AMR-PIC Simulation on Solar Wind Interaction
with Kinetic Scale Magnetosphere
Masaharu Matsumoto 1, Hideyuki Usui 1, Masanori Nunami 2, Masao Nakamura 3 and Iku Shinohara 4121

Graduate School of System Informatics, Kobe University, JapanFusion Theory and Simulation Research Division, National Institute for Fusion Research, Japan3
Department of Aerospace Engineering, Osaka Prefecture University, Japan
4
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Japan

Introduction

Magnetic Sail is an advanced space propulsion system [1]which uses the interaction between an artificial magnetospherearound a spacecraft and solar wind plasmas. The solar wind isdeflected in the magnetosphere and the momentum transfer
results in the drag force exerted on the spacecraft. Recently, theMini-Magnetospheric Plasma Propulsion (M2P2) [2], which isalso called Magneto-Plasma Sail (MPS) [3], is suggested by
Winglee et al. as a derivative system from Magnetic Sail. In theconcept of M2P2 and MPS, the original magnetic field attached
to a spacecraft is expanded by the injection of artificial plasmas
from the spacecraft to form finally a huge magnetosphere. Suchpropulsion systems which use the solar wind energy are
expected to achieve high energy conversion efficiency comparedwith conventional electric propulsion systems and many
feasibility studies have been conducted.
Fujita [4] has revealed that the drag (thrust) force of amagnetic sail, which is exerted on the spacecraft from the solar
wind, is characterized by the ratio of an ion Larmor radius of thesolar wind at the magnetopause rL to a representative length ofmagnetic field L. Figure 1 shows the schematic view of typicalion particle motions due to the difference in rL/L. On themagnetohydrodynamics (MHD) scale (rL/L<<1), the ion particle
motions depend strongly on the magnetic field line and themomentum of ion particles turn into the drag force of thespacecraft as shown in Fig.1. On the other hand, on the ion
inertial scale (rL/L>>1), the electromagnetic interactions of ion
particles with magnetic field become weak compared with thecase of MHD scale because ion kinetic effect becomes dominant.
Consequently, the thrust performance of magnetic sail decreaseson the ion inertial scale. In the propulsion system of magnetic
sail, at least the magnetospheric size of ion inertial scale or moreis needed to obtain the thrust performance higher thanconventional electric propulsion systems. Therefore, kinetic
approaches which address the small-scale physical mechanism
must be used to simulate the magnetic sail with such small
magnetosphere of ion and electron inertial scale.
In the past study of magnetic sail, hybrid particle-in-cell(PIC) simulation methods have been conducted mainly in order
to examine the solar wind flow field around magnetic sail andthe thrust performance [4, 5]. The hybrid PIC simulations, inwhich ions are treated as super particles and electrons areassumed as fluid, can include the kinetic effect of ion particles.
However, the solar wind flow field and thrust performance on
the smaller magnetospheric scale than ion inertial, namely,
electron inertial scale, have not been almost revealed. This isbecause the physical phenomena on electron inertial scalecannot be simulated by the hybrid PIC simulation method. On
the other hand, full PIC plasma simulation methods [6], inwhich both electrons and ions are treated as super particles, arewidely used in space plasma science and engineering. ThisFig. 1. Ion particle motion due to the difference on rL/L.

Level-0

Level-1

Level-2

Fig. 2. Grid system of adaptive mesh refinement
method calculates plasma particles motions governed by motion
equations and electromagnetic fields defined on the mesh ofcomputational domain by Maxwell equations, self-consistentlyand alternately. This method includes the kinetic effect of not
only ion but also electron particles. However, the computationalload of PIC simulation is extremely higher than hybrid PIC orMHD simulations because the grid width of computational
domain should be set to plasma characteristic lengths such as
Debye length or Larmor radius in the full PIC simulations.
Furthermore, over one hundred plasma particles per unit cell
(grid) are needed for high accuracy simulations.

