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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!