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Effective conductivity of collisionless plasma. Semenov, V. St. Petersburg University, Russia Divin , A. K. U. Leuven, Belgium Thanks to N. Erkaev , I. Kubyshkin , G. Lapenta , S. Markidis , and H. Biernat. Motivation. - PowerPoint PPT Presentation
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Semenov, V.St. Petersburg University, Russia
Divin, A. K. U. Leuven, Belgium
Thanks to N. Erkaev, I. Kubyshkin, G. Lapenta, S. Markidis, and H. Biernat
Effective conductivity of collisionless plasma
Motivation
Magnetic reconnection is one of the most important energy conversion process in various plasmas.
The process is determined by the presence of some sort of diffusivity in plasma, which breaks the magnetic field lines frozen-in constraint.
In collisionless plasma environments the problem of dissipation is not (yet) clear and several mechanisms are proposed (turbulent or laminar)
From global scales to EDR / History
Collisionless plasma: no collisional dissipation, but…
Turbulent: anomalous resistivity, wave-particle interaction
Laminar: electron inertia
dide ?From: [Hesse, 2001]
~10…500 km (magnetotail)
Harris equilibrium, L=0.5di , Ti/Te = 5, localized X-point perturbation
Ay =Ay0 cos(2x/Lx )cos( z/Lz )exp(-(x2+z2)/a2)
Variables are normalized to initial CS parameters: n0, B0, VA, di, etc.
Bz(t=0)=0
Runs reported:
mi/me=1836, c/vA= 274, L= 40dix20di, (1024x512) 2048 p.
mi/me=256, c/vA= 102, Ti/Te = 5, L= 200dix30di (2048x386) 940 p.
mi/me=64, c/vA= 51, Ti/Te = 5, L= 20dix10di (512x256), 32 p.
We use the following magnetotail parameters as a reference (e.g. Pritchett, 2004): B0~20 nT, n0~0.3 cm-3 , Ωci
-1~0.5s, c/pi~400km,vA~800km/s, EA=(vA/c)B0~16mV/m
)/(tanh)( 0 zBzBx 2.01.0,)/(cosh)( 20 ornnznzn bb
Model parameters
Diffusion region: Ohm’s law
yPneE yzz /)/1(
Anisotropy of electron pressure (mostly Peyz) supports Ez near X-point (in agreement with, see e.g. [Kuznetsova, 2000], [Pritchett, 2001])
Center of the EDR, Ey ~ -(1/ne)(dPyz/dz)y
Edges of the EDR, Ey = (ve X B)y
z
vv
x
vv
e
m
z
P
x
P
enBvBv
cE ey
ezey
exeeyzexy
ezexxezy
1)(
1
y
eyzee
eyexe
exy
e
eyz
e
ye
E
zvve
m
xvve
m
x
P
en
z
P
en
Bv
/
/
1
1
][
Generation of Pyz
Vy
Vz
n1 v1z
nacc vy
acc
21
1122
21 d))()((
nn
vnvnm
vffvvm
yze
zye
VVPyz
Vy
Vzn1 v1z
nacc vy
acc
yzee vvnm
Sweet-Parker analysis: Results
2/1
22
2
2
22
)π4(
,π4
e
xAexy
epe
e
nm
BVvv
dc
ne
mc
e
e
Ae
zz
A
y
L
d
V
v
B
B
E
E
0
EDR width: electron inertial length
Outflow velocity vx, electron Alfven
Reconnection rate (Ey/EA) connects all other parameters.
yy Ej xz B
cen
B
cen
1
~
Pressure-tensor based dissipation scales as Bohm diffusion !
Scaling: comparison to simulations (1)
x/di t/tA
mi/me=256
Scaling: comparison to simulations (2)
mi/me=1836
Rescaling
dide
ez
AeeLe L
eB
cVm
3.0~/ LeeLk
Rescaling
The scaling implies that Larmor gyroradius
Simulations reveal that This ratio is introduced into scaling:
Ae
yz
A
y
V
v
B
B
E
E
0
2/1)π4( e
xAexy nm
BVvv
eLe L
3.0~/ LeeLk
AexAey
e
kVvVv
d
,
,
A
y
Ae
zz
e
e
E
E
V
v
B
kB
L
kd
0
Scaling: comparison to simulations (2)
mi/me=1836
mi/me=256 k=0.3Rescaling
mi/me=1836 k=0.3
Rescaling
Summary & Results
1. Magnetic reconnection is investigated by means of PIC simulations.
2. Study of EDR structure is performed and model for the pressure anisotropy is developed.
3. Sweet-Parker-like analysis of the EDR is performed;
4. All typical EDR parameters are recovered, diffusivity scales as Bohm diffusion. Rescaled equations are presented
Vx
=kVAe
VA
e
ee kL
Vy =VAe
0BL
dB
e
ez
de
xB
cen
1
~z
Ey
vy