SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.
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Transcript of SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.
![Page 1: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/1.jpg)
SECTP LANL GSFC UMD
The Collisionless Diffusion Region:The Collisionless Diffusion Region:An IntroductionAn Introduction
Michael Hesse
NASA GSFC
![Page 2: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/2.jpg)
SECTP LANL GSFC UMD
Overview:
Diffusion region basics
The (electron) diffusion region for anti-parallel reconnection
The (electron) diffusion region for guide-field reconnection
An avenue toward fast MHD reconnection without Hall terms
Acknowledgements: J. Birn, M. Kuznetsova, K. Schindler,M. Hoshino, J. Drake
![Page 3: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/3.jpg)
SECTP LANL GSFC UMD
Magnetic Reconnection: Dissipation Mechanism(How does it work?)
time
DR
DR
DR
Conditions:IMPOSSIBLE (for species s) if
E
v s
B 0
![Page 4: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/4.jpg)
SECTP LANL GSFC UMD
Electric Field Equations
E
v e
B
1
nee
�P e
me
e
v et
v e
v e
v i
B 1
nee
j
B 1
nee
�P e
me
e
v et
v e
v e
ye
yeyyyzxy
ey vv
t
v
e
m
y
P
z
P
x
P
enE
1
Electron eqn. of motion
At reconnection site
small, limited by me?important?
x
z
![Page 5: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/5.jpg)
SECTP LANL GSFC UMD
Results for anti-parallel reconnection:
Brief review
![Page 6: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/6.jpg)
SECTP LANL GSFC UMD
Magnetic field and ion-electron flow velocities
P. Pritchett
M. Hoshino
![Page 7: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/7.jpg)
SECTP LANL GSFC UMD
F Bz
X
0
(x, z 0)dx
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 5 10 15 20 25 30 35 40
normal magnetic flux
mi/me = 9mi/me = 25mi/me = 64mi/me = 100
i t
evolution electron-mass independent!
Normal Magnetic Flux:
=> Local electron physics adjusts to permit large scale evolution
![Page 8: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/8.jpg)
SECTP LANL GSFC UMD
mi/me=9, i t = 18
mi/me=100, i t = 16
Compare extremes along dashed lines
- ion quantities- electron quantities
![Page 9: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/9.jpg)
SECTP LANL GSFC UMD
-> Ion scale features approx invariant.
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0 5 10 15 20 25
Bz magnetic field
Bz(9)Bz(100)
shifted x
-1.0 100
-5.0 10 -1
0.0 100
5.0 10-1
1.0 100
0 5 10 15 20 25
ion v x
vix(9)vix(100)
shifted x
Large (ion) Scale Features
![Page 10: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/10.jpg)
SECTP LANL GSFC UMD
Small (electron) Scale Features
-6.0 100
-4.0 100
-2.0 100
0.0 100
2.0 100
4.0 100
6.0 100
0 5 10 15 20 25
electron v x
vex(9)vex(100)
vex(
9)
shifted x
![Page 11: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/11.jpg)
SECTP LANL GSFC UMD
-6.0 10 -2
-4.0 10 -2
-2.0 10 -2
0.0 100
2.0 10-2
4.0 10-2
6.0 10-2
0 5 10 15 20 25
Pxye
pxye(9)pxye(100)
shifted x
Pressure Tensor
x
vpP x
zxy
~
![Page 12: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/12.jpg)
SECTP LANL GSFC UMD
xyeP
yzeP
![Page 13: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/13.jpg)
SECTP LANL GSFC UMD
10.0<x< 11.0 -0.5<z< 0.5
0.076
-0.739
-1.555
-2.370
-3.185
-4.000
log f
-0.4
0.2
0.0
0.4
-0.2
uy
-0.4 -0.2 0.0 0.2 0.4ux
Sample Electron Distribution (Pxye)
Thermal inertia (nongyrotropic pressure)-based dissipationseems key to anti-parallel reconnection
![Page 14: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/14.jpg)
SECTP LANL GSFC UMD
4/1
22 )/(
2
zBe
Tm
x
eez
E 2meTe vx'
[Biskamp and Schindler, 1971]
Can be explained by trapping scale:
=> Estimate of reconnection electric field
[Hesse et al., 1999][Kuznetsova et al., 2000]
“bounce motion” [Horiuchi and Sato, 1996]
![Page 15: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/15.jpg)
SECTP LANL GSFC UMD
realistic electron massRicci et al.
3D – no LHD, kink, …Zeiler et al.
![Page 16: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/16.jpg)
SECTP LANL GSFC UMD
But, some questions remain…
Sausage mode,Buechner et al.
