Magnetic fields generated by the Weibel Instability C. M. Ryu POSTECH, KOREA FFP14 Marseille 14.7.15-7.18
Outline I. Why Weibel instability? II. Simulations III. Conclusion
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
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, twostreaming 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.
Large scale magnetic field generation mechanisms
Mean field dynamo theory Induction equation = + η B/ t ( u B) B Mean field dynamo theory u= u + u', B= B + B', B / t = < u' B' >+ η B
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 B / t = ( δ u B ), u = u + δ u, n δ u = D n B ηc = + t 4π B (( u δu) B) D : diffusion coefficient
Baroclinic mechanism (or Biermann battery) overdense target x T laser beam n γ k B = T n t e e ene
Weibel Instability Magnetic field generation mechanism : Gamma-ray burst, collisionless shock, in the early universe, FIS Gamma-ray Burst (Fireball model) [Piran, Phys. Rep.(9)] plasma interaction shock formation particle heating & accelertion radiation Weibel/filamentation instability 9/ 34
Weibel(Filamentation) instability Weibel instability is induced by anisotropic temperature. (Filamentation instability is induced by two counter streams) y x z J J B z particle density increases at nodes of Bz
Laser beam experiment Vulcan Petawatt(1 15 ) Laser Facility λ = 153 nm 15 duration = 75 fs = 75 1 s CH-form target Measurement of the electron energy Density: 1 and mg/cm 3 d=5, 5, and 75 µm The optical emission due to electron transit through the rear side of coated foam targets (the optical transition radiation technique) [ R. Jung, et. al.,, PRL. 94, 1951 (5) ]
Electron energy spectrum Two temperature Boltzmann distribution hot temperature ~ 8.8 MeV cold temperature ~.6 MeV The laser ponderomotive force will lead to an effective temperature of I 18 18 = 5 1 W/cm and λl 1µm T ( ).511 5 /1.37 1 = 9.3 MeV.
Experiment and simulation supporting WI [ R. Jung, et. al.,, PRL. 94, 1951 (5) ]
Weibel Vs. Filamentation Weibel p z Filamentation p z p x pd α =68.5, α =1.96, = mc p y Same <v > p x pd α =α =5, =1 mc p y Two-stream.14.1 ε F /n e m e c.1.8.6.4 Weibel. Filament TS. 4 6 8 1 ω pe t Weibel & filamentation instability show different growing and saturation of energy. Similarity between Weibel and filamentation is broken in the relativistic regime. 14/ 34
Shock induced by counter streams shock direction upstream downstream n e u x u y anisotropic isotropic Magnetic field is generated [ Kato, ApJ (7) ]
Simulation Models for shock Instability Reflected B.C. Instability Reverse Shock CD Reverse Shock CD Forwar d Shock D PIC simulation [Kato, ApJ(7)] 3D PIC simulation [Nishikawa et al., ApJL(9)] 16/ 34
1.95544 1 6 1.95544 1 6.416 1 4 6.416 1.19 1 4.19 1 1 6 1 xω pe /c = 3.~ 35. ep jet injected into ep plasmas 1 6 1 1 5 p y / mc -1 1 4 1 3 6 5 4 elec jet e total. 1.. 3. p x / mc n e 3 1 p y / mc 1 xω pe /c = 1.~ 15. 1 3 4 x ω pe /c Reverse Shock xω pe/c = 5.~ 55. xω pe /c =.~ 5. 1 4 1 4 1 1 1 3 1 3 1 6 1 5-1 1 p y / mc 1 p y / mc 1 4. 1.. 3. p x / mc 1 1-1. 1.. 3. p x / mc 1 1-1. 1.. 3. p x / mc 1 3 1 17/ 34
1 6 1 1 6 1 1 6 1 CD &Forward Shock 6 5 4 elec jet e total n e 3 1 1 xω pe /c = 5.~ 55. 1 3 4 x ω pe /c 1 6 xω pe /c = 34.~ 345. 1 5 xω pe /c = 9.~ 95. 1 6 1 1 6 1 5 p y / mc 1 4 1 1 5 p y / mc 1 4-1 1 3 p y / mc 1 4-1 1 3. 1.. 3. p x / mc 1-1. 1.. 3. p x / mc 1 3 1. 1.. 3. p x / mc 1 18/ 34
