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!