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 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
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
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
results of linear analysis
• Oblique modes grow as fast as the
parallel modes
• Electric field fluctuations are multidimensional
• Do not expect electron trapping and
resultant surfing acceleration
• Confirmed by PIC simulation
2D Electro-static PIC Simulation
We investigate surfing acceleration in a system that
models the foot region of perpendicular shock
Up stream rest frame
SF
Down
Up
Upstream proton
upstream
electron
Simulation plane
Phase space of protons
reflected
proton
X
Amano&Hoshino 2006
Vx
-Vd
0
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
2eφ/meVd2
1
Potential Structure of 2D case
2eφ/meVd2
Ohira&Takahara(‘07)
Velocity Space
1D
2D
B = 90μG
Surfing acc.
T=720ωpe-1
Ohira&Takahara(‘07)
Energy Spectrum
B = 90μG
1D
2D
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）
Ohira&Takahara, arXiv:0808.3195
2Ue/mevd2
B=0μG
B=27μG
2Ue/mevd2
Ey
Ey
Ex
Ex
Ion Two-stream Ins.
Buneman Ins.
Ion Two-stream Ins.
Buneman Ins.
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
Te=100Tp , Vd=Vth,e
After Buneman ins. saturate,
(Te〜100Tp , Vth,e = Vd)
kyVd/ωpe
the growth rate of Ion two-
IT
stream (IT) ins. is larger than
that of Ion Acoustic (IA) ins..
Ohira&Takahara, arXiv:0808.3195
kxVd/ωpe
IA
γ/ωpe
Results（Electro-static potential structure
B=0）
t=270ωpe-1 (When Buneman Ins. saturate.)
t=1740ωpe-1 (When Ion two-stream Ins. saturate.)
2eφ/mevd2
2eφ/mevd2
Results（Temperature）
B=0μG
B=27μG
Te / T0
Te / T0
Ti / T0
Ti / T0
Te / Ti
Time [ωpe-1]
Te / Ti
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）
Maxwell distribution
（Te=0.5me<v2>=1.2keV）
B=27μG
No Surfing acc.
Time = 3000ωpe-1
B=０μG
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