Ehud Nakar California Institute of Technology Unmagentized relativistic collisionless shock Milos Milosavljevic (Caltech) Anatoly Spitkovsky (KIPAC) Venice 2006

External Shock Upstream Downstream Black Box  Generate collisionality  B - Generate long lasting magnetic field  e,p – Accelerate electrons

The transverse Wiebel instability (Weibel 59; Fried 59) Moiseev & Sagdeev 63 Medvedev & Loeb 98

The transverse weibel instability is expected to produce current filaments and build equipartition * magnetic field. This field provides collisionallity and produce a shock with the following properties (Moiseev & Sagdeev 63; Lee & Lampe 73; Gruzinov & Waman 99; Medvedev & Loeb 99, …) : The shock width is ~ s At the shock  B ~10 -1 The magnetic field coherence length is s The magnetic field is within the shock plane However – easy come easy go: A magnetic field on s scale is expected to decay within s as well (Grizinov 2001) *Assuming here that the equipartition, and therefore s, is with respect to the ions (A non-trivial assumption) R/  2 ~ 10 9 s !!!

3D Numerical simulations of interpenetrating plasmas (Silva et al; Nordlund et al.; Jaroschek et al.; Nishikawa et al.; Spitkovsky et al;) Currents Silva et al 2003 Size: [8×8×3] s ; time 50/  p Initial conditions: two interpenetrating pair-plasma shells Final state: current filaments The simulations have not yet achieved a steady-state shock!

The steady-state shock structure in pair plasma Structure guideline: Filamentation arises where cold upstream plasma and hot counter-stream plasma interpenetrate e+e+ e+e+ e-e- e-e-     Cold upstream e+e+ e+e+ e-e- e-e-     e+e+ e-e-   e+e+ e+e+ e-e- ee   e+e+ e+e+ e-e-   ee   Shock layer  Hot downstream e-e-  e+e+ All the discussion is in the shock frame

Two stages in the shock structure: I)Laminar charge separation layer: A nearly maximal charge separation of the upstream takes place in the first generation of filaments producing a quasi-static 2D structure II) Turbulent compression layer Unstable and interacting filaments produce a 3D turbulent layer that isotropize and compress the plasma

What prevents the counterstream particles from escaping the shock layer into the upstream? Filamentation: e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e-e- e-e- e-e- e-e- e-e- J J J Hot Counterstream Cold Upstream E E E  us >>  cs  E·J<0 The first generation of filaments functions as a diode protecting the upstream from the downstream The charge separation layer

The first generation of filaments >R L A quasi-static 2D structure with E An electrostatic layer with |    ~  mc 2 e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e+e+ e-e- e-e- e-e- e-e- e-e- J J J Hot Counter-stream Cold Upstream E E E x0x0

Stage II - electrodynamic compression layer Filaments become unstable (Milosavljevic & Nakar 05) Neighboring filaments interact (Silva et al 03; Medvedev et al 04, Kato 05, etc...) A 3-dimensional structure B ~B Liberation of particles from the filaments Decay of I and B Growth of filament size Onset of thermalization and compression

Conclusions Two stages in the shock structure: I)Quasi-static 2D charge separation layer: E with a significant electrostatic potential Highly charged filaments  /n~1  B ~1 Blocking most of the counterstream particles Some counterstream particles do escape to the upstream – candidates for accelerated particles II) Dynamic 3D compression layer Unstable interacting filaments Decaying  B B ~B

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