リコネクションと電離非平衡プラズマ

リコネクションと電離非平衡プラズマ
Shinisuke Imada (Nagoya Univ., STEL)
Plasmas condi>ons in solar corona
Weak Collision Plasma
Diﬀerence from collisionless plasma
•  Momentum transfer by coulomb collision 衝突による運動量交換
•  Thermal conduc>on along magne>c ﬁeld 衝突による熱伝導
•  Ioniza>on and recombina>on 衝突による電離・再結合
•  Radia>ve energy loss (not synchrotron radia>on)
衝突による輻射
Difference Summary
Solar Flare
Typical Spatial Scale = 100 Mm
Same
Substorm
Typical Spatial Scale = 100 Mm
希薄なプラズマ
濃いプラズマ
Macro > Collision >> Micro
Collision >> Macro > Micro
Collision-Macro Coupling
Micro-Macro Coupling
太陽物理学が解明すべき点 1. Sweet-‐Parker .vs. Petschek RX Bhattacharjee+, 2009
Sweet-Parker like RX
Heating occur inside CS
Yokoyama&Shibata, 1997
1. "Color online# Time-sequence of the nonlinear evolution of the current density Jy of a Sweet–Parker current sheet in a large system of Lundquist
er SL = 6.28! 105. The black lines represent surfaces of constant ".
s to settles down to a plateau, until about t ! 9. At this
of the third nonlinear phase, some of the small islands
uced by the secondary instability coalesce to form larger
ds that are convected toward the boundaries. "If the iss grow to large size but are constrained to stay fixed at
enter of the computational domain by reason of symmeimposed in the simulations, the third nonlinear phase
be short-lived, and the reconnection rate may fall rapAt about this point in time, the extended current sheet
ws yet another burst of secondary tearing activity producmultiple plasmoids, and a consequent enhancement in the
nnection rate, which at about t ! 12 attains nearly an
order of magnitude higher than the Sweet–Parker rate at this
value of SL. Due to insufficient spatial resolution, caused by
the slow drift of the current sheet away from the region
where the grid points along z are clustered, we are not able to
carry these simulations forward longer in time.
The plasmoid instability of Sweet–Parker sheets occurs
after SL exceeds a critical value, determined numerically to
be approximately 3 ! 104 in the present study. Like the black
curve, the blue dashed curve in Fig. 2 corresponds to another
value of SL "=2.51! 105# above the threshold and shows
generically similar behavior, while the red dashed curve corresponds to a value "=3.14! 104# at about the threshold. We
Petschek RX
Heating region is larger
by Slow-mode Shock etc.
s copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.47.145.22 On: Sun, 03 Aug 2014 04:20:26
熱的非平衡プラズマでのリコネクション Because RX is highly dynamic, plasma may not reached to
Equilibrium stage! This is new regime for Solar physics obs.
•  Non-‐Gaussian Distribu>on func>on ガウス分布でない
→　Power-‐law distribu>on, beam plasma >me scale for equilibrium is very short (kine>c regime or e-‐e or i-‐i collision) •  Diﬀerent temperature in diﬀerent species → Ti>Te >me scale for equilibrium is rela>vely long (e-‐i collision) プラズマ種で平衡でない
•  Ioniza>on non-‐equilibrium → strong hea>ng or ﬂare 電離非平衡
>me scale for equilibrium is long Target of MRX obs.
•  Hea>ng associated with/without slow-‐shock. Electron hea>ng Ion hea>ng (Possible???) •  Alfvenic ﬂow Doppler shiW measurement Ioniza>on informa>on •  Par>cle accelera>on Supra-‐thermal & High energy electron acc.
8
Standard model for Solar Flare
Hot & Fast Flow should be observed!
