Amari, T., Luciani, J. F., Aly, J. J., Mikic, Z., and Linker, J. 2003, ApJ, 585, 1073

Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. L. Bounda

ry Motion-Driven Evolution

Amari, T., Luciani, J. F., Aly, J. J., Mikic, Z., and Linker, J.

2003, ApJ, 585, 1073

2003.6.9 Taiyou Zasshkai Shiota

Abstract

They studied 3D MHD simulation of the triggering of CMEs.

1. A twisting velocity field to foot points at the bottom of the box

2. relaxation to numerical force-free state

3. converging motions of foot points of the force-free field

Introduction What is the nature of the triggering of CMEs ?Observations of preeruptive configuration (reviewed b

y Priest & Forbes 2002)1) shear between Ha fibrils and the inversion line2) converging motions toward the inversion lineAnother important feature of CMEs• the presence of a prominence • the ejection of a plasmoidImportant issue Is it necessary to have a twisted flux rope (in equilibrium) pri

or to disruption?or is the twisted flux rope created as a consequence of reconn

ection during the disruption ?

2D Modelizations of the triggering of CMEs

the evolutions are driven by slow motions of foot points

• purely shearing motion with Cartesian (Aly&Amari 1985; Aly 1990; Amari et al. 1996, 1997; etc.) and spherical geometry (Mikic & Linker 1994; Aly 1995)

=> the formation and ejection of plasmoid

• converging motions analytically (Priest & Forbes 1990; Forbes & Priest 1995)

=> catastropic non-equilibrium transition

with resistive simulations (Forbes 1991; Inhester, Birn, & Hesse 1992)

=> plasmoid and impulsive phase

3D Modelizations of the triggering of CMEs

the evolutions of bipolar magnetic configurations are also driven by slow motions of foot points

• shearing motion; twisting components (Amari et al. 1996; Tokman & Bellan 2002; Hagyard 1990)

=> the formation and ejection of plasmoid

• converging motions have not been considered yet

=> to investigate the possible effects of the boundary on a bipolar configuration

The important questions

The questions answered in this paper.• Do the converging motions contribute to the heli

city contents of the magnetic structure?• How long can the field evolve quietly in quasi-st

atic way?• What happens when quiet phase ends, is there pr

oduction of a twisted magnetic flux rope in equilibrium, or is the system subject immediately to a global disruption?

Definition of magnetic energy and helicity

• magnetic energy

• magentic helicity

where, π: potential field

dvBtW 2

8

1)(

dvH )( BABA

The tangential Electric field on S

• from Ohm’s law

• this can be decomposed into irrotational and solenoidal parts

• f(x,y,t), g(x,y,t) are

SzSS Bc vBvzEz )(ˆˆ

zv ˆ gfB SSSz

)(2SzSS Bf v

zv ˆ)]([2 SzSS Bg

Evolution of magnetic energy and helicity

• magnetic energy

• magentic helicity

dvBgdv

z

BftW

S zS

z

4

1)(

dvgBHS z 2

Initial Potential Configuration)0,,,()0,,,( zyxVzyxB

02 V

),( yxz

V

V

MHD equations

The equations are solved by semi-implicit scheme.

Twisting motions

The evolution

The evolution along this phase is almost quasi-static.

Magnetic energy increases monotonically

Magnetic helicity increases monotonically

Magnetic Energy and Helicity

Converging motions

Evolution of tS = 200tA

t = 480tAt = 450tA

Evolution of tS = 200tA

t = 498tA t = 530tA

Three part structure

Evolution of tS = 200tA

Transverse magnetic field at z=0

Evolution of tS = 50tA

Evolution of tS = 400tA

Conclusion

They reported the results of numerical simulations

• A series of initial stable force-free fields B0=B(t0) with |H(t0)|>0 are constructed by deforming a given potential field in two step process (twisting + relaxation)

This evolution is almost quasi-static.

• Imposing motions converging toward the inversion line, then quiet phase is stopped and configuration experiences a transition to a dynamic and strongly dissipative phase, during which reconnection leads to the formation of a twisted flux rope, however not in equilibrium.

Conclusion(cont.)• Their results may be relevant to the problem of the initiatio

n of CMEs,(global disruption may occur in a magnetic structure with nonzero helicity contents), driven by the converging motions.

• Helicity keeps constant value during quasi-static phase, therefore, it neds to have been produced during a prior phase.

• Helical structures associated with prominences ejected as part of the CMEs are sometimes observed. However, it is still open problem whether a rope does exist prior to disruption, thus possibly playing a role in its triggering.