Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks

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Magnetic-Field Amplification and Cosmic-Ray
Acceleration in Turbulent MHD Shocks

• Joe Giacalone and Randy Jokipii
• University of Arizona

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Galactic cosmic-rays and SNRs

• The power law, up to the knee at 1015 eV, is
  explained by diffusive shock acceleration at
  supernovae blast waves
• Lagage and Cesarsky (1983) estimated the maximum
  energy to be less than 1014 eV
• assuming Bohm diffusion and a hydrodynamic
  (parallel) shock.
• It has been shown that a higher maximum energy is
  achieved for a quasi-perpendicular shock

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The importance of the magnetic-field angle

• A SNR blast waves moves into a B with a preferred
  direction
• The angle between B and shock normal varies
• The physics of acceleration at parallel and
  perpendicular shocks is different
• Parallel shocks ? slow
• Perpendicular shocks ? fast
• (K- lt K)

• for a given time interval, a perpendicular shock
  will yield a larger maximum energy than a
  parallel shock.

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Maximum Energy Assumes Sedov solution for SNR
blast wave
Perpendicular Shock (Hard-sphere scattering)
Bohm Diffusion
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There is no injection problem

• Large scale turbulent magnetic field leads to
  field-line random walk
• This enhanced the trapping of low-energy
  particles near the shock
• Low-rigidity electrons are also efficiently
  accelerated

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CME Interplanetary Space
CME Solar Corona
Termination Shock (blunt)
Supernova remnants
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Berezhko et al., 2003
Bamba et al, 2003

• Berezhko et al. (2003) compared a model of shock
  acceleration of electrons (Ee 100 TeV)
  including synchrotron losses and concluded that
  the observed fine-scale x-ray emissions could
  only result if the field were very strong (B gt
  100µG)

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What enhances B near the shock?

• Bell and Lucek (2001) proposed that a cosmic-ray
  current drives an instability (because of a JcrxB
  force) leading to a large magnetic-field
  amplification
• There is no alternative process without ad
  hoc-assumptions in the literature, or a new one
  which we could reasonably imagine, that would
  amplify the MF in a collisionless shock without
  particle acceleration (Berezhko et al., 2003)

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Is the physics of shock-accelerated particles and
coupled hydromagnetic waves well understood?
Self-consistent plasma simulations of a parallel
shock The self-generated waves are generally
weaker than expected from theory Wave growth
rate depends on shock-normal angle need to
examine the effects of large-scale background
fluctuations
Theory (dashed line)
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Enhanced B downstream of a shock moving through a
plasma containing density turbulence(without
cosmic-ray excited waves!)
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New MHD Simulations of Strong Shocks Moving
Through Turbulence
Density
12Lc

• Numerical simulation of a shock wave moving into
  a turbulent plasma
• Solves the MHD equations for a fluid reflected
  off of a rigid wall
• Shock moves from right to left
• The upstream medium contains turbulent density
  fluctuations
• log-normal statistics, Kolmogorov spectrum
• The fluctuations do not suffer much numerical
  dissipation because they are continually injected
  at the upstream boundary.

8Lc
4Lc
0
0 2Lc 4Lc 6Lc
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Tycho seen at 3 different X-ray energies
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Note that Ellison and Blondin (2001) assume r gt
4 (due to efficient particle acceleration). If
this is the case, the distance above may be
shorter.
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Conclusions

• New results from MHD simulations of shocks moving
  through a medium containing density fluctuations
  indicate that B is significantly amplified
• For parameters typical of supernovae shocks
• B gt 100 µG within a coherence scale of the shock
• This can be understood in terms of the
  vortical/turbulent downstream flow forcing
  together and stretching B
• This is a natural explanation of the enhanced B
  at SNRs without relying on cosmic-ray generated
  fluctuations

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Extra slides
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Simulation Art
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Is there another way to enhance B without relying
on the cosmic rays to excite waves?

• Ellison and Blondin pointed out that strong
  shocks that accelerate particles very efficieenty
  have higher compression rations which shirinks
  the region betgween forward and recerse shocks.
  Thus, material associated with the ejecta can
  penetragte near the forward shock (as in the
  Richtmeyer-Meshkov instability)
• Balsara does something similar to us

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Recent simulations including pre-existing waves
Large 1D simulations of a parallel shock moving
into a turbulent medium
Transverse magnetic field

Zooming in on the region near the shock reveals
the existence of SLAMS
?
Ion density
Ion-inertial length
Ion-inertial length