1 6 1 1 6 1 1 6 1 Forward Shock Over the RS Jet acceleration Cross CD Ambient Plasmas beam excited 1 8 1 6 xω pe /c = 5. ~ 55. amb_ele jet_ele 1 8 1 6 xω pe /c = 9. ~ 95. amb_ele jet_ele 1 8 1 6 xω pe /c = 34. ~ 345. amb_ele jet_ele # of plasma 1 4 # of plasma 1 4 # of plasma 1 4 1 1 1 1 1 3 γ xω pe /c = 5.~ 55. xω /c = 34.~ 345. 1 1 1 3 1 3 γ γ xω pe /c = 9.~ 95. 1 6 1 6 pe 1 6 1 1 5 1 1 5 1 1 5 p y / mc 1 4 p y / mc 1 4 p y / mc 1 4-1 1 3-1 1 3-1 1 3. 1.. 3. p x / mc 1. 1.. 3. p x / mc 1. 1.. 3. p x / mc 1 19/ 34
3.3519 1 4 3.3519 1.681 1 4.681 1.796 1 5.796 1 1 8.71383 1 5 8.71383 1 1 3.461 1 6 3.461 1 High Jet Temperature effect initial p y / c 1-1 p y / c 1-1 xω xω pe /c = 3. ~ 35. pe /c = 3. ~ 35. # of plasma 1 3 1 1 1 1.. 4. 6. 4 8. 6 8 γ p x / c Before RS 1 8 1 6 1 4 1 amb_ele jet_ele xω xω pe /c = 13. ~ 135. pe /c = 13. ~ 135. # of plasma 1 3 1 1 1 1.. 4. 6. 4 8. 6 8 γ p x / c 1 8 1 6 1 4 1 1 4 amb_ele jet_ele 1 4 RS~CD p y / c 1-1 CD~FS p y / c 1-1 xω pe /c = 335. ~ 34.xω pe /c = 335. ~ 34. 1 3 1.. 4. 6. 4 8. 6 8 p x / c γ xω xω pe /c = 3. ~ 35. pe /c = 3. ~ 35. # of plasma 1 5 1 4 1 3 1 1 4 6 8.. 4. 6. 8. γ p x / c 1 8 1 6 1 4 1 # of plasma 1 8 1 6 1 4 1 amb_ele jet_ele amb_ele jet_ele 1 6 1 5 1 4 RS transition p y / c 1-1 xω xω pe /c =. ~ 5. pe /c =. ~ 5. # of plasma 1 4 1 3 1 No gyration! 1.. 4. 6. 4 8. 6 8 γ p x / c 1 8 1 6 1 4 1 amb_ele jet_ele 1 5 / 34
Magnetic field structures T cj /m e c =.1 wihtime. ω pe t= 1., xω pe /c= 3. ω pe t= 35., xω pe /c=19. B / [(γ j -1)nmc ] 1/.1. -.1 B / [(γ j -1)nmc ] 1/ 1-1 -. 4 6 8 1 1 z ω pe /c - 4 6 8 1 1 z ω pe /c 1/ 34
56.674.56 1.5 1 5 1. 1 1 1.5 1 5 1. 1 1 89.74.89 1D simulation of electron T anisotropy driven WI Weibel instability s growth and nonlinear damping in the relativistic regime..5 ω pe t =. 1 5.5 1 4 ω pe t = 81.9 1 5 1 4 1. KE e-1833 KE e-1 δb 1833 δb 1 p y / mc. p y / mc. 1 3 1 3.98 -.5 1 -.5 1 ε/ke e.96.94.6 -.5..5 p x / mc 1 1 -.5..5 p x / mc 1 1.4 B y n i.. 5 1 15 ω pe t ω pe t 15 1 1 1 1 ω pe t 15 1 1 1 1 5 1-1 5 1-1..5 1. 1.5 1 -..5 1. 1.5 1 - ck x / ω pe ck x / ω pe / 34
3 1-1 - -3.1.5. -.5 -.1 1 5 1 1 3 1-1 - -3.5. -.5 1 5 1 1 Momentum distribution M/m =1833 M/m =1 p y /mc 3 1-1 - -3 (a) ω pe t =. electron (b) ω pe t = 81.9 electron 1 5 1 4 p y /mc 3 1-1 - -3 (a) ω pe t =. electron (b) ω pe t = 81.9 electron 1 5 1 4.1-3 - -1 1 3 p x /mc (c) ω pe t =. ion -3 - -1 1 3 p x /mc (d) ω pe t = 81.9 ion 1 3-3 - -1 1 3 p x /mc (c) ω pe t =. ion -3 - -1 1 3 p x /mc (d) ω pe t = 81.9 ion 1 3 p y /mc.5. -.5 1 p y /mc.5. -.5 1 -.1 -.1 -.5..5.1 p x /mc -.1 -.5..5.1 p x /mc 1 1 -.5..5 p x /mc -.5..5 p x /mc 1 1 There is no difference in electron distribution. Ion distribution is changed for mass ratio 1.
Non-linear evolution By.4 11 11 15 ni 88.84 11 15 Ex.74551 1-6 1-6 15 1 1 1 ωpe t 1 ωpe t M/m=1833 ωpe t 1-7 1 1-1 1-8 5 1-1 5 5 1-.4 1-3..5 1. 1.5 ckx / ωpe By 56.674 1 1 ωpe t ωpe t 15 1-.56..5 1. 1.5 ckx / ωpe ni 89.74 15 11 1 1 5 1-1.89..5 1. 1.5 ckx / ωpe.74551 1-1 ckx / ωpe 1-1 5..5 1. 1.5 11 M/m=1 1-..5 1. 1.5 ckx / ωpe.89 1- Ex 1.858595 1-6 1-6 15 ωpe t 1-9 1-7 1 1-8 5 1-9 1.858595 1-1..5 1. 1.5 ckx / ωpe
Conclusions 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.