Strong nonresonant amplification of magnetic fields in particle accelerating shocks

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Strong nonresonant amplification of magnetic
fields in particle accelerating shocks

• A. E. Vladimirov, D. C. Ellison, A. M. Bykov

Submitted to ApJL
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In diffusive shock acceleration, the streaming of
shock-accelerated particles may induce plasma
instabilities. A fast non-resonant instability
(Bell 2004, MNRAS) may efficiently amplify
short-wavelength modes in fast shocks.
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• We developed a fully nonlinear model of DSA
  based on Monte Carlo particle transport
• Magnetic turbulence, bulk flow, superthermal
  particles derived consistently with each other

Vladimirov, Ellison Bykov, 2006. ApJ, v.
652, p.1246 Vladimirov, Bykov Ellison,
2008. ApJ, v. 688, p. 1084
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Our model for particle propagation in strong
turbulence interpolates between different
scattering regimes in different particle energy
ranges.
Turbulence
Particles
?p2
Turbulence spectrum, kW(k)
Particle mean free path, ?(p)
?(Wres)-1
?lcor
Wavenumber, k
Momentum, p
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k wavenumber of turbulent harmonics W(x,k)
spectrum of turbulent fluctuations, (energy per
unit volume per unit ?k).
Cascading
Dissipation
In this work we ignored compression for
clarity (does not affect the qualitatively new
results)
Compression (amplitude)
Compression (wavelength)
Amplification (? corresponds to Bells
instability)
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We study the consequences of two hypotheses
A. No spectral energy transfer (i.e., suppressed
cascading), ? 0
B. Fast Kolmogorov cascade, ? W5/2k3/2?-1/2
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Shock-generated turbulence with NO CASCADING
Effective magnetic field B 1.110-3 G
Shocked plasma temperature T 2.2107 K
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• Without cascading, Bells instability forms a
  turbulence spectrum with several distinct peaks.
• The peaks occur due to the nonlinear connection
  between particle transport and magnetic field
  amplification.
• Without a cascade-induced dissipation, the plasma
  in the precursor remains cold.

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Shock-generated turbulence with KOLMOGOROV CASCADE
Effective magnetic field B 1.510-4 G
Shocked plasma temperature T 4.4107 K
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• With fast cascading, Bells instability forms a
  smooth, hard power law turbulence spectrum
• The effective downstream magnetic field turns out
  lower with cascading, as well as the maximum
  particle energy
• Viscous dissipation of small-scale fluctuations
  in the process of cascading induces a strong
  heating of the backround plasma upstream.

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Summary

• We studied magnetic field amplification in a
  nonlinear particle accelerating shock dominated
  by Bells nonresonant short-wavelength
  instability
• If spectral energy transfer (cascading) is
  suppressed, turbulence energy spectrum has
  several distinct peaks
• If cascading is efficient, the spectrum is
  smoothed out, and significant heating increases
  the precursor temperature

With Cascading
Without Cascading
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Discussion

• With better information about spectral energy
  transfer (in a strongly magnetized plasma with
  ongoing nonresonant magnetic field amplification,
  accounting for the interactions with streaming
  accelerated particles) we can refine our
  predictions regarding the amount of MFA, maximum
  particle energy Emax, heating and compression in
  particle accelerating shocks (plasma simulations
  needed)
• If peaks do occur, they define a potentially
  observable spatial scale and an indirect
  measurement of Emax
• Peaks in the spectrum may help explain the rapid
  variability of synchrotron X-ray emission
• Observations of precursor heating may provide
  information about the character of spectral
  energy transfer in the process of MFA

Bykov, Uvarov Ellison, 2008 (ApJ)
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Q? A!
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Plots from the paper (just in case)
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The following sequence of slides shows how the
peaks are formed one by one in the shock
precursor. (model A, no cascading)
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Solution with NO CASCADING
Very far upstream
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Solution with NO CASCADING
Far upstream
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Solution with NO CASCADING
Upstream
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Solution with NO CASCADING
Particle trapping occured
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Solution with NO CASCADING
Second peak formed
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Solution with NO CASCADING
The story repeated
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Solution with NO CASCADING
And here is the result (downstream)
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The following sequence of slides shows how the
peaks are formed one by one in the shock
precursor. (model B, Kolmogorov cascade)
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Solution with KOLMOGOROV CASCADE
Far upstream
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Solution with KOLMOGOROV CASCADE
Amplification
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Solution with KOLMOGOROV CASCADE
Cascading forms a k-5/3 power law
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Solution with KOLMOGOROV CASCADE
Amplification continues in greater k
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Solution with KOLMOGOROV CASCADE
And a hard spectrum is formed downstream