SOME FUNDAMENTAL PROCESSES IN PULSE-PARTICLE INTERACTION

1. SOMEFUNDAMENTALPROCESSES 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. Whatyou will learn out of this talk. • 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? • What happens to cyclotorn resonance if wave ampitude becomes greater than the external magnetic fielｄ?

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.  <WAVEPACKET> ln = lωo / c = 2.0 <IMPULSE> 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) ｖｇ＝ｖｐ ≠０ ●Then results were extended to dispersive pulse: arbitrary dispersion：－∞＜ｖｇ，ｖｐ＜ ∞ (ES （EM） cases solved. Akimoto 2002(2003)) 

7. sinusoidal wave vs. pulse ■ 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（ｖo≠ｖp） 2. linear reflection（ｖo～ｖp） How about dispersive pulse? 3. Quasi-Trapping [QT] 4. Ponderomotive Reflection [PR]

10. Quasi-Trapping if vp-vtr < vo < vp+vtr （ｖo～ｖp）, where vtr= Linear reflection （ｖo～ｖp） Nonlinear (ponderomotive) reflection （ｖo～ｖｇ） if vg-vref < vo < vg+vref,

11. <WAVEPACKET> • Hamiltonian Contoursin Wave Frame

12. <MONOCYCLE PULSE> • Hamiltonian Contours in Wave Frame

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

14. <theory> Linear Polarization transit-time acceleration & cyclotron acceleration

15. ACCELERATIONSDUE TO EM PULSES

16. NUMERICAL RESULTS We solve the equation of motion numerically as a function of v0, increasing En=. <Parameters>  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. ACCELERATIONSDUE 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(ｖｇ＝ｖｐ)

22. En=0.001, ln=20

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

24. TEMPORAL EVOLUTION OF PARTICLE VELOCITIES

25. ACCELERATIONSDUE 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.