Page 1
Collisionless shocks formation,spontaneous electromagnetic fluctuations
and streaming instabilities
Antoine Bret, Erica Perez AlvaroAnne Stockem, Federico Fiuza, Luis SilvaCharles Ruyer, Laurent GremilletRamesh Narayan
UCLM, SpainIST, GoLP, PortugalCEA, France,Harvard CfA, USA
ATELIER PNHE – Paris, 3-5 octobre 2012
Page 2
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
Page 3
Shock Formation: PIC’s (OSIRIS)
1. Simplest possible: cold, symmetric, e-e+ shells,
no B0
ChocksSimulation
Window
Page 4
Shock Formation: PIC’s (Osiris)
1. Simplest possible PIC’s: cold, symmetric, e-e+ shells,
g = 1.05
Page 5
Shock Formation: PIC’s (Osiris)
1. Simplest possible PIC’s: cold, symmetric, e-e+ shells,
g = 1.05
Page 6
Shock Formation: Two Phases
1. Shells overlap: instability grows & saturates
2. Shock Forms
Unstable
Density
Page 7
Shock Formation: Two Phases
g = 25
Shockforms
Phase 1
Insta. triggered
Insta. saturates
B2 in central region
Phase 2
Page 8
First Phase: Instabilities
1. Which instability grows? All… but some do it faster Growth rate d(k)
For g > (3/2)1/2, “Weibel” wins
Page 9
First Phase: Instabilities
1. Instability is bad news in Fast Ignition for ICF
2. Here, it is good news
3. A flow aligned B0 can cancel Weibel (Godfrey
‘75)
4. What if not aligned (+ sym, cold flow)?
Bret & Perez-Alvaro, Phys. Plasmas, 18, 080706 (2011)
FLOW
B0
qGR for B0 ∞
Page 10
First Phase: Saturation Field
1. Weibel grows at d, from Bi to Bf.
2. What about Bf? Cyclotron freq. = d gives
3. Good agreement with PIC’s
Page 11
First Phase: Seed Field
1. What about Bi?
2. Instability amplifies spontaneous fluctuations
3. Focus on modes with k// = 0 (w integrated)
4. Their d3k density reads (Ruyet & Gremillet)
Not trivial
Page 12
First Phase: Seed Field
1. Need to integrate seed density on d3k
2. k-integration domain?
Numericallydetermined (?)
Page 13
First Phase: Seed Field
1. Need to integrate seed density on d3k
2. We thus compute
Page 14
First Phase: Saturation Time
1. Saturation time ts simply reads
2. “Final” result (so far)
Page 15
First Phase: Saturation Time
1. Saturation time ts simply reads
PIC
Page 16
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 ts.
Page 17
First Phase: Saturation Time
1. Not bad… but not good either
2. Possible issue 2:• Start from noise at w = 0 instead of integrating
?
• Can the instability select the amplified frequency?
• Yes, with an accuracy w = 0 ± d
• Laurent & Charles, Delicate…
Page 18
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 w = 0 ± d :
• Agreement slightly better. Still, weird at g ∞
3/2
Page 19
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
Page 20
Motivation
1 2 3
1. Collisionless shocks are key fundamental processes
2. Role in Fireball Scenario for GRB’s and HECR’s
1.Plasma shells “collision”2.Shock Formation - Collisionless3.Particle acceleration: GRB