Particle Simulations of Magnetic Reconnection with Open Boundary Conditions

A. V. Divin1,2, M. I. Sitnov1, M. Swisdak3, and J. F. Drake1

1Institute for Research in Electronics and Applied Physics, University of Maryland

2Saint-Petersburg State University, Russia3Naval Research Laboratory

Fall AGU Meeting December 13, 2006Fall AGU Meeting December 13, 2006

Acknowledgements

P. PritchettP. Pritchett

W. Daughton W. Daughton

D. SwiftD. Swift

Motivation

• Until recently simulations of magnetic reconnection were largely performed using a combination of periodic and conducting boundary conditions.

• Recent results, including [Daughton et al., 2006], reveal interesting new effects that appear in case of the so-called ‘open’ boundary conditions.

• We adjust the code P3D [Zeiler et al., 2002] to explore the effects of different open boundary conditions.

Simulations of reconnection: New aspect

?

Distant neutral line Reconnection onset (NENL)

Earth’s magnetotail

• Another new aspect of our studies is shifting the focus of interest from the central X-line vicinity to outflow regions, which resemble the tail of the magnetosphere.

P3D: Simulations of reconnection with conducting/periodic BC

Box size: (lx/d,lz/d)=(19.2x19.2), d= c/pi, mi /me=64, Ti/Te=3/2, c/vA=15, L=0.5oi,

Initial GEM-type perturbation: 0 0, cos / cos / , 0.3x zx z x l z l

Out-of-plane current Jy

density is color-coded

Z

X

Y

Conducting BC

Conducting BC

Per

iodi

c B

C

Per

iodi

c B

C

Construction of open boundaries: particles

, ,0, 0e i e in

x x

v

0T T t

New particles are injected with the shifted Maxwellian distribution, whose parameters are chosen to preserve first two moments of the distribution function

Temperature [e.g., Pritchett, 2001]

Construction of open boundaries: fields

,0, 0, 0, 0,y yxx z

B EBE

x x x

zB 0

Pritchett [1998, 2001]:

Daughton et al., [2006]:

Horiuchi et al. [2001]:

2nd order radiation (non-PML) BCs [Lindman, 1975; Engquist and Majda, 1977; Higdon, 1986; Renaut, 1992]: similar to 1st order radiation conditions in [Daughton et al., 2006], but often result in numerical instabilities.

Open field BC used in this work (x-boundary):

( Radiation BC) (Pritchett BC)

or

+

/ 1/ / 0zx c t B

2yx z

2

EE E0, 0, 0

x x x

z zB 0, E 0 yE 0, flux flow

/ 1/ / 0zx c t B

1st order radiation BC for light waves

Simulations of reconnection with open boundary conditions: Radiation BC / 1/ / 0zx c t B

0it=6

0it=8

0it=7

0it=12

Simulations of reconnection with open boundary conditions: Pritchett BC zB 0

0it=6 0it=7

0it=8 0it=12

Evidence of the ion tearing instability

Schindler [1974]: In the presence of the finite Bz the electron tearing instability can be replaced by the ion tearing, which is even faster:

1/ 4

3i i i

e e e

mT

m T

Electron tearing (0=0, periodic BC)

Ion tearing (0=0.3, open BC)

Ion tearing develops 3 times faster

Ion tearing (0=0.3, open BC)

Electric field evolution

Electron tearing (0=0, periodic BC)

Ion tearing develops spontaneously

ion tearing Ey

global Ey

electron tearing Ey

0 t 10 0 10 t 20 30

What causes the destabilization?According to the theory [Sitnov et al., 2002], the stabilizing effect of trapped electrons [Lembege and Pellat, 1982], which appears in the presence of a finite Bz, can be eliminated by passing electrons.

Same field BC with particle reintroductionFully open BC

Particle reintroduction stabilizes ion tearing

More detail on the case with Pritchett BCNormal magnetic field Bz(z=0)

t=0 (white), t=8 (green)

0it=8

Out-of-plane magnetic field By

Out-of-plane Electric field Ey Field-aligned current j||

0it=8 0it=8

The new effect has been detected for different mass ratios: mi/me=25, 64, 128.

However, it disappears with doubling the current sheet thickness: L=0i.

Summary

• Simulations with open BC show some CS stretching beyond Simulations with open BC show some CS stretching beyond electron scales, compared to periodic/conducting BC case.electron scales, compared to periodic/conducting BC case.

• Simulations with open BC reveal the excitation of the ion tearing Simulations with open BC reveal the excitation of the ion tearing instability, predicted by instability, predicted by SchindlerSchindler [1974] as a mechanism of [1974] as a mechanism of magnetospheric substorms.magnetospheric substorms.

• They also confirm the destabilizing effect of passing electrons They also confirm the destabilizing effect of passing electrons [[Sitnov et alSitnov et al., 2002].., 2002].

• A key parameter, which controls the reconnection onset in the tail, is A key parameter, which controls the reconnection onset in the tail, is current sheet thickness.current sheet thickness.

Our main result

THEMIS

MMS