1. 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

2. Problems Electrons in SNR shocks –thermal component at 1-2 keV –non-thermal component up to 100TeV Previous work (Cargill & Papadopoulos) suggests T e 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. ２ D Buneman Instability 2D linear analysis V d /V th,e =100,T p =T e V d /V th,e =10,T p =T e V d /V th,e =10,T p =10T e k x V d /ω pe k y V d /ω pe γ/ω pe Color contours show growth rate.

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 X Amano&Hoshino 2006 upstream electron reflected proton 0 -V d VxVx Upstream proton Phase space of protons We investigate surfing acceleration in a system that models the foot region of perpendicular shock Up stream rest frame SF Down Up Simulation plane

7. simulation parameters double periodic boundary conditions –L x =16-64λ B L y =16λ B (λ B =2πv d /ω pe ) –256(2048)×256(512) cells –80×256×256 electrons –v d =-0.04c, n r =0.25n p =0.2n e ω ce /ω pe =0-0.03 realistic mass ratio m p /m e =1836 electrostatic modes low initial temperature (1.75-7eV)

8. Potential Structure of 1D case 1 2eφ/m e V d 2

9. Potential Structure of 2D case 2eφ/m e V d 2 Ohira&Takahara(‘07)

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

11. Energy Spectrum B = 90μG 2D 1D 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 ） B=0μGB=27μG Ex Ey Ex 2U e /m e v d 2 Buneman Ins. Ion Two-stream Ins. Buneman Ins. Ohira&Takahara, arXiv:0808.3195

14. Ion Two-Stream Instability T e >> T p modes with k Dp >k>k De 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 (k x =ω pp /v d ) Obliquity is required for this instability

15. Oblique Ion two-stream Instability 2D electro static linear analysis After Buneman ins. saturate, (T e 〜 100T p, V th,e = V d ) the growth rate of Ion two- stream (IT) ins. is larger than that of Ion Acoustic (IA) ins.. γ/ω pe k y V d /ω pe IT IA T e =100T p, V d =V th,e k x V d /ω pe Ohira&Takahara, arXiv:0808.3195

16. Results （ Electro-static potential structure B=0 ） 2eφ/m e v d 2 t=270ω pe -1 (When Buneman Ins. saturate.) t=1740ω pe -1 (When Ion two-stream Ins. saturate.)

17. Results （ Temperature ） T e / T 0 T i / T 0 T e / T i T e / T 0 T i / T 0 T e / T i B=0μG B=27μG Time [ω pe -1 ] By ion two-stream ins. T e / T i becomes small. As a result, the growth rate of IA ins. becomes small.

18. Results （ Energy spectrum ） B=27μG B= ０ μG Maxwell distribution （ T e =0.5m e =1.2keV ） No Surfing acc. Time = 3000ω pe -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