Table 1. Working conditions
Number of Super Particles
mi/me
qi/qe
Ti/Te
ωce/ωpeVTe/cVin/VTirL/L

32 pair/cell
25
1.0
1.0
8.0 × 10-2
5.0 × 10-2
10.0
12.0
Fig. 4. Distribution of the electron number density, magnetic field lines
and refinement grid at t = 10 [1/ωpe]

Fig. 3. Computational domain used in the two-dimensional
AMR-PIC simulation.
Our research group has developed an adaptive meshrefinement PIC (AMR-PIC) simulation code in order to handle
the problems as mentioned above. The AMR-PIC code is PIC
simulation code which has method to modify the grid width ofcomputational domain in the midst of the simulations temporally
and locally as shown in Fig.2. The grid width is adjusted
automatically in accordance with the physical values of intended
plasma flow field. The AMR-PIC method can simulate thephysical phenomena in which more resolution is needed, andcan decrease the computational load such as memory andcomputing time compared to conventional PIC code withuniform grid width of computational domain.
Based on the above, the purpose of this study is to examine
the interaction of solar wind flow field and kinetic scale
magnetosphere around a magnetic sail by using AMR-PIC
simulation codes.
2

Result of Two-Dimensional Simulation

The two-dimensional AMR-PIC simulation is conducted inorder to examine the interaction of the solar wind plasma to theelectron inertial scale magnetosphere. Table 1 and Fig.3 show
the working conditions and computational domain used in thisstudy. The nomenclature in the table is commonly-used. The
scale parameter is set to the electron inertial scale (rL/L = 12.0)
although some solar wind parameters are set to arbitrary suitable
for the electron inertial scale simulation. An interplanetary
magnetic field is ignored in this study. The solar wind plasma
flows from left to right direction and the dipole magnetic field is
set on the centre of the computational domain in the figure. Theline dipole field is excited by the applied current which
increases linearly in the midst of the simulation. The damping
regions for electromagnetic waves are set to the left and rightboundary of the computational domain and top and bottom
boundary are periodic condition.
Figure 4 shows the distribution of electron number density
normalized by the solar wind at upstream, magnetic field lineand refinement grid at t = 10 [1/ωpe]. In this two-dimensional
simulation, for simplicity, the mesh refinement level is set toone-step, two levels (Lv.0: base grid, X: 256 × Y: 256 grid,Lv.1: refinement grid, corresponding to X: 512 × Y: 512 grid)and the criterion of mesh refinement is set when the electron
number density exceeds a critical limit. This criterion should
correspond to some characteristic length like the Debye lengthor Larmor radius. The electron number density increase at theupstream of dipole magnetosphere like a bow shock formation.
Moreover the wake region appears and the density decreases atthe downstream of dipole field. These are the result of deflection
due to the interaction of plasma particles to the dipole field. Thegrid width becomes finer where the electron number density
increases as shown in this figure. Furthermore, it is shown thatthe memory cost (4GB to 1GB) and computational time (24hours to 6 hours) are reduced by using the AMR-PIC code
compared to the conventional PIC code with uniform finer grid
(X: 512 × Y: 512 grid).
Acknowledgements
This work was supported by the Japan Science andTechnology Agency, Core Research for Evolutional Science andTechnology (JST-CREST) under the project “High Performance
Computing for Multi-Scale and Multi-Physics Phenomena”.
References
[1]

[2]

[3]

[4]
[5]

[6]

Zubrin, R. M. and Andrews, D. G., Magnetic Sails andInterplanetary Travel, J. Spacecraft Rockets, Vol.28, pp. 197-203,
1991.
Winglee, R. M., Slough, J., Ziemba, T. and Goodson, A., MiniMagnetospheric Plasma Propulsion: Tapping the Energy of theSolar Wind for Spacecraft Propulsion, J. Geophys. Res., Vol.105,
pp.21,067-21,077, 2000.
Yamakawa, H., Funaki, I., Nakayama, Y., Fujita, K., Ogawa, H.,Nonaka, S., Kuninaka, H., Sawai, S., Nishida, H., Asahi, R., Otsu,
H. and Nakashima, H., Magneto-Plasma Sail: An Engineering
Satellite Concept and Its Application for Outer Planet Missions,Acta Astronautica, Vol.59, pp.777-784, 2006.
Fujita, K., Particle Simulation of Moderately-Sized Magnetic Sails,
J. Space. Technol. Sci., Vol.20, pp.26-31, 2004.
Kajimura, Y., Funaki, I., Matsumoto, M., Shinohara, I., Usui, H.
and Yamakawa, H., Thrust and Attitude Evaluation of Magnetic
Sail by Three-Dimensional Hybrid Particle-in-Cell Code, J. Propul.
Power, Vol.28, pp.652-663, 2012
Birdsall, C. K. and Langdon, A. B., Plasma Physics via Computer
Simulation (Reprinted), Taylor & Francis, New York, 2005.