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 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

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

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.

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

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

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 = realistic mass ratio m p /m e =1836 electrostatic modes low initial temperature (1.75-7eV)

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

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

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

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

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

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:

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

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:

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.)

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.

Results （ Energy spectrum ） B=27μG B= ０ μG Maxwell distribution （ T e =0.5m e =1.2keV ） No Surfing acc. Time = 3000ω pe -1

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

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