PLASMA WAKEFIELD ACCELERATION
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PLASMA WAKEFIELD ACCELERATION PLASMA WAKEFIELD ACCELERATION
Pisin Chen
Kavli Institute for Particle Astrophysics and CosmologyStanford Linear Accelerator Center
Stanford University
• Introduction• A Brief History of Plasma Wakefields • Plasma Wakefield Excitation by Alfven Shocks• Simulations on Alfven Plasma Wakefields• Possible Applications to the Knee?• Summary
Workshop on Physics at the end of the Galactic Cosmic Ray Spectrum Aspen, April 26-30, 2005
A Brief History of Plasma Wakefields
Motivated by the challenge of high energy physics• Laser driven plasma wakefield acceleration T. Tajima and J. M. Dawson (1979)• Particle-beam driven plasma wakefield accel. P. Chen, J. Dawson, et al. (1984)
* Extremely efficient: eE ≥ √ n [cm-3] eV/cm For n=1018 cm-3, eE=100 GeV/m
→ TeV collider in 10 m!* Plasma wakefield acceleration principle
experimentally verified.
Cosmic Acceleration Mechanisms
• Conventional cosmic acceleration mechanisms encounter limitations:
- Fermi acceleration (1949) (= stochastic accel. bouncing off B-fields)
- Diffusive shock acceleration (1970’s) (a variant of Fermi mechanism)
Limitations for UHE: field strength, diffusive scattering inelastic
- Eddington acceleration (= acceleration by photon pressure)
Limitation: acceleration diminishes as 1/γ• Examples of new ideas:
- Zevatron (= unipolar induction acceleration) (R. Blandford,
astro-ph/9906026, June 1999)
- Alfven-wave induced wakefield acceleration in relativistic plasma
(Chen, Tajima, Takahashi, Phys. Rev. Lett. 89 , 161101 (2002).)
Addressing the Bottom–Up Scenario for Acceleration of Ordinary Particles:
Alfven Wave Induced Wake Field Simulations
Simulation parameters for plots: • e+ e- plasma (mi=me)• Zero temperature (Ti=Te=0)• Ωce/ωpe = 1 (normalized magnetic field in the x-direction) • Normalized electron skin depth c/ωpe is 15 cells long• Total system length is 273 c/ωpe • dt=0.1 ωpe
-1 and total simulation time is 300 ωpe
-1 • Aflven pulse width is about 11 c/ωpe
• 10 macroparticles per cell
Dispersion relation for EM waves inmagnetized plasma:
Simulation geometry:
y
x
z Bz
Ey
Alfven pulse vA~ 0.2 c
Work done by K. Reil (SLAC) and R. Sydora (U of Alberta)
ωpe2
= 4πe2n/mΩc = eB/mc
Start with a (1D) Plasma in a Boxrmass=2.0
Slowly Grow By and Ez
Particle Velocities Follow
Bz and Ey develop Self Consistently
Wakefield Develops
All Fields “Released”
Traveling
End of Show…
Particle momentum gain from Ex follows pulse
Longitudinalfields created by transverse Alfvenpulse
Alfven pulse (Bz, Ey)
VA ~ 0.2 c
120 230 c/ωpe
230 c/ωpe230 c/ωpe
Particle acceleration in the wake of an Alfven pulse
230 c/ωpe
120120
120
Momentum gain follows pulse
Longitudinalfields created by transverse Alfvenpulse
Particle acceleration in the wake of an Alfven pulse (later time)
VA ~ 0.2 c
Alfven pulse (Bz, Ey)
230 c/ωpe
230 c/ωpe
230 c/ωpe
230 c/ωpe
120
120 120
120
c/wpe=15
rmass=1 (e-e+ plasma)
B0/Bperp=10
Width=90
t=10
valf=0.66
Run_6300
c/wpe=15
rmass=1
B0/Bperp=10
Width=90
t=35
valf=0.66
Run_6300
c/wpe=15
rmass=1
B0/Bperp=10
Width=30
t=10
valf=0.66
Run_6302
c/wpe=15
rmass=1
B0/Bperp=10
Width=30
t=35
valf=0.66
Run_6302
c/wpe=15
rmass=1
B0/Bperp=1
Width=30
t=10
valf=0.66
Run_6341
c/wpe=15
rmass=1
B0/Bperp=1
Width=30
t=35
valf=0.66
Run_6341
c/wpe=15
rmass=1
B0/Bperp=1/4
Width=90
t=10
valf=0.9
Run_6344
c/wpe=15
rmass=1
B0/Bperp=1/4
Width=90
t=35
valf=0.9
Run_6344
c/wpe=15
rmass=1
B0/Bperp=1/4
Width=30
t=10
valf=0.9
Run_6345
c/wpe=15
rmass=1
B0/Bperp=1/4
Width=30
t=35
valf=0.9
Run_6344
Possible Applications to the Knee
• Is alternative acceleration mechanism necessary?
-- Exisitng Diffusive shock acceleration paradigm appears to work well.
• But,
-- Can Emax go beyond 1017eV?
-- What is the mechanism that accelerates e- or e+ to very high energy in order to induce the observed TeV photons?
Our main source of information about the wind is Pulsar Wind Nebulae in young supernova remnants. Box calorimeter for the wind.
Crab (Weisskopf et al 00) B1509 (Gaensler et al 02) Vela (Pavlov et al 01)
v<<c
Properties of pulsar winds:
Highly relativistic (~106) upstream, ~c/2 downstream
Kinetic energy dominated at the nebula
= B2/(4nmc2) ~10-3
Pole-equator asymmetry and collimation
Produce nonthermal particles A. Spitkovsky (2005)
shock
Pulsar wind nebulae
Kennel & Coroniti 84Rees & Gunn 74
CRAB NEBULA SN1054CRAB NEBULA SN1054
Synchrotron emission:
Lifetime: X-rays -- few years, -rays -- months. Need energy input!Crab pulsar: erg/s, 10-20% efficiency of conversion to radiation.
Max particle energy > eV, comparable to pulsar voltage.Nebular shrinkage indicates one accelerating stage:
require /sPSR also injects B field into nebula (~10-4 G)
Radio Infrared Optical X-ray -ray
e 1010 395.38
38105.
RE
15103
<100MeVS -0.3 (radio); -1.0 (X-ray)
A. Spitkovsky (2005)
Summary
• Plasma wakefields induced by Alfven shocks can in pirnciple efficiently accelerate UHECR particles.
• Preliminary simulation results support the existence of this mechanism, but more investigation needed.
• In addition to GRB, there exist abundant astrophysical sources that carry relativistic plasma outflows/jets.
• Its application to CR around the knee is unclear.• Pulsar winds are highly relativistic, and may perhaps
serve as the site for such acceleration for e.
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