CHAPTER 10. MAGNETIC RECONNECTION
with Solar-C
with Yohkoh and Hinode
Yokoyama&Shibata
2001
gure 10.21: Elaborate version of the standard 2D X-type reconnection model that also in-
Tsuneta et al., 1996
des the slow and fast shocks in the outflow region, the upward-ejected plasmoid, and the
ations of the soft X-ray bright flare loops (Tsuneta 1997).
erating particles in a downward direction and producing shock waves and plasmoid
Fast Flow・リコネクション領域の長さ
(a)
9
1.5×10 cm
Takasao et al. 2012
The Astrophysical Journal, 741:107 (20pp), 2011 November 10
(b)
太陽
表面
10 Mmくらい？
Hara et al. 2011 ApJ RX ﬂows
(a)
(b)
(c)
(d)
矢印：プラズマの流れ
電流シート
(e)
Line-of-sight
direction
W
t
~20 deg
Direction of
EIS raster scan
N
細かい構造の発生
Figure 10. Spatial relationships among (a) Fe xii 195 line-of-sight Doppler velocity VD showing an inflow structure to a site near S1, (b) enhancem
192 linewidth index as a signature of hot outflows, and (c) electron density from the intensity line ratio of Fe xii 186/Fe xii 195. (d) Schematic pictu
in the EIS velocity observations near the loop-top region with the RHESSI 4–6 keV thermal source at 12:50:30–12:52:30 UT in green contours. (e)
AIA Observa>on
193 A (1.5 and 15MK)
10 Mmくらい？
Spectroscopic obs: EIS Line Proﬁles
-400 km/s
0 km/s
FeXXIV強度はa few 1000くらい？
Imada et al., 2013 ApJL
400 km/s
観測的な要求
•  強度 a few 1000 erg/str (FeXXIVで) •  長さ 10 Mm　位 •  10^4 km / 1000 km s-‐1 = 10 s 以内で •  EISの１０倍のeﬀec>ve areaがあればOKか？ •  先ほどの観測　2arcsec slit, 5s exposure 10秒で2.5Mm（４秒角）くらいスキャンできる単純にはeﬀec>ve area10倍なら0.5s露出でOK
なので、25Mmくらいスキャンできる。
Thermal Non-‐Equilibrium Plasma
Because RX is highly dynamic, plasma may not reached to
Equilibrium stage! This is new regime for Solar physics obs.
•  Non-‐Gaussian Distribu>on func>on ガウス分布でない
→　Power-‐law distribu>on, beam plasma >me scale for equilibrium is very short (kine>c regime or e-‐e or i-‐i collision) •  Diﬀerent temperature in diﬀerent species → Ti>Te >me scale for equilibrium is rela>vely long (e-‐i collision) プラズマ種で平衡でない
•  Ioniza>on non-‐equilibrium → strong hea>ng or ﬂare 電離非平衡
>me scale for equilibrium is long Ioniza>on Process
Fe13+
FeXIV
Fe14+
FeXV
Fe15+
FeXVI
ionization
α
S
Fe16+
Fe17+
FeXVII
FeXVIII
recombination
collisional and dielectronic recombination
collisional ionization
We can discuss the history of heating!
Example of Ioniza>on Calcula>on
ournal, 742:70 (11pp), 2011 December 1
time-dependent ionization in magneticInitial
reconnection
(Run1). TimeEquilibrium
starts from shock crossing. The calculation was carri
: Ionization
Te: 1.5 MK à 31.3 MK @ t=0
Ne: 2.45 x 10^9 /cc
figure is available in the online journal.)
Table 1
ow-Mode Shock Jump Conditions
The continuity equations for iron are expres
How to diagnose MRX region?
Slow-mode Shock
Ionization process with line spectroscopy
Spatial resolution is enough to resolve.
Scanning time <100s
Fast scanning (<Alfven time~100s)
with high throughput spectrometer.
Wide temperature coverage.
Diagnose velocity, temperature, density
with spectroscopic observation!
Imada et al., 2011 ApJ
How to diagnose MRX region?
10sec:L2
1sec:L1
Density: Line ra>o (L2-‐L1)/9=v1 (L3-‐L2)/70=v2 80sec:L3 Assume V1~V2 Te and V can be inverted.
Density Ne=10^9 /cc
The Astrophysical Journal, 742:70 (11pp), 2011 December 1
Slow Shock
Imada et al.
