Aspen 2007

Magnetic-Field Amplification and Cosmic-Ray Acceleration in

Turbulent MHD Shocks

Joe Giacalone and Randy JokipiiUniversity of Arizona

Aspen 2007

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

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.

Aspen 2007

Maximum Energy Assumes Sedov solution for SNR blast wave

Bohm Diffusion

Perpendicular Shock(Hard-sphere scattering)

Aspen 2007

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

CME – Solar Corona CME – Interplanetary Space

Termination Shock (blunt)Supernova remnants

Aspen 2007

• 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

Aspen 2007

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

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)

Aspen 2007

Enhanced B downstream of a shock moving through a plasma containing density turbulence

(without cosmic-ray excited waves!)

Aspen 2007

• 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

Aspen 2007

Aspen 2007

Tycho seen at 3 different X-ray energies

Aspen 2007

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

Aspen 2007

Aspen 2007

Aspen 2007

Aspen 2007

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

Extra slides

Aspen 2007

Simulation Art

Aspen 2007

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

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