Buneman and Ion Two-Stre am Instabilities in the Foot Region of Collisionless Shocks Fumio Takahara with Yutaka Ohira (Osaka University) Oct. 6, 2008 at Krakow Co nference
Jan 01, 2016
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