Kink, LHD,Ozaki et al. Ion sound mode…
![Page 17: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/17.jpg)
SECTP LANL GSFC UMD
…and other limitations, such as
-Finite (small) system size-Finite (small) ion/electron mass ratio-Finite (small) speed of light-Periodicity
…there is work to be done!
![Page 18: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/18.jpg)
SECTP LANL GSFC UMD
What changes in the presence of guide field?
if guide field strong enoughelectrons are magnetizedno bounce orbitsno nongyrotropic pressures(?)bulk inertia dominant(?)
Method: Theory and PIC simulations
![Page 19: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/19.jpg)
SECTP LANL GSFC UMD
Simulation Setup
- 1-D “Harris” Equilibrium, Lx= 2Lz= 25.6 c/pi
- Flux function: A = -ln cosh(z/) - normal magnetic field perturbation (X type, 2.5% of lobe field) - 0, 40, 80% guide field - Sheet Full-Width = c/pi
- Ti/Te = 5
- mi/me=256
- 100x106 particles - 800x800 grid
Results averaged over 60 plasma periods
![Page 20: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/20.jpg)
SECTP LANL GSFC UMD
![Page 21: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/21.jpg)
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By
P. Pritchett
Change of symmetry
![Page 22: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/22.jpg)
SECTP LANL GSFC UMD
Parallel electric field it=16
…also analytic theory by Drake et al.
![Page 23: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/23.jpg)
SECTP LANL GSFC UMD
Electric Field Equations
E
v e
B
1
nee
�P e
me
e
v et
v e
v e
v i
B 1
nee
j
B 1
nee
�P e
me
e
v et
v e
v e
ye
yeyyyzxy
ey vv
t
v
e
m
y
P
z
P
x
P
enEE
1
ll
Electron eqn. of motion
At reconnection site
small, limited by me?important?
x
z
![Page 24: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/24.jpg)
SECTP LANL GSFC UMD
Magnitude of Bulk Acceleration Contribution
Time derivative of (negative) electron velocity in y direction:
-3
-2
-1
0
1
2
0
5
10
15
0 5 10 15 20 25 30
d/dt vey_max vey_max
time
![Page 25: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/25.jpg)
SECTP LANL GSFC UMD
Pxye
Pyze
![Page 26: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/26.jpg)
SECTP LANL GSFC UMD
-(vezBx-vexBz)
-me(ve.grad vey)/e
z
P
x
P
enyzexye
e
1
![Page 27: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/27.jpg)
SECTP LANL GSFC UMD
Electron Distribution Functions
F(vx,vy) F(vx,vz) F(vy,vz)
vx
vy
vx
vz
vy
vz
![Page 28: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/28.jpg)
SECTP LANL GSFC UMD
..pressure tensor nearly(?) gyrotropic
BBB
pppeg
engege
2
||
1P
PPP
But:0|
2
||
2
||
yyyeg BB
B
pp
B
ppBB
P
if Bx, Bz=0
-> nongyrotropy important. How to estimate?
![Page 29: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/29.jpg)
SECTP LANL GSFC UMD
QPPPPPP
T
eee
Teeeeee
e BBm
evvv
t
Scaling the pressure tensor evolution equation
P
L
vP Pe
L
Q
Assume
ijii
e
PP
vL
/,1
ignore heat flux…
![Page 30: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/30.jpg)
SECTP LANL GSFC UMD
y
xzzeyye
ey
e
zzexye B
BPP
z
vPP
y
zxxeyye
ey
e
xxeyze B
BPP
x
vPP
Hesse, Kuznetsova, Hoshino, 2001
Pressure tensor approximations
![Page 31: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/31.jpg)
SECTP LANL GSFC UMD
Electron Pressure Tensors
from simulation approximation
Pxye Pxye
Pyze Pyze
critical difference at reconnection site!