X-‐point
Figure 3. Intensities of Fe xii, Fe xviii, Fe xix, Fe xx, Fe xxi, Fe xxii, Fe xxiii, and Fe xxiv from the magnetic reconnection region (Run1). The time-dependent
Imada
et al.,
APJ,
ionization results
are shown
in y > 0,2011
and the results with ionization equilibrium are shown in y < 0. Note that the aspect ratio of the figure is different from the real
FeXVIII~FeXXIVまで撮るのが大事
scale.
(A color version of this figure is available in the online journal.)
by the fast outflow (∼1500 km s−1 ) toward the deep downstream
although the dynamical timescale does not change. Therefore,
Density Ne=10^10 /cc
The Astrophysical Journal, 742:70 (11pp), 2011 December 1
Figure 4. Result of Run2 (high-density condition, N1 = 1010 cm−3 ). The figure format is the same as Figure 3.
(A color version of this figure is available in the online journal.)
Imada et al.
Density Ne=10^8 /cc
Figure 4. Result of Run2 (high-density condition, N1 = 1010 cm−3 ). The figure format is the same as Figure 3.
(A color version of this figure is available in the online journal.)
Figure 5. Result of Run3 (low-density condition, N1 = 108 cm−3 ). The figure format is the same as Figure 3.
(A color version of this figure is available in the online journal.)
Sweet-‐Parker .vs. Petschek RX 電離進行 Bhattacharjee+, 2009
V = Va~1000km/s Nをmagne>c islandsの数 Δt = L / Va /N ~ 0.1s 仮にN=100
D =tends
(L/N)^2/Δt ~ 10^5 km^2/sの拡散方程式となって to settles down to a plateau,
until about
t ! 9. At this
order of magnitude higher than the Sweet–Parker rate at this
of the third nonlinear phase, some of the small islands
value of S . Due to insufficient spatial resolution, caused by
L ~stage
σ　なるのに１００秒 produced
by the secondary instability coalesce to form larger
the slow drift of the current sheet away from the region
islands that are convected toward the boundaries. "If the iswhere the grid points along z are clustered, we are not able to
lands grow to large size but are constrained to stay fixed at
carry these simulations forward longer in time.
電離平衡な成分を含む分光屋さんが言うmul>-‐thermal状態 FIG. 1. "Color online# Time-sequence of the nonlinear evolution of the current density Jy of a Sweet–Parker current sheet in a large system of Lundquist
number SL = 6.28! 105. The black lines represent surfaces of constant ".
L
the center of the computational domain by reason of symmetries imposed in the simulations, the third nonlinear phase
may be short-lived, and the reconnection rate may fall rapidly.# At about this point in time, the extended current sheet
shows yet another burst of secondary tearing activity producing multiple plasmoids, and a consequent enhancement in the
reconnection rate, which at about t ! 12 attains nearly an
The plasmoid instability of Sweet–Parker sheets occurs
after SL exceeds a critical value, determined numerically to
be approximately 3 ! 104 in the present study. Like the black
curve, the blue dashed curve in Fig. 2 corresponds to another
value of SL "=2.51! 105# above the threshold and shows
generically similar behavior, while the red dashed curve corresponds to a value "=3.14! 104# at about the threshold. We
L = 10 Mm This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
133.47.145.22 On: Sun, 03 Aug 2014 04:20:26
まとめ
• 
• 
• 
• 
Solar-‐Cでは格段にeﬀec>ve area が大きくなる高時間分解能で観測が可能になる多波長での分光観測(FeXVIII~FeXXIV) 迷光・散乱光等のノイズを極力軽減 •  電離過程から加熱の履歴（時間）を診断する事
を目指す •  Forward modeling または inversionから短い時間
スケールの現象を診断可能に！
リコネクションと弱電離プラズマ
京都大学附属天文台中村尚樹名大STE　今田晋亮部分電離プラズマにおけるMHD
完全電離プラズマにはない部分電離プラズマによ
るMHD効果 Ambipolar diﬀusion 中性粒子が存在することにより生じる磁場の拡散電離・再結合中性粒子と荷電粒子が入れ替わる R2 = −m
#! e ne νen (v"e − vn!) = mn nn νne"(vn −$ve )
me ni
e ni
ne e 1 + m
E
+
v
+
v ×B −
!
e
mi ne
mi ne i"
me"
! me ∂j "
!
