Magnetowave Induced Plasma Wakefield Acceleration for UHECR

1
Magnetowave Induced Plasma Wakefield Acceleration
for UHECR
Blois 2008

• 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) axXiv 0709.1177 (astro-ph)
3
Cosmic Ray Spectrum
12 decades of energies
GalacticExtragalactic Transition 1018 eV
Galactic origin
Extragalactic origin?
4
A closer look at ultrahigh energy
5
Source flux ?E-?
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,
  BlandfordOstriker)
• 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-decelerat
  ing 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-(2ß).

8
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)
  
• A single 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
Waves in Magnetized Plasma

• If kB, 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
lt1 One can always find a reference frame where
the wave has only B component.
?kc
?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
Acceleration Gradient
Maximum wakefield (Acceleration Gradient G)
excited by whistler wave in magnetized plasma is
?O(1) Form factor of pulse shape Vg c
where
Verified for a0 ltlt1 by simulation

Cold wavebreaking limit
Lorentz-invariant normalized vector
potential strength parameter
The wakefield acceleration is efficient only when
?p lt ? lt ?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 a0gtgt1 is done analytically
Varying Ew while fixing k and ? The dependence of
G on the strength parameter a0 verified!
Arbitrary unit
G? a0 for a0gtgt1
G
Fitted curve
Numerical result
Strength parameter a0eEw/mc?
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
Typical neutron star radius 10 km
Surface magnetic field B 1013 G Jet
opening angle ? 0.1 Total luminosity L
1050 erg/s Initial plasma density n01026
cm-3
R
Wakefield excitation most effective when ?p??c.
Where is the sweet spot (choose ?c/?p6)?
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
Rs10km
R 50 Rs 500km ?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
Rns10 km ?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 kB 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