22P046-P
Numerical Evaluation of Ring Current Inflation for the Application of Magneto
Plasma Sail
磁気プラズマセイルへの応用に向けたコイル磁場中のリングカレント生成による磁気圏拡大評価
Yoshihiro Kajimura, Masaharu Matsumoto, Ikkoh Funaki, Iku Shinohara,Hideyuki, Usui and Hiroshi Yamakawa
梶村 好宏, 松本 正晴, 船木 一幸, 篠原 育, 臼井 英之, 山川 宏
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency
3-1-1, Yoshinodai, Cyuo-ku, Sagamihara, Kanagawa 252-5210, Japan
宇宙航空研究開発機構 宇宙科学研究所 〒252-5210 神奈川県相模原市中央区由野台3-1-1
Magneto Plasma sail is a space propulsion system which can obtain the electromagnetic force from theinteraction between the solar wind plasma and the magnetic field inflated by plasma injection from MPS
spacecraft. In the present paper, the increase of the magnetic moment generated by the grad-B drift currentof injected thermal plasma has been estimated by 1D, steady state, diffusion equation. Under theassumption of plasma fluid approximation, MPS (coil radius is 2 m, coil current is 106 A turn) is expected
to obtain the thrust of 10 mN by the ring current inflation when the injected thermal plasma density is1.5×1023 m-3, the temperature is 10 eV.

1. Introduction
A space propulsion system with large thrust,high thrust to power ratio and high specificimpulse has been required for deeper spaceexploration missions. As one of candidates of thespace propulsion system for these requirements,
Magneto Plasma Sail (MPS) has been proposed[1]. The MPS can obtain the electromagnetic
propulsive force by the interaction between thesolar wind and an artificially generated dipolar
magnetic field inflated by the plasma injection
fromthespacecraft.
Byusing
MagnetoHydroDynamics (MHD) model, Nishidahas simulated the thrust production mechanism ofthe MPS, wherein magnetic inflation is achievedby the plasma injection from the spacecraft [2]. Ifthe MPS spacecraft is surrounded by a radial
super-Alfvenic flow of the injected plasma (i.e.
Mach Number Ma2 = plasma beta > 1), it seems
that no information is transferred upstream (i.e.,to the spacecraft); this implies that theelectromagnetic (Lorentz) force (thrust) cannot betransferred to the MPS spacecraft. In addition,Kajimura has conducted the Hybrid PIC
simulations for evaluating the MPS thrust andthen the simulation results indicating the sametendency of MHD results have been obtained [3].
In addition, it is found that the MPS thrust wascomparable to the sum of MPS thrust without
injection and the thrust in case for direct plasma
injection from the spacecraft. Hence, it isnecessary for achieving the magnetic inflation by
the plasma with lower energy to inject the plasma

with static pressure not dynamic pressure.
If the thermal plasma only with static pressure
is injected from the spacecraft, the gradient-B
drift current (this is the ring current) is induced.
This current can be seen the magnetosphere of theearth. The conceptual sketch of the ring current
generation is shown in Fig. 1. In the present study,
the increase of the magnetic moment generated
by the ring current is estimated by the simple 1D,
steady state, diffusion equation. Then the
expected thrust value of MPS is calculated fromthe thrust formula depending on the magneticmoment.

Fig.1. Conceptual sketch of ring current inflation

2. Evaluation of the ring current using 1D steadystate diffusion equation.
The simple structure of the ring current in themagnetic field produced by the coil is assumed asshown in Fig. 2. The thermal plasma is injectedfrom the location of the surface of the coil and thenthe plasma distributes following the 1D, steadystate and diffusion equation of Eq. (1). In thisequation, DB indicates the Bohn diffusion
coefficient proportional to r3 (DB ∝ 1/B ∝ r3）,
r is the distance from coil center.

Eq. (8) for the drag coefficient Cd as a function ofrLi/L. rLi is the ion Larmor radius at themagnetospheric boundary which location is definedas the distance L from the boundary to the coilcenter. In the present case, the distance L increases
to Linf by the ring current inflation.

(2F = C d ⋅ 0.5 ⋅ nsw mv sw
πL2infCd =)⎛ − 0.22 ⎞3.4⎟
⋅ exp⎜(rLi Linf ) ⎜⎝ (rLi Linf )2 ⎟⎠(7)(r LLiinf)> 1 (8)⎛ μ 0 (M p + M 0 )2 ⎞ 6⎟
Linf = ⎜2⎜ 8nsw mvsw⎟⎝⎠
1Fig.2. Simple model of structure of ring current.

1 ∂ ⎛2 ∂n ⎞⎜ DB r⎟=0r ∂r ⎝∂r ⎠(1)

The diffusion equation (1) for the density is solvedon the boundary condition (r = R, n = n0 and r ＝∞, n = 0). R is the injection location and n0 is thenumber density of injection plasma. The numberdensity and pressure distribution are Eq. (2) and (3).

n(r ) = n0 R 4 r −4(2)P(r ) = n0TR r4 −4(9)Figure 3 shows the MPS thrust depending on Ic
and T and n0 .Under the plasma fluid approximation,
MPS (coil radius is 2 m, coil current is 106 A turn)is expected to obtain the thrust of 10 mN by the ring
current inflation when the injected thermal plasma
density is 1.5×1023 m-3, the temperature is 10 eV.
The number density nsw, velocity vsw, and thetemperature Tsw of the solar wind is 5×106 m-3, 400km/s and 10 eV, respectively.

(3)

The ring current i.e. gradient B drift current iscalculated by Eq. (4) substituting Eq. (2) and (3). T
is the temperature of the injected plasma. M0 is theoriginal magnetic moment.

j =μ M ⎞∇p 16πn0TR 4 1 ⎛B = 0 30 ⎟=2 ⎜μ0 M 0 r ⎝B4πr ⎠(4)The magnetic moment Mp produced by this ring
current j is calculated from Eq. (5) and the ratio of
this magnetic moment to the original magnetic
moment is defined as Eq. (6).

16πn0TR 4M p = ∫ πr jrdθdr = ∫ drdθ
r
μ0 M
RR
Rout

Rout

Acknowledgments
This study is supported by the JST, CREST.

28πn0TR 4 2=
Rout − R 2 dθ
μ0 M 0[MpM0=][16n0 kTR 4 2
Rout − R 2
4 2
μ 0 rc I cFig.3. Thrust depending on Ic and T and N_sw.

(5)
References](6)3. Thrust estimation of MPS
The thrust obtained in MPS can be calculated byEq. (7). Fujita [4] proposed an approximate formula[1] R. M. Winglee et al., J. Geophys. Res., 105, 21,(2000), pp. 21067-21077.
[2] H. Nishida et al., Proc. of the 30th International
Electric Propulsion Conference, IEPC-2007-195,(2007).
[3] Y.
Kajimuraetal.,Proc.
of46thAIAA/ASME/SAE/ASEE
Joint
Propulsion
Conference, AIAA 2010-6686, (2010).
[4] K. Fujita et al., J. Space Tech. and Sci., 20, 2, (2005),
pp. 26-31.