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

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

Content

• Incident plasma +reflected proton beam• Linear Analysis • 2-D simulation under Double Periodic Conditi

on• 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 Instability2D linear analysis

Vd/Vth,e=100,Tp=Te Vd/Vth,e=10,Tp=Te Vd/Vth,e=10,Tp=10Te

kxVd/ωpe 　

kyVd/ωpe

γ/ωpe γ/ωpe γ/ωpe

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-Vd

Vx

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

DownUp

Simulation plane

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)

Potential Structure of 1D case

1

2eφ/meVd2

Potential Structure of 2D case

2eφ/meVd2

Ohira&Takahara(‘07)

Velocity Space

1D

2D

B = 90μG

T=720ωpe-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=0μG B=27μG

Ex

EyEy

Ex

2Ue/mevd2 2Ue/mevd

2

Buneman Ins.　 Ion Two-stream Ins. Ion Two-stream Ins.

Buneman Ins.

Ohira&Takahara, arXiv:0808.3195

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

Oblique Ion two-stream Instability

2D electro static linear analysis

After Buneman ins. saturate,

(Te 〜 100Tp , Vth,e = Vd)

the growth rate of Ion two-str

eam (IT) ins. is larger than th

at of Ion Acoustic (IA) ins..

γ/ωpe

kyVd/ωpe

ITIA

Te=100Tp , Vd=Vth,e

kxVd/ωpeOhira&Takahara, arXiv:0808.3195

Results（ Electro-static potential structure B=0）

2eφ/mevd2

2eφ/mevd2t=270ωpe

-1 　 (When Buneman Ins. saturate.)

t=1740ωpe-1 　 (When Ion two-stream Ins. saturate.)

Results（ Temperature）

Te / T0

Ti / T0

Te / Ti

Te / T0

Ti / T0

Te / Ti

B=0μG B=27μG

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.

Results（ Energy spectrum）

B=27μGB= ０ μG

Maxwell distribution（ Te=0.5me<v2>=1.2keV ）

　 No Surfing acc.

Time = 3000ωpe-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 sit

uations• Obliquely propagating modes are important i

n the existence of beams• Following the Buneman instability, Oblique i

on 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