UHECR Acceleration via Alfven Wave Induced Plasma Wakefield

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UHECR Acceleration via Alfven Wave Induced Plasma
Wakefield

• Kevin Reil
• Stanford Linear Accelerator Center

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Acknowledgements

• P. Chen (SLAC)
• T. Tajima and J. Koga (JAERI)
• Y. Takahashi (Huntsville)
• R. Sydora (Alberta)
• Alexander Yashin (SLAC)

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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle Cell Simulations.

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What is a Wakefield Accelerator?
Lake Como (near Milan)
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Wakefield Accelerator.
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Wake-Field Accelerator
When vgrad?c the acceleration gradient Will
co-move with the particle (vpart?c) Providing a
great deal of acceleration!
In our case the gradient is provided by An Alfven
wave. The velocity of the Gradient is valfven.
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Wakefield Accelerator
Laser Pulse
Electric Field
Pulse Propagation
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Wakefield Acceleration
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Other Plasma Wakefield Projects

• 1988 Argonne National Lab proof in principle.
• 1992 20 MeV/m at KEK reported.
• 1999 E-157 at SLAC wake of a 28.5 GeV e- beam
  (120 MeV over 1.4 m observed).
• 2001 Natural Wakefield Acceleration in the lunar
  wake (B.J. Kellet et al.)
• 2002 Ecole Poly. 200 GeV/m in laser wake.

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E-157
Ez
1GeV/m
Z and R
Ref R. Assmann et al.
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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle Cell Simulations.

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Alfven Wave Properies

• The Alfven wave is a transverse plasma wave that
  travels along a stretched string.
• The stretched string is a magnetic field line.
• Valfven B0 / sqrt(?0 ?).
• Propagation velocity is Alfven velocity.
• EE?(t). BB?(t) B0??.
• Does the propagating E? and B? create an E???

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Dispersion Relation
Stix, The Theory of Plasma Waves, McGraw-Hill,
1962 (page 31)
Derived following Stix technique but for moving
plasma.
Aleksandr Yashin
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Dispersion Relation
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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle Cell Simulations.

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Ultra High Energy Cosmic Rays
REF J. Cronin, T.K. Gaisser, and S.P. Swordy,
Sci. Amer. v276, p44 (1997) Everytime you
show this, please send 2cents to your favorite
charity. http//astroparticle.uchicago.edu/crspe
c_info.txt http//astroparticle.uchicago.edu/cosmi
c_ray_spectrum_picture.htm
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UHECR From Source to Detector
CMB ? _at_ 2.7 K
?
Threshold for ? resonance at 6x1019eV
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UHECR

• Particles with Egt1020 eV have been observed. A
  source of acceleration of at least 1020 eV is
  therefore needed.
• No immediately obvious nearby sources and almost
  isotropic arrival lead us to believe acceleration
  sources are distant.
• Knee and ankle may indicate changes in
  astronomical source of cosmic rays.

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UHECR Acceleration

• Top Down Models
• Heavy fundamental particle decays.
• Invoke exotic particles beyond the standard
  model.
• Do not explain the spectrum well (Farrar).
• Bottom Up Models
• Ordinary particle accelerated to UHE
• GZK cutoff inhibits distant sources (except Z
  burst).
• Efficient acceleration mechanism needed.
• Highly energetic source.

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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle Cell Simulations.

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Gamma Ray Bursts

• Traits of Gamma Ray Bursts
• Compactness of source.
• Short or long bursts (O(1) O(10) sec).
• Extremely Energetic (1052 erg/sec (1045 J/s)).
• Prompt signal spectrum (Epeak 100s of keV).
• Cosmological Distances (peaks at Z1).

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(Chen, Tajima and Takahashi)
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Theoretical Predictions

• Proton is accelerated collision-free.
• Power law energy spectrum.
• Gradient sufficient to produce Egt1024 eV p.
• Applicable to other astrophysical locations.
• IE. Blazars, AGN, etc.
• In addition to Eprotongt1024 eV, neutrinos of
  Egt1023 eV produced with flux consistent with the
  Weiler Z burst scenario.

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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle Cell Simulations.

