magnetic fields generated by the weibel instability
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Magnetic fields generated by the Weibel Instability C. M. Ryu POSTECH, KOREA FFP14 Marseille 2014.07.15-07.18 Outline I. Why Weibel instability ? II. Simulations III. Conclusion Why Weibel instability ? Why Weibel instability ? The


  1. Magnetic fields generated by the Weibel Instability C. M. Ryu POSTECH, KOREA FFP14 Marseille 2014.07.15-07.18

  2. Outline I. Why Weibel instability ? II. Simulations III. Conclusion

  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 Cosmic web dynamo mechanism.

  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 of 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.

  5. Large scale magnetic field generation mechanisms Large scale magnetic field generation mechanisms

  6. ������������������������ ������������������������ • Induction equation 2 ∂ ∂ =∇× × + ∇ η B / t ( u B ) B • Mean field dynamo theory = + = + u u u ', B B B ', 0 0 2 ∂ ∂ =∇×< × >+ ∇ η B / t u B ' ' B 0 0

  7. Magnetic field amplification by diffusive flow Magnetic field amplification by diffusive flow Line tying effect can be broken by the random particle motions, i.e., by diffusion. Diffusive flow can generate magnetic fields ∂ ∂ = ∇ × δ × = + δ B / t ( u B ), u u u , 0 2 ∂ − η ∇ B c n 2 ∇ =∇× + δ × δ = − B (( u u ) B ) u D ∂ π t 4 n D : diffusion coefficient

  8. Baroclinic mechanism (or Biermann Baroclinic mechanism (or Biermann battery) battery) ∇ T ⓧ overdense target laser beam ∇ n ⊙ γ k ∂ = ∇ × ∇ B T n t e e en e

  9. ������ ����������� Magnetic field generation mechanism : • Gamma-ray burst, collisionless shock, in the early universe, FIS Gamma-ray Burst (Fireball model) ������������������������� plasma interaction → shock formation → particle heating & accelertion → radiation Weibel/filamentation instability 9/34

  10. Weibel(Filamentation) instability Weibel(Filamentation) instability Weibel instability is induced by anisotropic temperature. (Filamentation instability is induced by two counter streams) � � � � � � � � � � � � � � � � � � � particle density increases at nodes of Bz

  11. Laser beam experiment Laser beam experiment Vulcan Petawatt(10 15 ) Laser Facility λ = 1053nm 0 − 15 = = × duration 750 fs 750 10 s Measurement of the electron energy CH-form target Density: 100 and 200 mg/cm 3 d=250, 500, and 750 � m The optical emission due to electron transit through the rear side of coated foam targets (the optical transition radiation technique) ����������� ������� ����������� ������� �������������������������� �������������������������� ����������� ����������� ������� ������� �������������������������� ��������������������������

  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 1 � m 18 2 = × λ ≈ I 500 10 W/cm and 18 L ( ) � × − = 0.511 500 /1.37 1 9.3 MeV. T

  13. �!���������������� ������� �!���������������� ������� � ����������"# � ����������"# ����������� ������� ����������� ������� �������������������������� �������������������������� ����������� ����������� ������� ������� �������������������������� ��������������������������

  14. ������������������������ Weibel Filamentation � � � � � � � � Two-stream � � � � p p d d α = 68.5, α = 1.96, = 0 α = α = 50, = 1 ⊥ � ⊥ � Same <v 2 > mc mc ���� ���� ���� • Weibel & filamentation instability show � ε � �� � � � � ���� different growing and saturation of energy. ���� ���� � ������ ε ε ε • Similarity between Weibel and filamentation � �������� ���� is broken in the relativistic regime. � �� �� ���� � �� �� �� �� ��� ω �� � ω ω ω 14/34

  15. Shock induced by counter streams Shock induced by counter streams shock direction upstream downstream n e u x u y anisotropic isotropic Magnetic field is generated �������������������� �������������������� �������������������� ��������������������

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

  17. ep jet injected into ep plasmas x ω pe /c = 30.0~ 35.0 1.955404•10 6 10 6 10 10 5 p y / mc 60 0 elec 10 4 jet e 50 total -10 10 3 40 1.955404•10 2 0 2 0.0 10.0 20.0 30.0 p x / mc n e 30 20 10 0 100 200 300 400 ������������� x ω pe /c x ω pe /c = 120.0~ 125.0 6.421600•10 4 x ω pe /c = 250.0~ 255.0 x ω pe /c = 200.0~ 205.0 10 6 10 6 10 4 2.019200•10 4 10 10 4 10 10 5 10 p y / mc 10 3 0 10 3 p y / mc p y / mc 0 10 4 0 10 2 10 2 -10 10 3 -10 10 1 -10 10 1 6.421600•10 0 0 2 0.0 10.0 20.0 30.0 p x / mc 10 2 10 2 0 2 0.0 10.0 20.0 30.0 2.019200•10 0 0 2 0.0 10.0 20.0 30.0 p x / mc 17/34 p x / mc

  18. ��� ���!��������� 60 elec jet e 50 total 40 n e 30 20 10 0 100 200 300 400 x ω pe /c x ω pe /c = 250.0~ 255.0 x ω pe /c = 340.0~ 345.0 10 6 10 6 10 6 10 6 x ω pe /c = 290.0~ 295.0 10 6 10 6 10 10 10 5 10 5 10 10 5 p y / mc p y / mc 0 0 10 4 10 4 p y / mc 0 10 4 10 3 10 3 -10 -10 10 3 -10 10 2 10 2 0 10 2 2 10 2 0 2 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 p x / mc p x / mc 10 2 10 2 0 2 0.0 10.0 20.0 30.0 18/34 p x / mc

  19. ���!��������� Jet acceleration Over the RS Ambient Plasmas beam Cross CD excited x ω pe /c = 250.0 ~ 255.0 x ω pe /c = 290.0 ~ 295.0 x ω pe /c = 340.0 ~ 345.0 10 8 10 8 10 8 amb_ele amb_ele amb_ele jet_ele jet_ele jet_ele 10 6 10 6 10 6 # of plasma # of plasma # of plasma 10 4 10 4 10 4 10 2 10 2 10 2 10 0 10 0 10 0 10 20 30 10 20 30 10 20 30 γ γ γ x ω pe /c = 250.0~ 255.0 x ω pe /c = 290.0~ 295.0 x ω pe /c = 340.0~ 345.0 10 6 10 6 10 6 10 6 10 6 10 6 10 10 10 10 5 10 5 10 5 p y / mc p y / mc p y / mc 0 0 0 10 4 10 4 10 4 10 3 10 3 10 3 -10 -10 -10 10 2 10 2 10 2 0 10 2 2 10 2 0 2 0 10 2 2 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 p x / mc p x / mc p x / mc 19/34

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