Collisionless shocks formation, spontaneous electromagnetic fluctuations and streaming instabilities Antoine Bret, Erica Perez Alvaro Anne Stockem, Federico Fiuza, Luis Silva Charles Ruyer, Laurent Gremillet Ramesh Narayan UCLM, Spain IST, GoLP, Portugal CEA, France, Harvard CfA, USA ATELIER PNHE – Paris, 3-5 octobre 2012

Understanding shock formation 1. How exactly do you form a shock? 2.Does it always form? 3.Are they really “ Weibel mediated”? 4.How much time does it take? 5.…? 6.Work in progress

Shock Formation: PIC’s ( OSIRIS ) 1.Simplest possible: cold, symmetric, e - e + shells, no B 0 Chocks Simulation Window

Shock Formation: PIC’s (Osiris) 1.Simplest possible PIC’s: cold, symmetric, e - e + shells,   = 1.05

Shock Formation: PIC’s (Osiris) 1.Simplest possible PIC’s: cold, symmetric, e - e + shells,   = 1.05

Shock Formation: Two Phases 1.Shells overlap: instability grows & saturates 2.Shock Forms Unstable Density

Shock Formation: Two Phases  = 25 Shock forms Phase 1 Insta. triggered Insta. saturates B 2 in central region Phase 2

First Phase: Instabilities 1.Which instability grows? All… but some do it faster Growth rate  (k) For  > (3/2) 1/2, “Weibel” wins

First Phase: Instabilities 1.Instability is bad news in Fast Ignition for ICF 2.Here, it is good news 3.A flow aligned B 0 can cancel Weibel (Godfrey ‘75) 4.What if not aligned (+ sym, cold flow)? Bret & Perez-Alvaro, Phys. Plasmas, 18, (2011) FLOW B0B0  GR for B 0  ∞

First Phase: Saturation Field 1.Weibel grows at , from B i to B f. 2.What about B f ? Cyclotron freq. =  gives 3.Good agreement with PIC’s

First Phase: Seed Field 1.What about B i ? 2.Instability amplifies spontaneous fluctuations 3.Focus on modes with k // = 0 (  integrated) 4.Their d 3 k density reads (Ruyet & Gremillet) Not trivial

First Phase: Seed Field 1.Need to integrate seed density on d 3 k 2.k-integration domain? Numerically determined (?)

First Phase: Seed Field 1.Need to integrate seed density on d 3 k 2.We thus compute

First Phase: Saturation Time 1.Saturation time  s simply reads 2.“Final” result (so far)

First Phase: Saturation Time 1.Saturation time  s simply reads PIC

First Phase: Saturation Time 1.Not bad… but not good either 2.Possible issue 1: Delay before interaction Evolution of the PIC noise from the beginning of the simulation Wait before shells collide to avoid numerically low noise, ie, large  s.

First Phase: Saturation Time 1.Not bad… but not good either 2.Possible issue 2: Start from noise at  = 0 instead of integrating ? Can the instability select the amplified frequency? Yes, with an accuracy  = 0 ±  Laurent & Charles, Delicate…

First Phase: Saturation Time 1.Not bad… but not good either 2.Possible issue 3: 3D Theory, but 2D simulations Laurent & Charles, with noise at  = 0 ±  : Agreement slightly better. Still, weird at   ∞ 3/2

Conclusion 1. Shock formation mechanism. How, When… 2. Two phases : Shells overlap and turn unstable. Instability saturates. Material piles up, + ?? = Shock. Theory for first phase. On track. Can we expect perfect agreement (Luis Silva)? Stay tuned… Thank you for your attention

Motivation Collisionless shocks are key fundamental processes 2.Role in Fireball Scenario for GRB’s and HECR’s 1.Plasma shells “collision” 2.Shock Formation - Collisionless 3.Particle acceleration: GRB