§5. Hierarchy-Interlocking Model in the
Using this new model, we perform a multi-hierarchy
simulation in which plasma flow satisfying a shifted
Maxwellian velocity distribution propagates from PIC to
MHD domains. Figure 1 shows the bird’s eye view of the
Usami, S., Horiuchi, R., Ohtani, H., Den, M. (NICT)
profiles of plasma mass density at Zcet=1300 and at
Zcet=2000. The simulation domain is divided as follows.
PIC domain: 0<x/(c/Zce)<88.0, interface domain:
Collisionless magnetic reconnection is one of the
88.0<x/(c/Zce)<96.0, MHD domain: 96.0<x/(c/Zce)<344.0.
fundamental processes in which magnetic field energy is
We can see that plasmas are smoothly and continuously
converted to kinetic and thermal energies. It plays an
ejected from PIC to MHD domains via the interface domain.
essential role in the rapid energy release in laboratory fusion
Now, we are constructing a two-dimensional
device and astrophysical plasmas such as solar flare. Also
hierarchy-interlocking model, in other words a
magnetic reconnection has an aspect of typical complex
hierarchy-interlocking model in the upstream and
phenomenon controlled by multiple spatiotemporal scale
downstream directions as shown in Fig. 2 and are examining
physics. In order to clarify the complete picture of magnetic
reconnection as a multi-hierarchy phenomenon, we have
We furthermore consider that a particle domain with
developed a multi-hierarchy simulation model which deals
Coulomb collision effect is inserted between PIC and MHD
with macroscopic and microscopic physics simultaneously
In our multi-hierarchy model, we employ the domain
decomposition method; the domains differ in algorithm.
Physics in the domain where some microscopic dissipation
mechanisms are required is solved in the first principle by
full particle-in-cell (PIC) algorithm. We call this domain PIC
domain. On the other hand, dynamics outside the PIC
domain is expressed by magnetohydrodynamics (MHD)
algorithm, in which the ideal MHD equations are calculated
as the basic equation, since electrical resistivity is assumed
to be generated self-consistently by microscopic kinetic
process only in the PIC domain. We refer to this domain as
MHD domain. Between the PIC and MHD domains, an
interface domain with a finite width is inserted in order to
Fig. 1: Bird’s eye view of the spatial profile of plasma
With the hierarchy-interlocking in the upstream direction,
mass density at Zcet=1300 and at Zcet=2000. Plasmas
we have performed the multi-hierarchy simulations of
smoothly propagate from the PIC to MHD domains.
driven reconnection, namely plasma inflows come from the
MHD domain and drive magnetic reconnection in the PIC
domain [3,4]. It was confirmed that reconnection process
found in the multi-hierarchy model is true physics.
Aiming to apply our multi-hierarchy model to a larger
region of the magnetic reconnection system, we develop the
hierarchy-interlocking model in the downstream direction,
in which the improved interlocking method is adopted. First,
we consider the configuration that the upstream region (PIC
domain) is located in the left side and the downstream
region (MHD domain) is in the right side. As the
Fig. 2: Schematic diagram of the two-dimensional
hand-shaking scheme for physical quantities except for
1) S. Usami, H. Ohtani, R. Horiuchi, and M. Den, J. Plasma
Fusion Res. 85 (2009) 585.
is used. On the other hand, for pressure
2) S. Usami, H. Ohtani, R. Horiuchi, and M. Den,
Comm. in Comput. Phys. 12 (2012) 1006.
3) S. Usami, H. Ohtani, R. Horiuchi, and M. Den, Plasma
Fusion Res. 4 (2009) 049.
where 'x can be regard as for instance one grid spacing.
4) S. Usami, H. Ohtani, R. Horiuchi, and M. Den, Phys.
This improved method can suppress unphysical noises in the

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