=
∇
·
P
−
P + Pn +
e
e m
∂te
mei i
∂(nn Vn )
m
∂(n
V
)
1#!+Rmi = R
+
1
+
R
+
m
n
n
! mi− ∇ 3· Pn"−n R3∂t
$
1"
2 me−m
n
∂t
ni
me ni
n
e
1
+
E
+
v
+
× B− v
−)
e
e
i (v
R3 = −mi nimνiinne(vi − vn ) = mmninnenv
νni
n
i
!
"
!
"
∂(nn Vn )
me
e
1+ m
R
+
1
+
R
+
m
1
3
n
mi
mi
∂t
!
"
∂j
me
Pn ) P
+ +
me ∂j e ∂t = ∇ · (Pem+
n
Ion + ele Fluid e ∂t = ∇ · Pe − mei Pi +
∂(nn Vn )
!
"
$
ne e#!
(E +∂ve(m
×"
B)
−
R
+
R
+
m
1
3
n
n
v
+
m
n
v
)
∂t
e
e
e
i
i
i
me ni
e ni
ne e 1 +m∂tm
E
+
v
+
v ×B −
e
mi ne i
i ne
em∂j
= −∇ ·!(Pe + P"
) +=
(n∇
ne )e eE
+nj) ×
· (P
+"P
+ B + R2 + R3
i!−
ei ∂t
∂(nV
me
me
n Vn )
∂(n
n n)
1
+
R
+
1
+
R
+
m
1
3
n
ne e (E m
+i ve × B) − R1m+i R3 + mn ∂t∂t
Ion + ele Fluid j × B ∼ −R3 = mi νin ni (vi − vn )
Generalized Ohm’s law
∂
(m n v + mi ni vi + mn nn vn )
Generalized Ohm’s ∂tlaw emee ∂je
= ∇)·m
(P(n
Pnni))−
+ vn+) j × B
e+
× eB+∼
−R
eP∂t
= −∇ ·j(P
inin−
i (v
i + 3P=
n +i ν
e eE
n Vn )
×−B)
R1v+
R3(v+i −
mnv∂(n
vnee e×(E
B+
= v[v
(v−
×B
en
n−
i) −
e )]∂t
j
= vn × B + mnj×B
×
B
−
×B
nn νni
ne e
ve × B = [vn − (vn − vi ) − (vi − ve )] × B
BB∼+−R3j×B
= m×
i νin
i (vji −×vB
n)
= jv××
Bn−
n
mn nn νni
ne e
ρ = eAmbipolar
(ni − ne ) ∼ 0 Hall
j = e (ni vi − ne ve )
me
n +n
(
(
(
(
me ∂j
= ∇ · Pe + ne e (E + ve × B) − R1
me ∂j
e ∂t
= ∇ · Pe + ne e (E + ve × B) − R1
e ∂t = ∇ · Pe + ne e (E + v × B) − j × B − R1
= ∇ · Pe + ne e (E + v × B) − j × B − R1
Intui>ve Understanding of Ambipolar term
Ion Fluid
R1
R2
∂
1
ne e
(n
v
)
=
−
∇
·
P
−
(E
+
v
×
B)
+
+
e
e
e
e
∂t ∂
me 1
mene e
meR1 meR2
(n
v
)
=
−
∇
·
P
−
(E
+
v
×
B)
+
+ me
e
e
e
e
∂t
me
me
me
Electron ni e
R1
R3
∂ Fluid
1
(n
v
)
=
−
∇
·
P
+
(E
+
v
×
B)
−
+
i
i
i
i
∂t ∂
mi 1
mini e
miR1 miR3
∂t
(ni vi ) = − mi ∇ · Pi +
mi
(E + vi × B) −
mi
+
mi
R2
R3
∂
1
(n
v
)
=
−
∇
·
P
−
−
n
n
n
∂t ∂ mn 1
mnR2 mnR3
(n
v
)
=
−
∇
·
