25G08
Particle Simulation of Merging Process of Two Spheromaks
スフェロマク合体過程の粒子シミュレーション
Ritoku Horiuchi, and Yasushi Ono1)
堀内利得, 小野靖1)
National Institute for Fusion Science, 322-6, Oroshi, Toki 509-5292 , Japan
核融合科学研究所 〒509-5292 土岐市下石町322-6
1) University of Tokyo, Tokyo 113-8656, Japan東京大学 〒113-8656 , 東京都文京区本郷
In order to investigate merging process of two spheromaks in a cylindrical vessel with a central conductor,
multi-scale simulation model is developed based on the domain decomposition method. Particle-in-cell(PIC) model is applied to a central reconnection region with the width of several ion Larmor radii along thegeometric axis, and transfer process of two spheromaks outside the reconnection region is described by
MHD model. In this paper outline of simulation model and preliminary simulation result obtained fromdeveloped model are given.

1. Introduction
In order to investigate physics of magnetic
reconnection such as kinetic triggering
mechanism, plasma heating, particle accelerationand so on, merging experiments of spheromaks
and spherical tokamaks have been performed inmany experimental plasma devices such as TS-3
device at Tokyo University and MAST at Culham
Laboratory [1]. On the other hands, various
particle and magnetohydrodynamic (MHD)
simulations have been carried out for the same
purpose in simple slab geometry. As a result,common pictures of magnetic reconnection havebeen extracted from the experiments andnumerical simulations. However, their closecomparison did not be done due to big gaps
between the simulation models and theexperimental devices as yet.
In this study multi-scale simulation model isdeveloped in the cylindrical system for realizing
more close comparison between experimental andresults and extracting more fruitful commonpictures of magnetic reconnection.
2. Multi-Scale Model
Suppose that plasmas are confined in a
conducting vessel with a central conductor.
Simulation domain is implemented on a(256×2048) space grid in two-dimensional
cylindrical coordinates (r,z), assuming that physicalquantities are axially symmetric (  /   0) . The
simulation model is based on the domain
decomposition method [2] in which particle-in-cell(PIC) model is applied to a central reconnection
region, while transfer process of two spheromaks

outside the reconnection region is described by
MHD model. Reconnection region, where twospheromaks can merge, has a disk structure with thewidth of several ion Larmor radii along thegeometric axis.
Two-dimensional low-beta equilibrium solution,
which satisfies Grad-Shafranov equation, is adopted
for an initial profile. The equation of state satisfying
the adiabatic condition is assumed in an initialprofile, i.e., P /    constant with the ratio ofspecific heats  ( 5/3) . Two spheromaks with
opposite magnetic helicity and opposite averagevelocity are located far from the reconnection
region, as shown in Fig. 1. In the MHD region thefrozen-in condition is satisfied inside the plasma,i.e., E  v  B  0 . Two spheromaks behave as anincompressible fluid outside the reconnection
regions and approach to each other as time goes on.
For the PIC simulation we have typical following
parameters;
total
numberof
particles
N pt  20480000,   0.01,  pe / ce  2, Rin  0.2Rl ,,M i / M e  100, Z l / Rl  8, i / Rl  0.058
where Z l Rl , Rin , and  i are axial and radial
sizes of simulation domain, radius of central
conductor, and typical ion Larmor radius,respectively.

3. Simulation Results
Figure 1 shows the mass density profile (colormaps) and magnetic flux profile (lines) at initial(top) and reconnection (bottom) phases for thereconnection region with the width of four Larmor
radii along the geometric axis. Two spheromaks
with opposite magnetic helicity collide in thecentral reconnection region at ce t  805 .
Toroidal current with opposite sign to that of thespheromak current, namely, reconnection current isgenerated
near the contact surface of two
spheromaks, as shown in Fig. 2. The reconnection
current drives the change in magnetic field topology
and plasma heating (see top panel of Fig. 2). We
also observed the generation of quadra-polestructure in toroidal magnetic field through the Halleffect. These results are consistent with theprevious experimental and simulation results [1, 3].

Multi-scale simulation model has been developedin the cylindrical system for realizing more closecomparison between experimental and simulation
results and extracting more fruitful common
pictures of magnetic reconnection. The simulation
model is based on the domain decomposition
method in which PIC model is applied to a central
reconnection region, while transfer process of two
spheromaks outside the reconnection region is
described by MHD model. Preliminary results
obtained from the developed simulation model are
now examined.

4. Summery

Fig.1. The mass density profile (color maps) and magnetic flux profile (lines) at initial (top) and reconnection(bottom) phases.

Fig.2. The ion temperature profile (top) and toroidal current density profile at ce t  805 .
References[1] M Yamada, R. Kulsrud and H. Ji: Rev. Mod. Phys.
82 (2010) 603.
[2] S. Usami, H. Ohtani, R. Horiuchi, and M. Den,
Comm. Comput. Phys. 4, (2008) 537.
[3] R. Horiuchi, S. Usami, H. Ohtani, and T. Moritaka,Plasma Fusion Res. 5, (2010) S2006.