Magnetowave Induced Plasma Wakefield Acceleration for UHECR

1. Blois 2008 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

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. Cosmic Ray Spectrum 12 decades of energies Galactic—Extragalactic Transition ~1018 eV Galactic origin Extragalactic origin?

4. A closer look at ultrahigh energy

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

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 InductionAcceleration (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 Three Ways of Driving Plasma Wakefield • 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) But high intensity lasers or e-beams may be hard to find in astrophysical settings • Magnetowave Plasma Wakefield Accelerator (MPWA) • Asingle short magneto-pulse in magnetized plasma • P. Chen, T. Tajima, Y. Takahashi, Phys. Rev. Lett. (2002) A magneto-pulse can be excited in a magnetized plasma  more relevant to astrophysical application

9. + – right-handed , – + left-handed Waves in Magnetized Plasma • If k║B, the dispersion relation of wave in magnetized plasma pi ,pe : plasma frequency for ion& e- ci,ce :cyclotron frequency for ion & e- and 4 possible modes exist 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 = vph/c <1 One can always find a reference frame where the wave has only B component. ω=kc 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 Perpendicular to k and B Amplitude of whistler pulse This leads to the plasma wakefield Simulation results whistler pulse plasma wakefield

12. a0 <<1 linear a0 >>1 nonlinear if Acceleration Gradient Maximum wakefield (Acceleration Gradient G) excited by whistler wave in magnetized plasma is χ~O(1): Form factor of pulse shape Vg ~ c where Verified for a0 <<1 by simulation Cold wavebreaking limit Lorentz-invariant normalized vector potential “strength parameter” The wakefield acceleration is efficient only when p <  < c

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. Extension to a0>>1 is done analytically Varying Ew while fixing kand  The dependence of G on the strength parameter a0 verified! Arbitrary unit G a0 for a0>>1 G Fitted curve Numerical result Strength parameter a0=eEw/mc

15. θ Acceleration in GRB Assume NS-NS merger as short burst GRB progenitor, where trains of magneto-pulses were excited along with the out-burst Typical neutron star radius ~ 10 km Surface magnetic field B ~ 1013 G Jet opening angle θ ~ 0.1 Total luminosity L~ 1050 erg/s Initial plasma density n0~1026 cm-3 R Wakefield excitation most effective when p~~c. Where is the sweet spot (choose c/p=6)? Due to the conservation of magnetic flux, B decreases as 1/r2. The plasma density also decrease as 1/r2. Therefore while Location for the sweet spot: R ~ 50 RNS ~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. The acceleration gradient at the sweet spot R Rs~10km R~ 50 Rs~ 500km θ~0.1 *Just need 100 km to accelerate particle to 1020 eV provided 10-4!

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

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  Attainable energy 1020 eV for 10-4 No explicit dependence on magnetic field and plasma density!

20. Acceleration in AGN Take nAGN  1010 cm-3, B104 G at the core of AGN L1046 erg/s ** 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 Acceleration distance for achieving 1021 eV is about 10 pc, much smaller than typical AGN jet size

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/E2 spectrum. • Same mechanism is also applicable to AGN