P
−
− mn
n
n
n
∂t
mn
mn
Loretz force (ele)
Loretz force (ion)
R1 = −me ne νei (ve − vi ) = mi ni νie (vi − ve )
1 = −me ne νei (ve − vi ) = mi ni νie (vi −
ve ) neutral
VeR
Vi
e-‐
B
(
p+
R2 = −me ne νen (ve − vn ) = mn nn νne (vn − ve )
R2 = −me ne νen (ve − vn ) = mn nn νne (vn − ve )
J
neutral drag
(
Vn
(
電離・再結合の影響
Vishniac & Lazarian (1997) 電離・再結合のタイムスケールが(アルフベン
タイムに対して)十分小さいとき、電離・再結合
過程がリコネクションを速める Sweet-‐Parker current sheet
拡散領
域
Leake et al. 2012 電離・再結合の影響
Vishniac & Lazarian (1997) 電離・再結合のタイムスケールが(アルフベン
タイムに対して)十分小さいとき、電離・再結合
過程がリコネクションを速める電離再結合 current sheet
再結
合
拡散領域でプラズマが再結合 => 中性流体として逃げていく
Leake et al. 2012 電流シートの時間発展
電流
電離度 ξn = nn/(nn + np)
プラズモイド形成時のドリフト
電流
橙矢印:プラズマ速度青矢印:中性粒子速度
プラズモイド形成領域で中性粒
子が逃げるリコネクションの観測可能性 -‐ドリフト-‐
中性流体とプラズマはローレンツ力が働くとドリフトする（Sweet-‐Parker リコネクションのinﬂow 領域) 直接中性流体とプラズマの速度差を測定可能か? ドリフト速度 Vd=JxB/acρnρp　〜　VA2/νnpχpΔ 彩層　νnp〜 103 s-‐1, χp〜0.1 (VA,Δ)=(5x10 km/s, 100km) à 0.2 km/s =(5x10 km/s, 10km) à 2 km/s プラズモイド合体と放出
形成されたプラズモイド
は合体電流
電離度 ξn = nn/(nn + np)
プラズモイド合体と放出
電流
電離度 ξn = nn/(nn + np)
大プラズモイド放出後さらに小さなプラズモイド
ができる大プラズモイドと
ともに低電離プラズマ
も放出リコネクションの観測可能性2 -‐電離非平衡-‐ の
領域では電離度が
Dynamics　>me scale < I R – >me 熱平衡のものからずれる =>荷電粒子(CaII,MgII..)と中性粒子(H)を同じくらいの高
さで観測すればリコネクションポイント(電流シート、プラ
ズモイド)の電離度が周辺と違う？再結合時間　水素(~ 10-‐100 s) とするなら必要な時間スケールは1-‐10s 空間スケールは10~100km (VA=10km/s)の場合 Birn+ 2001
動機
分散性アルベン波
• どうしてMHDモデルでは運動論モデルに対し
てリコネクション率が低くなるのか??
• ホイッスラーが鍵? (Rogers+ 2001)
– Vphase∝k1のため、セパラトリックスが傾いて（開い
てい）S-PからPetscheck的になる
– これが正しいとしたら、MHDシミュレーションの解
像度を上げるだけでは収束しない?
弱電離プラズマのアルベン波
中性が応答できない周波数アルベン速度増大イオン-‐中性衝突周期 0.01-‐0.001sec?
まとめ
•  彩層は非常にパラメータレンジの大きくプラズ
マは部分電離プラズマである •  部分電離効果(ambipolar diﬀusion)により、電
流シートはプラズモイド不安定性を起こしうる
程度まで薄くなる •  彩層でのパラメータ(イオン-‐中性粒子ドリフト
速度, 電離度, 3成分磁場など)を直接観測す
ることで部分電離プラズマにおける磁気リコ
ネクションの特徴をとらえられる可能性がある

Download Report