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Buneman and Ion Two-Stream Instabilities in the Foot Region of Collisionless Shocks

Buneman and Ion Two-Stream Instabilities in the Foot Region of Collisionless Shocks. Fumio Takahara with Yutaka Ohira (Osaka University) Oct. 6, 2008 at Krakow Conference. Problems. Electrons in SNR shocks thermal component at 1-2 keV non-thermal component up to 100TeV

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Buneman and Ion Two-Stream Instabilities in the Foot Region of Collisionless Shocks

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  1. Buneman and Ion Two-Stream Instabilities in the Foot Region ofCollisionless Shocks Fumio Takahara with Yutaka Ohira (Osaka University) Oct. 6, 2008 at Krakow Conference

  2. Problems • Electrons in SNR shocks • thermal component at 1-2 keV • non-thermal component up to 100TeV • Previous work (Cargill & Papadopoulos) suggests Te up to 100keV by Buneman & ion acoustic instabilities Overheating Problem • Acceleration (DSA) is promising but injection mechanisms are not well understood • surfing acceleration has been advocated but it is open if it works for 2-D & 3-D cases

  3. Content • Incident plasma +reflected proton beam • Linear Analysis • 2-D simulation under Double Periodic Condition • Conclusions • No surfing acceleration occurs • Overheating by ion acoustic instability is avoided by ion two-stream instability • based on Ohira & FT 2007 Ap.J.L. 661, L171 Ohira & FT 2008 Ap.J in press

  4. ２D Buneman Instability 2D linear analysis Color contours show growth rate. γ/ωpe γ/ωpe γ/ωpe kyVd/ωpe kxVd/ωpe Vd/Vth,e=100,Tp=Te Vd/Vth,e=10,Tp=Te Vd/Vth,e=10,Tp=10Te

  5. results of linear analysis • Oblique modes grow as fast as the parallel modes • Electric field fluctuations are multi-dimensional • Do not expect electron trapping and resultant surfing acceleration • Confirmed by PIC simulation

  6. 2D Electro-static PIC Simulation We investigate surfing acceleration in a system that models the foot region of perpendicular shock SF Up stream rest frame Upstream proton Down Up upstream electron Simulation plane Phase space of protons reflected proton Vx X 0 -Vd Amano&Hoshino 2006

  7. simulation parameters • double periodic boundary conditions • Lx=16-64λB Ly=16λB (λB=2πvd/ωpe ) • 256(2048)×256(512) cells • 80×256×256 electrons • vd=-0.04c, nr=0.25np=0.2ne • ωce/ωpe =0-0.03 • realistic mass ratio mp/me=1836 • electrostatic modes • low initial temperature (1.75-7eV)

  8. Potential Structure of 1D case 2eφ/meVd2 1

  9. Potential Structure of 2D case 2eφ/meVd2 Ohira&Takahara(‘07)

  10. Velocity Space 1D 2D B = 90μG Surfing acc. T=720ωpe-1 Ohira&Takahara(‘07)

  11. Energy Spectrum B = 90μG 1D 2D Ohira&Takahara(‘07)

  12. Subsequent Evolution • What occurs after Buneman instability saturates? • Previous thought was the onset of ion acoustic instability • We have found instead ion two-stream instability is excited

  13. Results（Electric Fields） Ohira&Takahara, arXiv:0808.3195 2Ue/mevd2 B=0μG B=27μG 2Ue/mevd2 Ey Ey Ex Ex Ion Two-stream Ins. Ion Two-stream Ins. Buneman Ins. Buneman Ins.

  14. Ion Two-Stream Instability • Te >> Tp • modes with kDp>k>kDe called ion plasma oscillations (electrons make uniform background and do not suffer from Landau damping) • Ion plasma oscillations excited by the resonance with ion beam (kx=ωpp/vd) • Obliquity is required for this instability

  15. Oblique Ion two-stream Instability γ/ωpe 2D electro static linear analysis Te=100Tp , Vd=Vth,e After Buneman ins. saturate, (Te〜100Tp , Vth,e = Vd) the growth rate of Ion two-stream (IT) ins. is larger than that of Ion Acoustic (IA) ins.. kyVd/ωpe IT IA kxVd/ωpe Ohira&Takahara, arXiv:0808.3195

  16. Results（Electro-static potential structure B=0） 2eφ/mevd2 t=270ωpe-1 (When Buneman Ins. saturate.) t=1740ωpe-1(When Ion two-stream Ins. saturate.) 2eφ/mevd2

  17. Results（Temperature） B=0μG B=27μG Te / T0 Te / T0 Ti / T0 Ti / T0 Te / Ti Te / Ti Time [ωpe-1] Time [ωpe-1] By ion two-stream ins. Te / Ti becomes small. As a result, the growth rate of IA ins. becomes small.

  18. Results（Energy spectrum） Maxwell distribution （Te=0.5me<v2>=1.2keV） B=０μG B=27μG No Surfing acc. Time = 3000ωpe-1

  19. Implications • Ions are heated by ion two-stream instability • growth of ion acoustic instability is suppressed and overheating of electrons is avoided • Expected downstream electron temperature is a few percent of ion temperature matching observations

  20. Summary • Multi-dimensional studies are indispensable • No surfing acceleration occurs in realistic situations • Obliquely propagating modes are important in the existence of beams • Following the Buneman instability, Oblique ion two-stream instability is excited to heat ions and suppress the overheating of electrons in the foot region • Resultant electron temperature is compatible with observations

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