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.