1. Relativistic Collisionless Shocks in the Unmagnetized Limit
Milos Milosavljevic
Department of Astronomy, The University of Texas at Austin

2. Plan
Summary of: Milosavljevic & Nakar, “Weibel Filament Decay and Thermalization in Collisionless Shocks and Gamma-Ray Burst Afterglows” 2006 ApJ, 641, 978.
Summary of: Milosavljevic & Nakar, “The Cosmic Ray Precursor of Collisionless Shocks: A Missing Link in Gamma-Ray Burst Afterglows” 2006, ApJ, 651, 979.
Outlook.

3. Anatomy of a Weibel Filament (Alfven 1939, Hammer & Rostoker 1970)

4. The Weibel Tissue (Pair Plasma)

5. The Lining (Pair Plasma)
Spitkovsky 2006

6. The Lining (Pair Plasma)
Spitkovsky 2006

7. Validity of the Fluid Theory e. g
Validity of the Fluid Theory e.g., Zenitani & Hoshino, “Relativistic Particle Acceleration in a Folded Current Sheet” 2005, ApJ 618, L111
Caution (Jon Arons, priv. comm.): It still remains to be checked whether the magnetic walls are stabilized by the shear (bulk streaming of the plasma) on the sides of the filament. Shear stabilization could prevent a pressure-driven instability, but the filaments could still be disrupted by another instability.

8. Where is the shock? electrons ions Frederisken et al. 2004

9. Can Coulomb shielding prevent decay in electron-ion shocks?
Hededal et al. 2005
If decay is pressure driven and not Coulomb or Ampere driven, shielding does not prevent decay.

10. Deconfinement

11. Long Term Evolution of Weibel Turbulence

12. Long Term Evolution of Weibel Turbulence

13. Summary of Part I
Weibel “filaments” (at least in pair shocks) are a really network of skin-depth thick magnetic walls with field-free interior.
Optimistically granting Coulomb shielding and negligible Ampere interactions, the “filaments” are MHD unstable (sausage-kink, etc.) and move (but see the caveat on page 7).
Synchrotron emission in the small-scale field depolarizes.
Instability compromises the confining power of the magnetic walls. The particles drift, escape, and isotropize. The magnetic field decays.
In electron-ion shocks, the decay time scale is unknown. Simulations will measure the decay time scale, but published electron-ion simulations have not converged.

14. The Weibel Shock: The Scorecard
Shock transition?
Persistent strong magnetic field?
Particle acceleration beyond electron-ion equilibration?
Are we missing something?

15. The Upstream frame The Shock frame scattering Energy grows by x2 each
shock at t e-
shock moves in this direction
shock at t+Dt
The Upstream frame p e-
The Shock frame
scattering
Energy grows
by x2 each
time around
energetic ions running
ahead of the shock

16. Bell’s Precursor Assume that the shock accelerates electrons and ions.
Electrons cool efficiently but ions do not.
The cosmic rays carry a current into the shock upstream.
Thermal electron Debye screen the cosmic ray protons, and carry an equal and opposite return current.
A seed field in the shock upstream interacts with the return current, and the upstream thermal plasma accelerated sideways.
Nonlinear magnetic field growth is possible, but not proven.
Bell 2004

17. In relativistic and Newtonian shocks, cosmic rays going into the shock upstream can drive different processes:
Bell / Bell & Lucek
Firehose
Gyroresonant
If magnetic fields are amplified in the precursor, the amplification length is much larger than the plasma skin depth, and decays resistively.
The amplified field prevents the Weibel instability! (e.g., Hededal & Nishikawa 2005). The shock is mediated by cosmic rays interacting with large-scale magnetic fields. Other processes must equilibrate the plasma.
In relativistic external GRB shocks, the maximum magnetic field length scale is ~ R/2. This field is insufficient to confine UHECR, and thus UHECR are not accelerated in external GRB shocks.

18. Summary of Part II
If the shock generates a power-law spectrum of accelerated particles, the ions will go farther than the electrons.
The ion cosmic ray precursor of the shock may excite disturbances in the shock upstream, e.g., by current-driven interactions.
In GRB afterglows, the precursor has enough energy to drive turbulence in the shock upstream, but the outcome of the precursor-upstream interaction is not well understood.
If upstream turbulence is excited, it could generate a magnetic field on scales much larger than the plasma skin depth, which could in turn quench the Weibel instability, and yield a very different shock structure.