Magnetic fields generated by the Weibel Instability C. M. Ryu - - PowerPoint PPT Presentation

SLIDE 1

• C. M. Ryu

POSTECH, KOREA FFP14 Marseille 2014.07.15-07.18

Magnetic fields generated by the Weibel Instability

SLIDE 2

I. Why Weibel instability ? II. Simulations

• III. Conclusion

Outline

SLIDE 3

Why Weibel instability ? Why Weibel instability ?

The existence of the magnetic field in the universe is evidenced by observations of Faraday rotation and synchrotron radiation . The origin of the magnetic field in the universe is not yet known: Seed magnetic field seem to have been amplified by the dynamo mechanism.

Cosmic web

SLIDE 4

• For a seed magnetic field generation mechanism,

there are two mechanisms proposed so far: Biermann battery and Weibel instability .

• Understanding microscopic plasma physic is

necessary: Plasma waves and their associated instabilities ( the Buneman instability, two- streaming instability, and the Weibel instability) created in the shocks involve particle acceleration (electrons, positrons, and ions).

• Weibel instability has attracted attention as a mechanism of

magnetic generation in the core of galaxies or in the formation

• f universe. Strong magnetic fields generated at shock waves

associated with the formation of galaxies or clusters of galaxies by the Weibel instability, in collisionless plasmas may have affected the formation of stars in protogalaxies, GRBs etc.

SLIDE 5

Large scale magnetic field generation mechanisms Large scale magnetic field generation mechanisms

SLIDE 6

• Induction equation
• Mean field dynamo theory

2

/ ( ) B t u B B η ∂ ∂ =∇× × + ∇

2

/ ' ' B t u B B η ∂ ∂ =∇×< × >+ ∇

', ', u u u B B B = + = +

SLIDE 7

Line tying effect can be broken by the random particle motions, i.e., by diffusion. Diffusive flow can generate magnetic fields / ( ), , B t u B u u u δ δ ∂ ∂ = ∇ × × = +

n u D n δ ∇ = −

: D diffusion coefficient

Magnetic field amplification by diffusive flow Magnetic field amplification by diffusive flow

2 2

(( ) ) 4 B c B u u B t η δ π ∂ − ∇ =∇× + × ∂

SLIDE 8

laser beam

T ∇ n ∇

• verdense target

ⓧ ⊙

t e e e

k T n en γ ∂ = ∇ × ∇ B

Baroclinic mechanism (or Biermann battery) Baroclinic mechanism (or Biermann battery)

SLIDE 9

• Gamma-ray Burst

(Fireball model)

plasma interaction→ shock formation → particle heating & accelertion → radiation

Weibel/filamentation instability

• Magnetic field generation mechanism :

Gamma-ray burst, collisionless shock, in the early universe, FIS

9/34

SLIDE 10

Weibel instability is induced by anisotropic temperature. (Filamentation instability is induced by two counter streams)

• particle density increases at nodes of Bz

Weibel(Filamentation) instability Weibel(Filamentation) instability

SLIDE 11

Vulcan Petawatt(1015) Laser Facility

15

1053nm duration 750 fs 750 10 s λ

−

= = = ×

The optical emission due to electron transit through the rear side of coated foam targets (the

• ptical transition radiation technique)

Measurement of the electron energy CH-form target Density: 100 and 200 mg/cm3 d=250, 500, and 750 m

• Laser beam experiment

Laser beam experiment

SLIDE 12

• Two temperature Boltzmann distribution

“hot” temperature ~ 8.8 MeV “cold” temperature ~ 2.6 MeV

• The laser ponderomotive force will lead to an

effective temperature of

( )

18 2 18

500 10 W/cm 1 m 0.511 500 /1.37 1 9.3 MeV.

L

I and T λ = × ≈ × − =

SLIDE 13

• !

"# ! "#

SLIDE 14

• 14/34
• p

⊥

• d

α = 68.5, α = 1.96, = 0 mc

Weibel

• p

⊥

• d

α = α = 50, = 1 mc

Filamentation Two-stream

• ε

ε ε ε

• ω

ω ω ω

• Weibel & filamentation instability show

different growing and saturation of energy.

• Similarity between Weibel and filamentation

is broken in the relativistic regime.

Same <v2>

SLIDE 15

• e

n

shock direction

Magnetic field is generated

x

u

y

u

anisotropic isotropic upstream downstream

Shock induced by counter streams Shock induced by counter streams

SLIDE 16

• Instability

Reflected B.C. Instability $#% &'() CD Reverse Shock *$#% +,-'(. CD Reverse Shock Forwar d Shock 16/34

SLIDE 17

100 200 300 400 x ωpe /c 10 20 30 40 50 60 ne

elec jete total

• xωpe/c = 120.0~ 125.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 6.421600•100 6.421600•104

101 102 103 104

xωpe/c = 250.0~ 255.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 200.0~ 205.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 2.019200•100 2.019200•104

101 102 103 104

xωpe/c = 30.0~ 35.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 1.955404•102 1.955404•106

103 104 105 106

17/34

ep jet injected into ep plasmas

SLIDE 18

100 200 300 400 x ωpe /c 10 20 30 40 50 60 ne

elec jete total

!

xωpe/c = 250.0~ 255.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 340.0~ 345.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 290.0~ 295.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

18/34

SLIDE 19

!

xωpe/c = 250.0~ 255.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 340.0~ 345.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 250.0 ~ 255.0

10 20 30 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

xωpe/c = 340.0 ~ 345.0

10 20 30 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele xωpe/c = 290.0~ 295.0