![Page 32: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/32.jpg)
SECTP LANL GSFC UMD
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0.004
-0.4 -0.2 0 0.2 0.4
Pyze
at x=13.15, t=16
z coll. skin depth
![Page 33: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/33.jpg)
SECTP LANL GSFC UMD
z
Q
B
BPP
x
vP
z
Q
x
Q
B
BPP
x
vPP
xyze
ey
zxxeyye
ey
e
xxe
xyzexxye
ey
zxxeyye
ey
e
xxeyze
1
1
QxxyeQxyze
Pyza approximation
![Page 34: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/34.jpg)
SECTP LANL GSFC UMD
ss fudm ))()((3 vuvuvuQ�
0
][
][
][
)(
rsisjkrrjks
rsjsikrriks
rsksijrrijs
srs
s
jl
likl
il
ljkl
kl
lijl
lijkkijlkjiljiklijklll
ijk
BQBQ
BQBQ
BQBQ
m
e
vx
Qvx
Qvx
Q
vQvvPvvPvvPx
Qt
Heat Flux Tensor Time Evolution
lots of work
![Page 35: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/35.jpg)
SECTP LANL GSFC UMD
022
)2(
xxxzzxxxyxyzzxyye
yl
lxxl
xl
lyxl
xl
lxyl
lxyxxxylyxxlll
BQBQBQBQm
e
vx
Qvx
Qvx
Q
vQvvPvvPx
22 5.05.0
1xyzyxxzxxyyxxx
yxyz vPvvP
zvPvvP
xQ
x
vvPvvP
xQ x
y
yxxyxxx
yxyz
)(
1
Approximations for Qxyze
neglect ;0t
Assume near gyrotropy, By>>Bx, Bz
Leading order, Pii>>Pjk
x,y,x component:
![Page 36: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/36.jpg)
SECTP LANL GSFC UMD
-0.008
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0.008
-0.4 -0.2 0 0.2 0.4
Q xyze and approximation, x=13.15
Q xyze
Q xyze approximation
z
Approximations for Qxyze
From simulation:
Approximation:
Ok in center, differencedue to 4-tensor?
![Page 37: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/37.jpg)
SECTP LANL GSFC UMD
21
2
2
21
2
2
020
02
1
1||
11~|~|
L
cE
L
cvB
ne
mvB
Lx
vv
e
mE
pe
convection
pe
ze
ezyz
einertial
x
vvP
zB
BPP
x
vPP x
y
yxx
ey
zxxeyye
ey
e
xxeyze
1
22
2
222
2
2
2
2
||11
|~|
11~
11|~|
L
rE
mn
P
LE
z
vvP
zenx
vvP
zenE
Linertial
eey
xxinertial
z
y
yxx
ee
x
y
yxx
eepressure
Scaling of diffusion region
=> 2 Scale lengths: Collisionless skin depthElectron Larmor radius in guide field
![Page 38: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/38.jpg)
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Physical Mechanism:
Larmor orbit interacts with “anti-parallel” B components
![Page 39: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/39.jpg)
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3D Modeling
M. Scholer et al.: Formation of“2D” channel
J. Drake et al.: Buneman modes,electron holes, anomalous resistivity
![Page 40: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/40.jpg)
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P. Pritchett: inertia important
![Page 41: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/41.jpg)
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…and other limitations, such as
-Finite (small) system size-Finite (small) ion/electron mass ratio-Finite (small) speed of light-Periodicity
…there is work to be done!
![Page 42: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/42.jpg)
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Results from GEM reconnection challenge:
•Hall effect (dispersive waves) speeds up reconnection rate
•Reconnection rate otherwise independent on model
•MHD models with simple resistivity show only slow reconnection rates
Question:
Are Hall effects the only way to include fast reconnection in MHDmodels?
![Page 43: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/43.jpg)
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Approach:
•Hall effect result of ion-electron scale separation
•Eliminate scale separation by- Choosing equal ion and electron mass- Choosing equal ion and electron temperatures
•Simple and cheap…, includes ion and “electron” kinetic physics
•“Small” GEM runs with and without guide field
•“Large” runs, with and without guide field
![Page 44: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/44.jpg)
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GEM-size run, no By
![Page 45: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/45.jpg)
SECTP LANL GSFC UMD
0
0.02
0.04
0.06
0.08
0.1
0.12
0
0.4
0.8
1.2
1.6
2
2.4
0 5 10 15 20 25 30
small, no By
reconnection E recflux
time
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
mi/me=256
rec. E
recflux/0.0
time
GEM-size run, no By
me=1 me=1/256
![Page 46: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/46.jpg)
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GEM-size run, By=0.8
![Page 47: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/47.jpg)
SECTP LANL GSFC UMD
GEM-size run, By=0.8
0
0.05
0.1
0.15
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
typical
d flux/dt
recflux
time
0
0.05
0.1
0.15
0.2
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25 30
typical
rec. E recflux
time
me=1 me=1/256
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SECTP LANL GSFC UMD
large run, By=0.
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SECTP LANL GSFC UMD
large run, By=0.8
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SECTP LANL GSFC UMD
large run, By=0.
