1. PLASMA WAKEFIELD ACCELERATION Pisin Chen Kavli Institute for Particle Astrophysics and Cosmology Stanford 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

2. 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=10 18 cm -3, eE=100 GeV/m → TeV collider in 10 m! * Plasma wakefield acceleration principle experimentally verified.

5. 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:

10. Alfven Wave Induced Wake Field Simulations Simulation parameters for plots: e+ e- plasma (mi=me) Zero temperature (Ti=Te=0) Ω ce /ω pe = 1 (normalized magnetic field in the x-direction) Normalized electron skin depth c/ω pe is 15 cells long Total system length is 273 c/ω pe dt=0.1 ω pe -1 and total simulation time is 300 ω pe -1 Aflven pulse width is about 11 c/ω pe 10 macroparticles per cell Dispersion relation for EM waves in magnetized plasma: Simulation geometry: y x z BzBz EyEy Alfven pulse v A ~ 0.2 c Work done by K. Reil (SLAC) and R. Sydora (U of Alberta) ω pe 2 = 4πe 2 n/m Ω c = eB/mc

11. Start with a (1D) Plasma in a Box r mass =2.0

12. Slowly Grow By and Ez

13. Particle Velocities Follow

14. Bz and Ey develop Self Consistently

15. Wakefield Develops

16. All Fields “Released”

17. Traveling

18. End of Show…

19. Particle momentum gain from E x follows pulse Longitudinal fields created by transverse Alfven pulse Alfven pulse (B z, E y ) V A ~ 0.2 c 120230 c/ω pe Particle acceleration in the wake of an Alfven pulse 230 c/ω pe 120

20. Momentum gain follows pulse Longitudinal fields created by transverse Alfven pulse Particle acceleration in the wake of an Alfven pulse (later time) V A ~ 0.2 c Alfven pulse (B z, E y ) 230 c/ω pe 120

21. c/wpe=15 rmass=1 (e - e + plasma) B0/Bperp=10 Width=90 t=10 valf=0.66 Run_6300

22. c/wpe=15 rmass=1 B0/Bperp=10 Width=90 t=35 valf=0.66 Run_6300

23. c/wpe=15 rmass=1 B0/Bperp=10 Width=30 t=10 valf=0.66 Run_6302

24. c/wpe=15 rmass=1 B0/Bperp=10 Width=30 t=35 valf=0.66 Run_6302

25. c/wpe=15 rmass=1 B0/Bperp=1 Width=30 t=10 valf=0.66 Run_6341

26. c/wpe=15 rmass=1 B0/Bperp=1 Width=30 t=35 valf=0.66 Run_6341

27. c/wpe=15 rmass=1 B0/Bperp=1/4 Width=90 t=10 valf=0.9 Run_6344

28. c/wpe=15 rmass=1 B0/Bperp=1/4 Width=90 t=35 valf=0.9 Run_6344

29. c/wpe=15 rmass=1 B0/Bperp=1/4 Width=30 t=10 valf=0.9 Run_6345

30. c/wpe=15 rmass=1 B0/Bperp=1/4 Width=30 t=35 valf=0.9 Run_6344

31. Possible Applications to the Knee Is alternative acceleration mechanism necessary? -- Exisitng Diffusive shock acceleration paradigm appears to work well. But, -- Can E max go beyond 10 17 eV? -- What is the mechanism that accelerates e - or e + to very high energy in order to induce the observed TeV photons?

33. 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 (  ~10 6 ) upstream, ~c/2 downstream Kinetic energy dominated at the nebula  = B 2 /(4  n  mc 2 ) ~10 -3 Pole-equator asymmetry and collimation Produce nonthermal particles A. Spitkovsky (2005) shock What are pulsar wind properties at the source? Pulsar wind nebulae Kennel & Coroniti 84 Rees & Gunn 74

34. CRAB 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 /s PSR also injects B field into nebula (~10 -4 G) Radio Infrared Optical X-ray  -ray <100MeV Radio mystery: lifetime > nebular age. Need /s S  -0.3 (radio); -1.0 (X-ray) A. Spitkovsky (2005)

35. 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.