1. Joe Giacalone and Randy Jokipii University of Arizona
Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks
Joe Giacalone and Randy Jokipii
University of Arizona
Aspen 2007

2. 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
Aspen 2007

3. 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┴ < K║)
for a given time interval, a perpendicular shock will yield a larger maximum energy than a parallel shock.
Aspen 2007

4. Maximum Energy Assumes Sedov solution for SNR blast wave
Perpendicular Shock
(Hard-sphere scattering)
Bohm Diffusion
Aspen 2007

5. 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
Aspen 2007

6. CME – Interplanetary Space CME – Solar Corona
Termination Shock (blunt)
Supernova remnants
Aspen 2007

7. 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 > 100μG)
Aspen 2007

8. 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)
Aspen 2007

9. 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)
Aspen 2007

10. Enhanced B downstream of a shock moving through a plasma containing density turbulence (without cosmic-ray excited waves!)
Aspen 2007

11. 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
Aspen 2007
Lc Lc Lc

12. Aspen 2007

13. Tycho seen at 3 different X-ray energies
Aspen 2007

14. 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.
Aspen 2007

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19. 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
Aspen 2007

20. Extra slides
Aspen 2007

21. Simulation Art
Aspen 2007

22. 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 …
Aspen 2007

23. 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
Aspen 2007