitary holes in coasting beams Phys. Rev. Lett Schamel

11 Most recent work.., for the longitudinal distribution function, it is shown that weakly nonlinear disturbances moving near the sound speed evolve to KortewegdeVries equation

12 Outline of the talk Introduction Basic theory of solitons Previous work on soliton transport Experiments and Recent results from UMER Conclusion and Proposal

13 Drive Laser Setup E-beam UV (355nm) Laser FWHM = 5ns Electron Gun Nd:YAG Laser KTP/BBO Crystals

14 Laser-induced Perturbation: Near the cathode I=18mA η=0.2 UMER Top View

15 I=18mA η=0.2 TURN 6 TURN 5 TURN 4 TURN 3 TURN 2 Fast wave Slow wave TURN 1 2/3 of RING Head Tail TURN 0

16 Experimental data of multi-turn operation (I=18mA)

17 Nonlinear space charge waves Near the cathode Perturbation near tail Beam Current (ma) I = 36mA; Ip=17.5mA Time (ns)

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19 Wave steepens to form a pulse-train 2.5ns

20 Width 2 Vs 1/Amplitude(Left) Velocity Vs Amplitude (Right) Beam Current = 21.5mA ; Perturbation Current = 27 ma

21 Width 2 Vs 1/Amplitude(Left) Velocity Vs Amplitude (Right) Beam Current = 25.4 ma ; Perturbation Current = 16.7 ma

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23 Conclusion A large amplitude perturbation in an intense beam Has been shown to agree with all the properties of a KdV soliton in terms of width, height, velocity and profile. The number of solitons increase with the amplitude of the initial perturbation

24 Proposal for new experiments in UMER Two soliton experiment: Introduce two large perturbations on the beam. One at the head and the other at the tail of a long beam ( > 120 ns). Observe crossing of the solitary waves. Can solitary waves be generated through energy modulation?

25 Some of the ideas proposed for A0/NML Experiment Ellipsoidal beam generation Microbunching investigations Flat beam transformation Emittance exchange (Charge scaling) Motivation/ application Low emittance beams Beam physics; diagnostics Colliders and Soft x-ray sources Proof-of-principle; possible application in FELs and X-ray sources Can UMER help answer some of these PHYSICS questions? Open to the workshop discussion session

26 A0 Photoinjector solenoid Cs 2 Te photocathode Nd:YLF drive-laser Typically the bunch charge is set to 1nC, it can be higher 1.5-cell 1.3 GHz NC rf-gun with three solenoids for emittance manipulation 9-cell TESLA type booster cavity Beam energy ~15 MeV

27 Injection Beamline Layout (~40 MeV) skew quads chicane high intensity dump matching section 1 st cryomodule RF gun accelerating cavities 3 rd harm. cavity test beamlines low intensity dumps normal conducting 1.3 GHz photocathode RF gun 2 superconducting 1.3 GHz accelerating cavities 1 superconducting 3.9 GHz cavity for bunch linearization 3 skew quads for flat beam generation 4-dipole chicane for bunch compression 2.5 KW dump area for two additional low energy test beamlines