1. Magnetowave Induced Plasma Wakefield Acceleration for UHECR Guey-Lin Lin National Chiao-Tung University and Leung Center for Cosmology and Particle astrophysics, National Taiwan University Blois 2008

2. Work done with F.-Y. Chang (KIPAC/Stanford & NCTU), P. Chen (KIPAC/Stanford & NTU) K. Reil (KIPAC/Stanford) and R. Sydora (U. of Alberta) axXi:v: 0709.1177 (astro-ph)

3. Galactic origin Extragalactic origin? Cosmic Ray Spectrum Galactic—Extragalactic Transition ~10 18 eV 12 decades of energies

4. A closer look at ultrahigh energy

5. Alan Watson at ICRC2007 Greisen-Zatsepin-Kuzmin cutoff Look for viable acceleration mechanisms Source flux  E -γ

6. Cosmic Particle Acceleration Models Conventional models  Fermi Acceleration (1949) (= stochastic accel. bouncing off magnetic domains)  Diffusive Shock Acceleration (1970s) (a variant of Fermi mechanism) ( Krymsky, Axford et al, Bell, Blandford&Ostriker) Limited by the shock size, acceleration time, synchrotron radiation losses, etc. Examples of new ideas  Unipolar Induction Acceleration (R. Blandford, astro-ph/9906026, June 1999)  Plasma Wakefield Acceleration (Chen, Tajima, Takahashi, Phys. Rev. Lett. 89, 161101 (2002))  Many others We shall focus on the plasma wakefield acceleration

7. plasma wakefield acceleration Idea originated by Chen, Tajima and Takahashi in 2002 Plasma wakefield generated in relativistic astrophysical outflows. Good features of plasma wake field acceleration: —The energy gain per unit distance does not depend (inversely) on the particle's instantaneous energy. —The acceleration is linear. The resulting spectral index Stochastic encounters of accelerating-decelerating phase results in the power-law spectrum: f(E) ~ E -2. Energy loss (not coupled to the acceleration process) steepens the energy spectrum to f(E) ~ E -(2+β).

8. B Laser Plasma Wakefield Accelerator (LPWA) A Single short laser pulse T. Tajima and J. Dawson, Phys. Rev. Lett. (1979) Plasma Wakefield Accelerator (PWFA) A High energy electron bunch P. Chen, et al., Phys. Rev. Lett. (1985) Magnetowave Plasma Wakefield Accelerator (MPWA) A single short magneto-pulse in magnetized plasma P. Chen, T. Tajima, Y. Takahashi, Phys. Rev. Lett. (2002) Three Ways of Driving Plasma Wakefield A magneto-pulse can be excited in a magnetized plasma  more relevant to astrophysical application But high intensity lasers or e-beams may be hard to find in astrophysical settings

9. Waves in Magnetized Plasma If k║B, the dispersion relation of wave in magnetized plasma + – right-handed, – + left-handed and 4 possible modes exist ω=kc We call the branches below the light curve (  =kc) “Magneto- waves” because of their phase velocities are lower than the speed of light. E/B = v ph /c <1 One can always find a reference frame where the wave has only B component.  pi,  pe : plasma frequency for ion& e-  ci,  ce :cyclotron frequency for ion & e- ω=kc

10. Whistler Mode Dispersion Relation v.s. Magnetic Field B We aim for the large B case. As B increases, the relation approaches to a linear curve and the slope is closed to c. The range of k in simulation

11. Take k and B to be along +z direction, the whistler wave packet induces the ponderomotive force Amplitude of whistler pulse Perpendicular to k and B This leads to the plasma wakefield Simulation results whistler pulse plasma wakefield

12. Acceleration Gradient Maximum wakefield (Acceleration Gradient G) excited by whistler wave in magnetized plasma is where χ~O(1): Form factor of pulse shape V g ~ c Cold wavebreaking limit Lorentz-invariant normalized vector potential “strength parameter” a 0 <<1 linear a 0 >>1 nonlinear if The wakefield acceleration is efficient only when  p <  <  c Verified for a 0 <<1 by simulation

13. Applications to UHECR acceleration The astrophysical environment is extremely nonlinear, while our simulations are performed in the linear regime In view of successful validation of linear regime, we have confidence to extend the theory to the nonlinear regime.

14. Strength parameter a 0 =eE w /mc  G Varying E w while fixing k and  The dependence of G on the strength parameter a 0 verified! G  a 0 for a 0 >>1 Numerical result Fitted curve Arbitrary unit Extension to a 0 >>1 is done analytically

15. Acceleration in GRB Assume NS-NS merger as short burst GRB progenitor, where trains of magneto-pulses were excited along with the out-burst R Typical neutron star radius ~ 10 km Surface magnetic field B ~ 10 13 G Jet opening angle θ ~ 0.1 Total luminosity L~ 10 50 erg/s Initial plasma density n 0 ~10 26 cm -3 θ Due to the conservation of magnetic flux, B decreases as 1/r 2. The plasma density also decrease as 1/r 2. Therefore while Wakefield excitation most effective when  p ~  ~  c. Where is the sweet spot (choose  c /  p =6)? Location for the sweet spot: R ~ 50 R NS ~500 km

16. Whistler Mode Dispersion Relation v.s. Magnetic Field B We aim for the large B case. As B increases, the relation approaches to a linear curve and the slope is closed to c. The range of k in simulation

17. R~ 50 Rs~ 500km θ~0.1 R Rs~10km The acceleration gradient at the sweet spot *Just need 100 km to accelerate particle to 10 20 eV provided  10 -4 !

18. R ns =10 km θ~0.1 R Does acceleration gradient really depend on surface B field and plasma density?  

19. Let us take the range of the sweet spot of order 0.1R. Then, within the 0.1R range, a proton can be accelerated to the energy  No explicit dependence on magnetic field and plasma density! Attainable energy  10 20 eV for  10 -4

20. Acceleration in AGN Take n AGN  10 10 cm -3, B  10 4 G at the core of AGN L  10 46 erg/s  Acceleration distance for achieving 10 21 eV is about 10 pc, much smaller than typical AGN jet size **  is the fraction of total energy imparted into the magnetowave modes. ** Frequency of magnetowave in this case is in the radio wave region.  can be inferred from the observed AGN radio wave luminosity

21. Summary The plasma wakefield acceleration is a possible mechanism to explain the UHECR production. Our simulations confirm, for the first time, the generation of the plasma wakefield by a whistler wave packet in a magnetized plasma. We have studied k||B case, simulation for a general angle is in progress. Simulations for production of whistler wave packet is also in progress. When connecting it to relativistic GRB outflow, we suggest that super-GZK energy can be naturally produced by MPWA with a 1/E 2 spectrum. Same mechanism is also applicable to AGN