Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks
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Transcript of Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks
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Aspen 2007
Magnetic-Field Amplification and Cosmic-Ray Acceleration in
Turbulent MHD Shocks
Joe Giacalone and Randy JokipiiUniversity of Arizona
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Galactic cosmic-rays and SNR’s
• 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 slowPerpendicular shocks fast
(K┴ < 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
Bohm Diffusion
Perpendicular Shock(Hard-sphere scattering)
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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 – Solar Corona CME – Interplanetary Space
Termination Shock (blunt)Supernova remnants
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• 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 > 100μG)
Bamba et al, 2003
Berezhko et al., 2003
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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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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
Is the physics of shock-accelerated particles and coupled hydromagnetic waves well understood?
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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• 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.
0 2Lc 4Lc 6Lc
12Lc
8Lc
4Lc
0
DensityNew MHD Simulations of
Strong Shocks Moving Through Turbulence
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Tycho seen at 3 different X-ray energies
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Note that Ellison and Blondin (2001) assume r > 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 > 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
Zooming in on the region near the shock reveals the existence of “SLAMS”
Transverse magnetic field
Ion density
→
Ion-inertial length
Ion-inertial length