buneman and ion two-stream instabilities in the foot region of collisionless shocks fumio takahara...
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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)
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
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