23F03
Multi-Hierarchy Simulation Model for Magnetic Reconnection IV
磁気リコネクション研究のための多階層シミュレーションモデルの開発 IV
Shunsuke Usami1), Hiroaki Ohtani1) 2), Ritoku Horiuchi1) 2) and Mitsue Den3)
宇佐見俊介, 大谷寛明，堀内利得，田 光江
1)

National Institute for Fusion Science, Toki 509-5292, JapanThe Graduate University for Advanced Studies (SOKENDAI), Toki 509-5292, Japan3)
National Institute of Information and Communications Technology, Tokyo, Koganei, 184-8795, Japan2)

核融合科学研究所 〒509-5292 岐阜県土岐市下石町322-6
総合研究大学院大学（総研大） 〒509-5292 岐阜県土岐市下石町322-6
情報通信研究機構 〒184-8795 東京都小金井市貫井北町4-2-1
For magnetic reconnection studies, a multi-hierarchy simulation model which deals with both macroscopic
and microscopic physics self-consistently and simultaneously has been developed. In this paper, ourmulti-hierarchy model is improved based on the dynamical domain conversion method, in which initially
MHD simulation runs, and a part of simulation domain is converted to the PIC domain when someconditions are satisfied. We have successfully demonstrated collisionless driven reconnection with theimproved model.

1. Introduction
Collisionless magnetic reconnection is one of
the fundamental processes in which magnetic
field energy is converted to kinetic energy. It
plays an essential role in the rapid energy releasein laboratory fusion device and astrophysicalplasmas. Furthermore, magnetic reconnection
attracts considerable attention as a typicalmulti-scale phenomenon. When magnetic
reconnection takes place, the global change infield topology and large plasma transport occur,
while electrical resistivity controlled by
microscopic process is necessary in the vicinityof reconnection points. In order to understand its
multi-hierarchy structure completely, we develop
a multi-hierarchy simulation model, which deals
with both microscopic and macroscopic physics
consistently and simultaneously.
2. Multi-Hierarchy Simulation Method
The multi-scale structure of magnetic
reconnection has a special feature that thecharacteristic space-time scales change with
distance from the neutral sheet [1, 2]. Dynamics in
the ion meandering orbit scale near the neutral sheet
is controlled by kinetic physics, while plasma
behaviors far away from the neutral sheet (outsidethe ion skin depth) relax to one-fluid.
Based on the above feature, the domaindecomposition method [3-6] is employed for ourmulti-hierarchy model, in which the domains differ
in algorithm. Figure 1 shows the schematic diagramof the multi-hierarchy simulation box. The
simulation domain is divided into three

Fig.1. Schematic diagram of multi-hierarchy model formagnetic reconnection simulation

domains. The macroscopic domain covers theregion where microscopic kinetic effects play
crucial roles. Since physics in the microscopic
domain is solved by particle-in-cell (PIC) algorithm,
we refer to this domain as “PIC domain”. On theother hand, macroscopic domain treats theperiphery of the PIC domain, and dynamics in thisdomain is expressed by magnetohydrodynamics(MHD) algorithm. Then we call this domain “MHDdomain”. Between the PIC and MHD domains, atechnical interface domain with a finite width is put.
Physics in the interface domain is calculated by
the PIC and MHD algorithms (Therefore notethat MHD condition should be fully satisfied in theinterface domain). Macroscopic physical quantities
in the interface domain Qinterface (magnetic field,fluid velocities, pressure, etc) are obtained by ahand-shake scheme, Qinterface = FQMHD + (1F) QPIC,
where QMHD and QPIC indicate the values of Q
calculated by the MHD and PIC algorithms,respectively. The interconnection function F is afunction of the coordinates.
On the other hand, in order to solve the physics
in the interface domain with the PIC algorithm,
microscopic quantities such individual particle
positions and velocities are needed. Individual
particle velocities in the interface domain are newly
determined so as to satisfy the (shifted) Maxwelliandistribution using the obtained macroscopic
quantities at every PIC time step.
In 2009, we have performed the simulation ofcollisionless driven reconnection with themulti-hierarchy model, namely plasma inflows
come from the MHD domain and drive magnetic
reconnection in the PIC domain [7, 8]. It wasconfirmed that reconnection process found in themulti-hierarchy model is true physics.
3. Improvement of Model: Dynamical Domain
Conversion
In nature, however reconnection points movewith time dynamically and then region which need
to be expressed by kinetic algorithm also move.
Therefore we have been developing improved
model which automatically detects kinetic region
and converts calculation domain (in other word,changes a calculation algorithm from MHD to PICalgorithms) as simulation is running. As the firststep of the dynamical domain conversion method,
we perform the following simulation. Initially,
whole domain is taken to be the MHD domain.
When the certain time passes, a part of MHD
domain is converted to the PIC domain, namely theMHD simulation is switched to the multi-hierarchy
simulation described in Sec. 2.
Let us show a simulation result with the above
model. Figure 2 display magnetic field lines. An
external electric field is applied at the top andbottom boundary of the MHD domain, and thenplasmas are injected inward. In this simulation, we
take cet=3150 as the conversion time from theMHD simulation to the multi-hierarchy simulation,
since the MHD simulation demonstrated that thewidth of current layer decreased to be nearly equal
to an ion Larmor radius at cet~3150. At theconversion time, physical quantities are correctlysent from MHD to multi-hierarchy simulations.
Magnetic field line is smoothly and continuously

Fig.2. Magnetic field line. At cet=3150, MHD
simulation is switched to the multi-hierarchy simulation
shown in Fig. 1.

connected not only at cet=3150 but also until
cet=4950. We can see that at cet=4950, an X
point exists at the center of the PIC domain.
Magnetic reconnection is found to be driven in theframework the improved multi-hierarchy model
based on the dynamical domain conversion method.
4. Summary
We have developed multi-hierarchy simulation
model for complete understanding of magnetic
reconnection as a multi-scale phenomenon. In ourmodel, microscopic physics is described by the PIC
algorithm, while macroscopic physics is expressedby the MHD algorithm.
We improve our model and perform simulationthat initially whole domain is the MHD domain,
and a part of domain is converted to the PIC
domain when the width of current layer decreased
to be nearly equal to an ion Larmor radius. We
observe that magnetic reconnection occur in the
improved multi-hierarchy model.
References[1] A. Ishizawa and R. Horiuchi, Phys. Rev. Lett. 95,(2005) 045003.
[2] R. Horiuchi and H. Ohtani, Comm. Comput. Phys. 4,(2008) 496.
[3] T. Sugiyama and K. Kusano, J. Comput. Phys. 227,(2007) 1340.
[4] S. Usami, H. Ohtani, R. Horiuchi, and M. Den,
Comm. Comput. Phys. 4, (2008) 537.
[5] S. Usami, H. Ohtani, R. Horiuchi, and M. Den, J.
Plasma Fusion Res. 85, (2009) 585.
[6] S. Usami, H. Ohtani, R. Horiuchi, and M. Den,Comm. Comput. Phys. in press.
[7] S. Usami, H. Ohtani, R. Horiuchi, and M. Den,Plasma Fusion Res. 4, (2009) 049.
[8] R. Horiuchi, S. Usami, H. Ohtani, and T. Moritaka,
Plasma Fusion Res. 5, (2010) S2006.