0
0.05
0.1
0.15
0.2
2
3
4
5
6
7
8
9
10
0 10 20 30 40 50 60
typical
rec. E recflux
time
2
3
4
5
6
7
8
9
10
0
0.05
0.1
0.15
0.2
0 10 20 30 40 50 60
typical
recflux reconnection E
time
large run, By=0.8
Reconnection rates similar to GEM problem
![Page 51: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/51.jpg)
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initial By=0.8 initial By=0.
By, both large runs, t=40
no quadrupole or quadrupolar modulation!
![Page 52: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/52.jpg)
SECTP LANL GSFC UMD
large run, By=0., t=40
Pxye
Pyze
vix
jiy
![Page 53: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/53.jpg)
SECTP LANL GSFC UMD
large run, By=0.8, t=40
Pxye
Pyze
vix
jiy
![Page 54: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/54.jpg)
SECTP LANL GSFC UMD
Electric Field Equations
E
v e
B
1
nee
�P e
me
e
v et
v e
v e
v i
B 1
nee
j
B 1
nee
�P e
me
e
v et
v e
v e
Electron eqn. of motion
x
z
Approximate representation in MHD:
ii
i Pen
BvE�
1
![Page 55: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/55.jpg)
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Additional slides
![Page 56: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/56.jpg)
SECTP LANL GSFC UMD
Pxye Pyze
jyi jye By
A tour of the reconnection region…
![Page 57: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/57.jpg)
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Mass Dependence of Electron Diffusion Region:Simulation Setup
- 1-D “Harris” Equilibrium, Lx= 2Lz= 25.6 c/pi
- Flux function: A = -ln cosh(z/) - normal magnetic field perturbation (X type, 5% of lobe field) - Sheet Full-Width = c/pi
- Te/Ti = 0.2 - me/mi=1/9-1/100
- pe/ce=5
- 50x106 particles - 800x400 grid
![Page 58: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/58.jpg)
SECTP LANL GSFC UMD
0
0.5
1
1.5
2
2.5
3
0
0.05
0.1
0.15
-5 0 5 10 15 20 25 30 35
typical
recflux d flux/dt
time
mi=me, By=1
rate slightly reduced due to higher plasma mass
![Page 59: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/59.jpg)
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Additional Material
![Page 60: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/60.jpg)
SECTP LANL GSFC UMD
Pyze
18.028
25.0
35.0
1~
1|
1
E
E
z
P
enenE yz
eye
ey P
Magnitude of Pressure Tensor Contribution
ne
![Page 61: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/61.jpg)
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Particle Picture: Straight Acceleration and Thermalization
Question: Are electrons transiently accelerated while crossingthe diffusion region, or is some of the energy thermalized?
Approach: Integrate 104 electron orbits in vicinity of reconnection region
Relevance: straight acceleration ->
thermalization ->e
e
eyee
en
ve
m
P
v
1
![Page 62: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/62.jpg)
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-0.5
0
0.5
1
1.5
2
-12 -10 -8 -6 -4 -2 0 2
kinetic energy change as function of delta y
delta Ek
y = -2.5605e-05 - 0.17785x R= 0.98882
delta y
-0.5
0
0.5
1
1.5
2
-12 -10 -8 -6 -4 -2 0 2
delta y-component of kinetic energy vs. delta y
delta Eyk
y = -0.027939 - 0.16877x R= 0.9873
delta y
yE
yE
ykin
kin
67.1
78.1
,
Approximately 6% of energyis thermalized
y
kin
Ee
Ey
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SECTP LANL GSFC UMD
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
13.15 13.2 13.25 13.3 13.35 13.4 13.45
orbit( 6293): x-z plane
x
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.05
0.1
0.15
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
orbit( 6293): Ekin y and x-z
Ekin_y
Ekin_xz
time
x-z energization
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
13.15 13.2 13.25 13.3 13.35 13.4 13.45
orbit( 6293): z-x acceleration phase
z
x
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Contours of Poloidal Magnetic Field
Scale length related to electron Larmor radius
![Page 65: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/65.jpg)
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Vmax= 0.65
Vmax= 2.8
![Page 66: SECTPLANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649d415503460f94a1b561/html5/thumbnails/66.jpg)
SECTP LANL GSFC UMD
Scaling the pressure tensor evolution equation
0T
eee
Teeeeee BB
m
evvv
PPPPP
zxy
,
0
yzyxxyyzxzx
xzyzxxxyxxxyyzxzyxxxxye
PPPP
vPvPvPvPvPPv
xy component
near reconnection site:
ijii
zxy
PP
BBB
,
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SECTP LANL GSFC UMD
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30
magnetic flux normal to current sheet
recflux/0.0recflux/0.4recflux/0.8
time
Reconnection faster for smaller guide fields