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Dispersion Relation
Stix, The Theory of Plasma Waves, McGraw-Hill,
1962 (page 31)
Derived following Stix technique but for moving
plasma.
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Relativistic Alfven Waves
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Derivation
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Derivation
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Derivation
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Outline

• Plasma Wakefield Accelerators.
• Alfven Waves.
• Ultra High Energy Cosmic Rays.
• Relativistic Plasma Wakefield Acceleration of
  Cosmic Rays.
• Relativistic Alfven Waves.
• Particle in Cell Simulations.

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Simulation

• Other plasma wakefield work has been applied to
  terrestrial accelerator settings. This concept is
  applicable to astrophysical sources.
• Can this theory withstand the scrutiny of
  simulation?
• Can an experiment be designed to test any
  positive simulation results?
• Start small and look at best case scenarios

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First Look Initial Conditions

• Define an initial E field
• EyE0 sin (kx). EzE0 cos (kx).
• B field and initial particle velocities
• Additionally, a constant external Bx defined.
• Use these as initial conditions in a 1D PIC then
  allow time development.

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First Look With PIC Code

• External Blong is applied.
• Initialize Ey, Ez to be a few wavelengths of a
  sinusoidal pulse.
• By, Bz, vy, vz follow as derived.
• Let the system develop in time.
• In all cases, ensure that energy is conserved
  (ie. code is not broken).

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Eperp
Elong
Bperp
Square 9 1001 0.3 1.0 1.0 5.0
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Gaussian 9 1001 0.3 0.5 2.0 5.0
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Gaussian 81 1001 0.1 0.5 2.0 15.0
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Gaussian 1 1001 0.1 0.5 8.0 10.0
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ConclusionWork in Progress

• Investigating a theoretical astronomical plasma
  wakefield accelerator with UHE gradient.
• Initial look at launching an pure Alfven wave
  in a PIC code under way.
• Hope that simulation will lead to eventual
  experiment to test Alfven wave induced plasma
  wakefield accelerator.

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Alfven Wave Studies

• E-157 is a laser induced plasma wakefield
  experiment. We wish to study an Alfven wave
  induced wakefield.
• Collaborators have a great deal of experience in
  using PIC code to study Alfven Waves.
• Prior use of the PIC code used was Magnetosonic
  Alfven wave propagation.
• Studies by Rick Sydora of U of Alberta.

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Particle Acceleration in Magnetosonic Alfven
Waves

• Simulation Model
• 1D spatial, 3D velocities
• Relativistic electromagnetic particle-in-cell
• Full ion and electron dynamics
• Magnetosonic Wave Propagation
• Wave propagation in x-direction
• External B-field in (x,z) plane

z
B
y
(Ref. Bessho, Ohsawa,1999)
x
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Magnetic Field Evolution
Magnetic Field Evolution
Alfven Mach Number 2.3
Bz /Bo
4
0
100
350
x /(c/w )
pe
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Momentum and E fields of Alfven Shock
g120
100
p
x
0
100
p
y
0
1
E
x
0
-1
2
E
y
0
300
400
x /(c/w )
pe
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Misc
Hi Kevin, You have made a fairly accurate
assessment. This is a brief reply to your
questions on the slides Slide 1 Adding to
your remarks the magnetosonic Alfven wave pulse
is launched by setting up a localized density
perturbation. The strength of the
density perturbation is 4 times the background
density. Particles in the density perturbation
are given a drift velocity to the right (this
sets up a piston) and if the drift speed is
larger than the local Alfven speed, a shock forms
(i.e. the wave steepens). Slide 2 This
displays the propagation of the z-component of
the magnetoacoustic shock wave. It is moving at a
speed V2.3Va, where Va is the Alfven speed. The
Alfven Mach number is the ratio V/Va. In other
words the piston is moving the plasma at 2.3
times the Alfven speed. Slide 3 The particles
(electrons) gain a lot of energy in the shock
front in the x-direction as is seen in the phase
space with gamma's exceeding 100. There is a lot
of energy gain from the Ex electrostatic field
BUT notice the shock front wake does lead to some
acceleration of the electrons. The Ey field is a
purely electromagnetic, transverse field
component and partially contributes to the
acceleration but not as much. As a side note
these results were obtained as a benchmark of my
code with those of Bessho and Ohsawa, 1999 who
first investigated this effect. I have been
extending this work to 2 and 3d to see if this
mechanism still applies. We must be careful about
the 1D model of shocks for the magnetoacoustic
mode since it most likely overestimates the
actual energy gain.