Upload
orli-lowery
View
35
Download
0
Embed Size (px)
DESCRIPTION
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. < METHOD > - PowerPoint PPT Presentation
Citation preview
SOME FUNDAMENTAL PROCESSES
IN PULSE-PARTICLE INTERACTION Kaz AKIMOTO
School of Science & EngineeringTEIKYO UNIVERSITY
For US-Japan Workshop on Heavy Ion Fusion and High Energy Density Physics,
Utsunomiya UniversitySeptember 28-30, 2005
< 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.
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 ?
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?
E(z,t) Ee {(z vgt)/ l}
2 i(koz ot )
Ey(z, t)Eo e {(z v
gt)/ l}2 i(k
oz
ot )
<WAVEPACKET> ln = lωo / c = 2.0
<IMPULSE> ln=0.2
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-1 -0.5 0 0.5 1
En
zn
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
-4 -2 0 2 4
En
zn
< 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))
■ sinusoidal wave ( l → ∞)
highly symmetric
⇒ no net acceleration
■ nondispersive pulse
• transit-time acceleration
• reflection
SINUSOIDAL WAVE VS. PULSE
Z Vp
V PULSE
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]
vqE cos tmo
e o
2t2 /4
v2 vp vo
Quasi-Trapping
if vp-vtr < vo < vp+vtr (v o ~v p ) , where
vtr=
Linear reflection (v o ~v p )
Nonlinear (ponderomotive) reflection (v o ~vg) if vg-vref < vo < vg+vref,
2 q E0mk0
v2 vp vo
vref 1
2m
qEo0 k0 vg
v2 vg vo
v2 vp vo
<WAVEPACKET>
• Hamiltonian Contours in Wave Frame
-0.01
-0.005
0
0.005
0.01
-4 -2 0 2 4Zn
0.4
0.6
0.8
1
1.2
1.4
1.6
-3 -2 -1 0 1 2 3
V/V
p
Zn'
<MONOCYCLE PULSE>
• Hamiltonian Contours in Wave Frame
0
0.5
1
1.5
2
-1 -0.5 0 0.5 1
V/V
p
Zn'
Question:
What happens if the pulse is nonlinear EM,
& Bo is applied?
<theory> Linear Polarization
transit-time acceleration
& cyclotron acceleration
Ey(z, t)Eo e {(z v
gt)/ l}2 i(k
oz
ot )
(v)max 2qEtmo
e (o/o )2t2 /4 e (o /o )
2t2 /4
1 v0 / vp
t l / ( vp )
(v0 vg ) / (v0 vp )
ACCELERATIONS DUE TO EM
PULSES
Vperpp
Vz
Ho: Hamiltonian
Voz Vp
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.
00 / mceE
NUMERICAL RESULTS
En= = 0.001 .00 / mceE
0
0.01
0.02
0.03
0.04
-0.02 -0.01 0 0.01 0.02
dvzmaxdvzmindvperptheoryno-disp theoryno-disp calc
v0 /c
dispersive
non-dispersive
vz/c
En=0.01
En=0.1
Now the center of resonance has moved to =0.1c.
0
0.02
0.04
0.06
0.08
0.1
-0.04-0.03-0.02-0.01 0 0.01 0.02
dvzmaxdvzmindvperptheorydvpnodisp
v0 /c
LinearTheoryNo Disp.
00 / kv p
ACCELERATIONS DUE TO EM
PULSES
Vperpp
Vz
Ho: Hamiltonian
Voz Vp
Phase-Trapping
IF
then v/ / 2 vp vzo
pzo
o
o vvm
qEv
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 )
• En=0.001, ln=20
ANALYSIS OF PARTICLE VELOCITIES
• En=0.01, ln=2
TEMPORAL EVOLUTION OF PARTICLE VELOCITIES
ACCELERATIONS DUE TO EM
PULSES
Vperpp
Vz
Ho: Hamiltonian
Voz Vp
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.
0
3.3
vv
l
g
vE
cvT
n
ptr
/20
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.