Multi-Coil Magnetic Sail Experiment in Laboratory

By Kazuma UENO,1) Yuya OSHIO,2) Ikkoh FUNAKI,3) and Hiroshi YAMAKAWA4)2)

1)
Department of Electrical and Electronic Engineering, Chukyo University, Nagoya, Japan
Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Koganei, Japan
3)
Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan

4) Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Japan

Magnetic Sail is a space propulsion system capturing the solar wind stream with an artificial magnetic field to produce
thrust. Conventional magnetic sail use a coil magnetic field with a single-coil and that configuration is suitable for proof-ofconcept. Multi-Coils Magnetic Sail generates a more complicated magnetic field than the conventional magnetic field. In
this paper, Multi-Coils Magnetic Sail scale model consisted of three 22 mm-diameter coils was developed and direct thrustmeasurement of the Multi-Coils Magnetic Sail was conducted to observe thrust production with the multi-coil configuration
using Magnetoplasma Sail Ground Simulator in ISAS/JAXA.
Key Words: Magnetic Sail, Deep Space Propulsion, Magnetosphere, the Solar Wind, Experiment

NomenclatureBB0CdeFILMMimiNnRmrLircoilSu
0Subscriptsv
inf
mpfsw

1.

an artificial magnetic field capturing the solar wind. Anefficient capturing with the magnetic field increase a force on
the coil and the spacecraft deploying the coil is accelerated
towards the solar wind direction. In order to increase
Magnetic Sail thrust, it is necessary to expand amagnetosphere or improve efficiency of capturing the solarwind. Multi-Coil Magnetic Sail concept is the latter approach.
In this paper, Multi-Coil Magnetic Sail was developed and its
thrust was measured with thrust stand directly to confirm
thrust generation of Multi-Coil configuration.

:magnetic flux density (T):magnetic flux density at the center of the coil(T):thrust coefficient:elementary charge (1.6×10-19 C):thrust (N):coil current (A):standoff distance of magnetic cavity (m):magnetic moment (Tm3):ion Mach number

2.

:mass of proton (1.67×10-27 kg):number of turns

Multi-Coil Magnetic Sail

Multi-Coil Magnetic Sail is 50 mm-outer-diameter
multiple-coils consisted of three small coils which is 22 mmdiameter, 20 mm-height and 20 number of turns. The detailsof coil parameters are determined by referring ourconventional magnetic sail, a single coil (50 mm-diameter, 20mm-height and 20 number of turns). The small coils areconnected in series. The total wire length and the total weightof Multi-Coil Magnetic Sail is about the same length andweight as the conventional coil. Thus, conventional
experimental facility and:number density (m-3):magnetic Reynolds number:ion Larmor radius (m):coil radius (m):representative area of magnetic cavity (m2):velocity (m/s):skin depth (m):permeability in vacuum (1.26×10-6 H/m):ion
:after inflation:magnetopause:frozen-in point:solar wind

Introduction
A conventional Magnetic Sail use a single coil to produce1are shown in Fig. 1.

Fig. 1. Top and Side views of the developed Multi-Coil Magnetic Sail.

3. Experimental Setup
3.1. Facility for Multi-Coil Magnetic Sail Experiment
The experimental setup for a Multi-Coil Magnetic Sail isshown in Fig. 3. It consisted of two simulators, a solar windsimulator and a Multi-Coil Magnetic Sail simulator, both ofwhich were developed in ISAS/JAXA10,11).
Three MagnetoPlasmaDynamic (MPD) arcjets, which caneasily produce a high-velocity and high-density plasma jet,were used as the solar wind simulator and it was mounted on
the wall of the chamber. A multiple coil, simulating the coil of
Magnetic Sail, was also installed inside the chamber, and it
was immersed in the plasma flow. The details and operating
conditions of these simulators are summarized in Table 1.
These simulators were operated in a quasi-steady mode ofabout 0.5-1.0 ms duration using pulse forming networks.
3.2. Thrust Measurement of Pure Magnetic Sail
Thrust measurements were carried out by theparallelogram-pendulum method. The coil simulating a Pure
Magnetic Sail was mounted on a thrust stand suspended byfour steel wires (Fig. 3). For each shot of the MPD arcjets andcoil combination, the impulse was measured from themaximum swing of the pendulum. The displacement of thependulum in the X-direction was measured with a laser
displacement sensor. For calibration of the pendulum andposition sensor combination, impulses of known magnitude
were applied to the coil using a simple pendulum consisting ofa steel ball and string in an atmospheric pressure environment.
The impulses of the ball were calculated from its mass and thestriking velocity evaluated from energy conservation for thecalibration pendulum.
The impulse of a Magnetic Sail is calculated by thefollowing equation:

Fig. 2. Comparison view of the difference between conventional singlecoil Magnetic Sail (red line) and Multi-Coil Magnetic Sail (blue line).

