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

Ehud Nakar California Institute of Technology

Unmagentized relativistic collisionless shock

•Milos Milosavljevic (Caltech) •Anatoly Spitkovsky (KIPAC)

Venice 2006

ExternalShock

Upstream Downstream

BlackBox

Generate collisionalityB- Generate long lasting magnetic fielde,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 ~ 109 s !!!

3D Numerical simulations ofinterpenetrating 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 shellsFinal 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-

Cold upstream

e+

e+

e-

e-

e+

e-

e+

e+

e-e

e+

e+

e-

e

Shock layer

Hot downstream

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 upstreamtakes place in the first generation of filamentsproducing a quasi-static 2D structure

II) Turbulent compression layerUnstable 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-J

J

J HotCounterstream

ColdUpstream

E

E

E

2 us

cs

us>>cs E·J<0The first generation of filaments functions as a diode protecting the upstream from the downstream

The charge separation layer

The first generation of filaments >RL

A quasi-static 2D structure with E

An electrostatic layer with | ~ mc2

e+

e+

e+ e+

e+

e+e+

e+

e-

e-

e-

e-

e-J

J

J HotCounter-stream

ColdUpstream

E

E

E

x0

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

ConclusionsTwo 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

Thanks!