Transcript DIAMAGNETIC STABILIZATION OF COLLISIONLESS MAGNETIC

The Structure of Thin Current
Sheets Associated with
Reconnection X-lines
Marc Swisdak
The Second Workshop on Thin Current Sheets
April 20, 2004
Collaborators
• J. Drake
• M. Shay
U. of Maryland
• J. McIlhargey
UMBC
• B. Rogers
Dartmouth College
• A. Zeiler
MPP-Garching
z
y
Simulation:
x
Bguide
J
Breconn
Reconnecting field: x
Inflow velocity:
y
Guide field/Current: z
p3d Details
• Relativistic PIC code
• Boris algorithm for particles
• Trapezoidal leapfrog for fields
• Multigrid for Poisson’s equation
• MPI parallelization
• Biggest runs:
• 512x256x256
• 2048 processors
• ~109 particles
• How we cheat:
• me/mi large
• c/cA small
• Also:
• Double Harris sheet
• Periodic BCs
The Point
Q: At what strength does the guide
field become important?
A: Bg  0.1 B0
No Guide Field: Overview
y
Box size: 6.4  6.4 di
c / cA  20
Guide field: 0 B0
mi / me  100
Grid: 1024 1024
Ti / Te  10
Background Density: 0.2n0
x
Jz
y
2D Simulation
Development of Bifurcation
Jz
Total time: 4.5 ci1
y
x
Temperature
Txx
Tyy
y
y
x
x
Tzz
y
x
y
Velocity Distributions
vy
vz
@ x-line:
Beams are due
to Speiser
figure-8 orbits
@ bifurcation:
Multiple peaks
from two
beams
Balancing the Reconnection Electric
Field
1
Ez   (vex By  vey Bx )
c
1 Pe , xz Pe , yz
 (

)
ne z
z
me vez
vez
vez
 (
 vex
 vey
)
e t
x
y
Ideal MHD
Pressure tensor
Electron Inertia
Balancing the Reconnection Electric Field
1
 (vex By  vey Bx )
c
1 Pe, xz Pe, yz
 (

)
ne z
z
*  Ez
me vez

e t

me
v
v
(vex ez  vey ez )
e
x
y
Guide Field: Bg=1B0
y
• Current sheet not bifurcated
• Electrons magnetized at
the x-line
• Canted separtrices
J z • E|| interacting with Bg
x
y
Temperature, Bg=1
T
T
vy
Balancing the Reconnection Electric Field
1
 (vex By  vey Bx )
c
1 Pe, xz Pe, yz
 (

)
ne z
z
*  Ez
me vez

e t

me
v
v
(vex ez  vey ez )
e
x
y
Guide Field Criterion
• What is the minimum Bg so that the eexcursions are less than de?
0.1c A
di
c Ae
de
cA
Reconnection Rate:
 cEz
v ExB

~ 0.1
t cA B0
cA
0.1cAe
0.1v Ae
vin
c
L 


ce ce ( Bg / B0 )  pe
 Bg  0.1B0
X-line Structure: Bg = 0, 0.2, 1
Temperature, Bg=0.2
T
T
vy
Off-Diagonal Pressure Tensor, Pyz
X-line Distribution Functions
Ions
Bg  0
Bg  0.2
Bg  1
vz
Why is this important? Development of x-line turbulence.
Why does it happen? Bg means longer acceleration times.
Conclusions
• Bg ~ 0.1B0 is enough to influence the
structure of x-lines.
– Affects: Flow geometries, separatrices, particle
orbits (temperatures), particle energization,
development of turbulence (?)
– Doesn’t affect: Reconnection rate, breaking of
frozen-in condition
• Implication: Anti-parallel reconnection is
rare in real systems. Most reconnection is
component reconnection
Cut Through the X-line
Tyy
Txx
Tzz
Reconnection Rate & Guide Field
Reconnected Flux
Bg  0
Bg  1
Time
Why the difference?
Anti-parallel reconnection
Within the diffusion region
electrons are unmagnetized
& execute wandering orbits.
Tinit
Tfinal
Electrons are always
magnetized and are not
heated.
Guide field reconnection
1
 (vex By  vey Bx )
c
1 Pe, xz Pe, yz
 (

)
ne z
z
me vez
vez
vez
 (
 vex
 vey
)
e t
x
y
Ez
Generalized Ohm’s Law
What terms does MHD neglect?
vi
me d v e
1
1
E    B  J +
J  B   Pe 
c
nec
ne
e dt
Ideal MHD
Hall term
Resistive MHD
Electron Inertia
Pressure tensor
The final three terms become important at different scales:
di  c/pi
s, bedi
de
y
3D Reconnection with Guide Field
Jz
Jz
z
vez
z
Ez
y
x
Box size: 4  2 1 di
c / cA  20
Guide field: 5B0
mi / me  100
Number of Particles: O(109 )
Buneman Instability
• Electron-ion two-stream instability. If the
distribution functions do not (roughly) overlap
then the system is unstable.
~J
Electrons
Ions
k  pe /vd
 
(me / mi )1/3 pe
3D Reconnection w/o Guide Field
early
• Initial turbulence
(LHDI) disappears as
reconnection
strengthens.
• X-line shows no sign
of instability at late
times.
Jz
late
vez
Temperature
Txx
Tyy
y
y
x
x
Tzz
y
x
y
Temperature, Bg=0.2
T
T
Temperature, Bg=1
T
T
vy
Dissipation mechanism
• What balances Ep during guide field reconnection?
• Scaling with electron Larmor scale suggests the nongyrotropic pressure can balance Ep (Hesse, et al, 2002).
4 dJz
1
1
 E z  (v e  B) z  (  pe ) z
2
 pe dt
c
ne
Bz=0
Bz=1.0

y
y
Transition from anti-parallel to guide field
reconnection
Bz0=0
Bz0=0.1
Bz0=1.0
• Structure of non-gyrotropic part of the pressure
tensor, Pyz
– Remove gyrotropic portion
– Significant changes for Bz0=0.1