Fig. 3. Experimental configuration of Multi-Coil Magnetic Sail.
Table 1. Specification of the experimental setup for Multi-Coil
Magnetic Sail simulations.
Multi-Coil Magnetic Sail Simulator
Outer diameter, mm

25

Number of coils

3Coil radius, mm

11Wire diameter, mm

2

Number of turns
Coil area perpendicular to the flow, mm2
Operating condition
Maximum coil current, A
Solar Wind Simulator (MPD arcjets)
Number of MPD arcjets
Inner diameter of a MPD arcjet, mm
Injection gas(Ft )Magsail201800
350To derive Eq. (2), a rectangular waveform against time isassumed for the impulse, which seems a reasonableapproximation based on the discharge current profiles in Fig.
4.

HydrogenOperating condition
Total gas flow rate, g/s

0.72
7.9×1017
29

Diameter of test section, mm511(1)

When only the solar wind simulator is operated, the pressure
on the coil surface produces thrust; this impulse corresponds
to (Ft)SWS in Eq. (1). If the coil current is initiated during thesolar wind operation, the impulse, (Ft)total, becomes larger
than (Ft)SWS. The thrust of a Magnetic Sail is defined as thedifference between the two impulses divided by the SWS
operation duration (t = 0.5 ms):(Ft )MagsailFMagsail =(2)t1263

Plasma number density, m-3
Plasma velocity, km/s

= (Ft)total − (Ft )SWS

4.

Experimental Results and Discussion

All the experiments were operated for the same simulated
solar wind conditions (usw = 29 km/s, n = 7.9×1017 m-3) andthe same coil position (1250 mm away from the Solar windconditions are adopted on the Multi-Coil Magnetic Sailexperiments. A comparison view of these coils is shown in Fig.
2 and top/side views of developed Multi-Coil Magnetic Sail2simulator exit).
4.1.

Displacement of Multi-Coil Magnetic Sail

The measured displacements with the laser sensor for various
coil currents are plotted in Fig. 5. The coil current was set in total
7 stages from 0 A to1.9 kA at an interval of 0.35 kA. In the caseof 0 A-coil-current, magnetosphere was not existed because amagnetic field was not generated and the displacement of about
0.7 mm was mainly caused by neutral particles colliding with thecoil. In the other cases, the displacement increase from 0.8 mm to
1.3 mm with increasing of coil current from 0.35 kA to 1.9 kA.
These differences from the displacement of 0 kA indicates thatthe force exerted on the coil depending on the coil current.

4.2. Thrust of Multi-Coil Magnetic Sail
The impulse is estimated using the first peak of the swingof the thrust stand. The thrust of Multi-Coil Magnetic Sail iscalculated using Eq. (1), (2). Thrust data for Magnetic Sailwith various magnetic moments are shown in Fig. 6. We canfind the thrust increases as the magnetic moments increases.
The magnetic moment is calculated by the following equation;
2M = 3 × µ0NInrcoiS(3)
Assuming multi coils as a single hoop coil, theoretical thrustis predicted by the following equation; 1Fig. 4. Profiles of the current of SWS (charging voltage = 2.7 kV) andthe coil current (charging voltage = 1.5 kV).

n2

F = Cd 4{µ(ncw Ni ucw 2 )}3 M310(4)Theoretical thrust of Multi-coil Magnetic Sail is calculatedfrom Eq.(4) . For example, F= 0.04 N is for usw = 27 km/s, n =7.9×1017 m-3, M= 0.05 mTm3 (1.8kA-coil-current), Cd= 0.8(from Ref. 12). At this stage, we see that the measured thrust
is much larger than the theoretical prediction. However, wecan conclude that the interaction between the plasma flow andthe magnetic field produced with the multi-coil is produced
and the thrust was observed.
7. Conclusion and Future work
Thrust measurements of a Multi-coil Magnetic Sail wereconducted in the laboratory. The experimental setup consists of asolar wind simulator and 25-mm-outer-radius coil simulating aMulti-Coil Magnetic Sail spacecraft placed inside a large vacuumchamber. Multi-Coil consists of three-small coils (20-turns, 11mm-radius). The thrust of the Multi-coil Magnetic Sail wasobserved and increased as the magnetic moment increased.

Fig. 5. Measured displacements of thrust stand for various coil currents(SWS charging voltage = 2.7 kV).

Acknowledgments
We would like to thank the space plasma laboratory of
ISAS/JAXA, and the members of the MPS research group for
their valuable advice and support in conducting ourexperiment. A part of this research is supported by The
Chukyo University Research Fund.
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Fig. 6.

Thrusts of multi-coil magnetic sail for various magnetic

1)

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