0.0 10.0 20.0 30.0 px / mc

• 10

10 py / mc

2 102 106

102 103 104 105 106

xωpe/c = 290.0 ~ 295.0

10 20 30 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

Jet acceleration

Over the RS

Ambient Plasmas beam excited

Cross CD

19/34

SLIDE 20

"#$%&

xωpe/c = 130.0 ~ 135.0

0.0 20.0 40.0 60.0 80.0 px / c

• 10

10 py / c

2 2.608100•100 2.608100•104

101 102 103 104

xωpe/c = 30.0 ~ 35.0

0.0 20.0 40.0 60.0 80.0 px / c

• 10

10 py / c

2 3.351900•100 3.351900•104

101 102 103 104

xωpe/c = 200.0 ~ 205.0

0.0 20.0 40.0 60.0 80.0 px / c

• 10

10 py / c

2 2.796200•101 2.796200•105

102 103 104 105

xωpe/c = 230.0 ~ 235.0

0.0 20.0 40.0 60.0 80.0 px / c

• 10

10 py / c

2 8.713830•101 8.713830•105

102 103 104 105

xωpe/c = 335.0 ~ 340.0

0.0 20.0 40.0 60.0 80.0 px / c

• 10

10 py / c

2 3.024612•102 3.024612•106

103 104 105 106

xωpe/c = 30.0 ~ 35.0

20 40 60 80 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

xωpe/c = 130.0 ~ 135.0

20 40 60 80 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

xωpe/c = 200.0 ~ 205.0

20 40 60 80 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

xωpe/c = 230.0 ~ 235.0

20 40 60 80 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

xωpe/c = 335.0 ~ 340.0

20 40 60 80 γ 100 102 104 106 108 # of plasma

amb_ele jet_ele

initial Before RS

RS transition RS~CD CD~FS No gyration!

20/34

SLIDE 21

#

T

cj/mec2=0.0001 ωpet= 350.0 , xωpe/c=190.0

2 4 6 8 10 12 z ωpe /c

• 2
• 1

1 2 B / [(γj -1)nmc2]1/2

ωpet= 100.0 , xωpe/c= 30.0

2 4 6 8 10 12 z ωpe /c

• 0.2
• 0.1

0.0 0.1 0.2 B / [(γj -1)nmc2]1/2

wih time 21/34

SLIDE 22

'%&

• δ

δ δ δ

• δ

δ δ δ

• ε

ε ε ε ω ω ω ω

• Weibel instability’s growth and nonlinear damping in the relativistic

regime.

ωpet = 81.92

• 0.5

0.0 0.5

• 0.5

0.0 0.5

px/ mc

py/ mc

2 1.0•101 1.5•105

101 102 103 104 105

ωpet = 0.00

• 0.5

0.0 0.5

• 0.5

0.0 0.5

px/ mc

py/ mc

2 1.0•101 1.5•105

101 102 103 104 105

By

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 0.0056 56.2674

10-2 10-1 100 101

ni

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 0.0089 89.0074

10-2 10-1 100 101

22/34

SLIDE 23

There is no difference in electron distribution. Ion distribution is changed for mass ratio 10.

/ /

(a) ωpet = 0.00

• 3
• 2
• 1

1 2 3

• 3
• 2
• 1

1 2 3

px/mc

py/mc

electron

(b) ωpet = 81.92

• 3
• 2
• 1

1 2 3

• 3
• 2
• 1

1 2 3

px/mc

electron

(c) ωpet = 0.00

• 0.10 -0.05 0.00 0.05 0.10
• 0.10
• 0.05

0.00 0.05 0.10

px/mc

py/mc

ion

(d) ωpet = 81.92

• 0.10 -0.05 0.00 0.05 0.10
• 0.10
• 0.05

0.00 0.05 0.10

px/mc

ion

2 101 105

101 102 103 104 105

M/m =1833

(a) ωpet = 0.00

• 3
• 2
• 1

1 2 3

• 3
• 2
• 1

1 2 3

px/mc

py/mc

electron

(b) ωpet = 81.92

• 3
• 2
• 1

1 2 3

• 3
• 2
• 1

1 2 3

px/mc

electron

(c) ωpet = 0.00

• 0.5

0.0 0.5

• 0.5

0.0 0.5

px/mc

py/mc

ion

(d) ωpet = 81.92

• 0.5

0.0 0.5

• 0.5

0.0 0.5

px/mc

ion

2 101 105

101 102 103 104 105

M/m =10

SLIDE 24

+01 +01

M/m=1833

By

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 0.0056 56.2674

10-2 10-1 100 101

Ex

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 1.858595•10-10 1.858595•10-6

10-9 10-8 10-7 10-6

ni

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 0.0089 89.0074

10-2 10-1 100 101

Ex

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 2.274551•10-10 2.274551•10-6

10-9 10-8 10-7 10-6

By

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 2.24•10-3 2.24•101

10-2 10-1 100 101

ni

0.00 0.50 1.00 1.50 0.00 0.00

50 100 150 200

ckx / ωpe

ωpe t

2 0.0089 88.8420

10-2 10-1 100 101

M/m=10

SLIDE 25

• The Weibel instability generates the localized magnetic field

which merges into a longer wave length mode in the nonlinear stage.

• Beyond the quasilinear saturation stage, an inverse cascade

process via nonlinear decay instability(and other microscopic plasma interactions) involving electrostatic fluctuation seems to take place.

• The magnetic field generated is weaker than expected.

% %