1. The Physics of the Collisionless Diffusion Region
Michael Hesse
NASA GSFC

2. Diffusion region basics – focus on component merging
Overview:
Diffusion region basics – focus on component merging
Thermal- or bulk inertia-based diffusion?
Scaling of the electron diffusion region
Particle orbit analysis
Acknowledgements: J. Birn, M. Kuznetsova, K. Schindler,
M. Hoshino, J. Drake

3. Simulation Setup - 1-D “Harris” Equilibrium, Lx= 2Lz= 25.6 c/wpi
- Flux function: A = -ln cosh(z/a)
- normal magnetic field perturbation (X type, 2.5% of lobe field)
- 80% guide field
- Sheet Full-Width a= c/wpi
- we/We=2
- Ti/Te = 5
- mi/me=256
- 100x106 particles
- 800x800 grid
Results averaged over 60 plasma periods

4. x z

5. Change of symmetry By
P. Pritchett

6. Electric Field Equations
Electron eqn. of motion
At reconnection site
important?
small, limited by me?

7. Magnitude of Bulk Acceleration Contribution
Time derivative of (negative) electron velocity in y direction:

8. Pxye
Pyze

9. -(vezBx-vexBz)
-me(ve.grad vey)/e

10. Scaling the pressure tensor evolution equation
Assume
ignore heat flux…

11. Pressure tensor approximations
Hesse, Kuznetsova, Hoshino, 2001

12. Electron Pressure Tensors
approximation
from simulation
Pxye
Pxye
Pyze
Pyze
critical difference at reconnection site – need to include Q!

13. Qxyze
Qxxye

14. Div Q|xy
Pyza approximation

15. Approximations for Qxyze
x,y,x component:
Assume near gyrotropy, By>>Bx, Bz
Leading order, Pii>>Pjk

16. Approximations for Qxyze
From simulation:
Approximation:
Ok in center, difference
due to 4-tensor?

17. Scaling of diffusion region
=> 2 Scale lengths: Collisionless skin depth
Electron Larmor radius in guide field

18. coll. skin depth

19. Physical Mechanism:
Larmor orbit interacts with “anti-parallel” B components

20. Straight Acceleration and Thermalization
Particle Picture:
Straight Acceleration and Thermalization
Question: Are electrons transiently accelerated while crossing
the diffusion region, or is some of the energy thermalized?
Relevance: straight acceleration ->
thermalization ->
Approach: Integrate 104 electron orbits in vicinity of reconnection region

21. Parallel electric field Wit=16

22. Idea:
If Ey approximately constant, then, for each particle (electron):
If there is no scattering, then all additional energy is deposited into:
Approach:
Plot total and “y” kinetic energy change vs. y-displacement for
ensemble of electrons in diffusion region

23. Approximately 6% of energy is thermalized
-0.5
0.5 1
1.5 2
-12
-10 -8 -6 -4 -2
kinetic energy change as function of delta y
delta Ek
y = e x R=
delta y
-0.5
0.5 1
1.5 2
-12
-10 -8 -6 -4 -2
delta y-component of kinetic energy vs. delta y
delta Eyk
y = x R=
delta y
Approximately 6% of energy
is thermalized

24. orbit( 6293): z-x acceleration phase
-0.08
-0.06
-0.04
-0.02
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
-0.08
-0.06
-0.04
-0.02
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

25. Orbit of “typical electron” in poloidal magnetic field
Scale length: electron Larmor radius

26. 3D Modeling M. Scholer et al.: Formation of “2D” channel
J. Drake et al.: Buneman modes,
electron holes, anomalous resistivity

27. P. Pritchett: inertia important

28. …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!

29. Additional slides

30. Electron Distribution Functions
F(vx,vy)
F(vx,vz)
F(vy,vz) vx vy vz

31. ..pressure tensor nearly(?) gyrotropic
But:
if Bx, Bz=0
-> nongyrotropy important. How to estimate?