1. SOME FUNDAMENTAL PROCESSES IN PULSE-PARTICLE INTERACTION Kaz AKIMOTO School of Science & Engineering TEIKYO UNIVERSITY For US-Japan Workshop on Heavy Ion Fusion and High Energy Density Physics, Utsunomiya University September 28-30, 2005

2. ＜ METHOD ＞ Velocity shifts of particles are calculated after interaction with an ES or EM pulse that is dispersive and propagating. ＜ APPLICATIONS ＞ particle acceleration （ cosmic rays/accelerators ） particle heating （ laser fusion etc. ） plasma instabilities and turbulence plasma processing etc.

3. What you will learn out of this talk. 1.What kind of waves have more acceleration mechanisms? => By breaking the symmetry of a wave acceleration mechanisms can be pair-produced. 2. What happens to cyclotron resonance if instead of a sinusoidal wave a pulse is used? 3.What happens to cyclotorn resonance if wave ampitude becomes greater than the external magnetic fiel ｄ ?

4. METHOD ２： Equation of motion for a particle with charge q, mass m is solved analytically and numerically in the presence of a generalized wavepacket: ES, EM. What do they look like?

5. ln = lω o / c = 2.0 ln=0.2

6. ＜ background ＞ ●Acceleration of particles by a standing-wave pulse had been studied (e.g. Morales and Lee, 1974) extreme dispersion ：ｖｇ ＝０，ｖｐ＝ ωo/ ko ＝ ∞ (ko=0) ●Non-dispersive pulse was also studied. (Akimoto, 1997) ｖ ｇ ＝ｖ ｐ ≠ ０ ●Then results were extended to dispersive pulse: arbitrary dispersion ：－ ∞ ＜ｖｇ，ｖｐ＜ ∞ (ES （ EM ） cases solved. Akimoto 2002(2003))

7. ■ sinusoidal wave ( l → ∞) highly symmetric ⇒ no net acceleration ■ nondispersive pulse transit-time acceleration reflection

8. SINUSOIDAL WAVE VS. PULSE

9. Non-dispersive pulse can accelerate particles via 2 ways. 1. transit-time acceleration （ｖ o ≠ ｖ p ） 2. linear reflection （ｖ o ～ｖ p ） How about dispersive pulse? 3. Quasi-Trapping [QT] 4. Ponderomotive Reflection [PR]

10. Quasi-Trapping if v p -v tr < v o < v p +v tr （ｖ o ～ｖ p ）, where v tr = Linear reflection （ｖ o ～ｖ p ） Nonlinear (ponderomotive) reflection （ｖ o ～ｖ ｇ ） if v g -v ref < v o < v g +v ref,

11. Hamiltonian Contours in Wave Frame

12. Hamiltonian Contours in Wave Frame

13. Question: What happens if the pulse is nonlinear EM, & Bo is applied?

14. Linear Polarization transit-time acceleration & cyclotron acceleration

15. ACCELERATIONS DUE TO EM PULSES

16. NUMERICAL RESULTS We solve the equation of motion numerically as a function of v 0, increasing En=. 1. Phase Velocity: Vp=0.1c 2. Group Velocity: Vg=0.1c &0.05c 3. Field Strength: Ωe ＝ ωo 4. Pulse Length: ln=2.0 etc.

17. NUMERICAL RESULTS En= ＝ 0.001.

18. En=0.01 En=0.1 Now the center of resonance has moved to =0.1c.

19. ACCELERATIONS DUE TO EM PULSES

20. Phase-Trapping IF then

21. What is the mechanism for multi-peaking? The band structure becomes more significant as the pulse is elongated. En=0.01, ln=5 or 10( ｖ ｇ ＝ｖ ｐ )

22. En=0.001, ln=20

23. ANALYSIS OF PARTICLE VELOCITIES En=0.01, ln=2

24. TEMPORAL EVOLUTION OF PARTICLE VELOCITIES

25. ACCELERATIONS DUE TO EM PULSES

26. trapping ＆ band structure Owing to trapping, some electrons exit pulse when accelerated, while others do when not. The trapping period is given by. If this becomes comparable to the transit time=, the trapping becomes important and multi-resonance occurs.

27. CONCLUSIONS AS WAVE IS MADE LESS SYMMETRIC, MORE ACCELERATION MECHANISMS EMERGE. AS PULSE AMPLITUDE AND/OR PULSE WIDTH ARE ENHANCED, LINEAR CYCLOTRON ACCELERATION BY A PULSE BECOMES NONLINEAR, AND TENDS TO SHOW BAND STRUCTURE. IT IS DUE TO PARTICLE TRAPPING AND THE FINITE SIZE OF PULSE. AS THE NONLINEARITY IS FURTHER ENHANCED, THE INTERACTION TRANSFORMS INTO PHASE TRAPPING.