24P124-P
Investigation on a momentum of the charged particles
in permanent-magnets-expanded plasma
永久磁石利用発散プラズマ中の荷電粒子モーメントの検討
Haluna Itoh1, Kazunori Takahashi1,2, Tamiya Fujiwara1,2
伊藤 陽菜1，高橋 和貴1,2，藤原 民也1,2
1

Department of Electrical Engineering and Computer Science, Iwate University
4-3-5, Ueda, Morioka, Iwate 020-8551, Japan
岩手大学工学部 電気電子・情報システム工学科 〒020-8551 岩手県盛岡市上田4-3-5
2Soft-Path Engineering Reserch Center (SPERC), Faculty of Engineering, Iwate University,
4-3-5, Ueda, Morioka, Iwate 020-8551, Japan
岩手大学ソフトパス工学総合研究センター 〒020-8551 岩手県盛岡市上田4-3-5

An electron pressure and a momentum of a supersonic ion beam downstream of thepermanent-magnets-expanded plasma source are experimentally investigated using a retarding field energy
analyzer and a Langmuir probe. As the previously reported thrust from a magnetically-expanding or simple
rf plasma thruster can be well explained by the electron pressure force inside the source tube, the present
measurements downstream of the source are compared with the upstream electron pressures. There are
significant disagreement between the upstream electron pressure and the total momentum from the electronand drifting ions downstream of the source; it is discussed from the viewpoint of the ion-neutral
charge-exchange collision and the radially non-uniform electron energy distribution.

Diffusion chamber

Glass tube
(Source tube)

RFEA

Ar gasRF antenna
RF power
Matching
supplycircuit
-20-9

LP

26 cm

Permanentmagnet arrays

6.6 cm

1. Introduction
Conventional electric propulsion devices, e.g.,
ion engines, hall thrusters, and magneto-plasmadynamic thrusters, require electrodes for ion
accelerations and/or plasma productions. In thesetypes of propulsion devices, the electrodes aredamaged by thermal loads and ion bombardment;
the development of the long-lived thruster has been
progressed so far. One of the candidates for thelong-lived propulsion devices is an electrodelesssystem such as helicon thruster including ion
accelerations by ambipolar or double-layer (DL)electric fields [1,2]. More recently, thepermanent-magnets helicon source has beendeveloped in order to reduce the consumed electric
power by the solenoids [3].
The investigation on the thrust generation
mechanisms in the helicon-type plasma thrusters
are now vigorous topic in experiments and theories[4-7]. A directly measured thrust from thepermanent-magnets-expanded
plasmasource(custom built in Iwate Univ. and operated in theAustralian National Univ.) has been about 3-4 mN
for rf power of about 800 W, which are well
explained by the electron pressure force inside thesource tube. In the present study, the density andvelocity, i.e., a momentum of the ion beam inducedby the DLs are experimentally investigated using aLangmuir probe (LP) and a retarding field energy

To Pump030 z (cm)Fig.1. Schematic of the PMPI machine.

analyzer (RFEA). A total momentum from the ion
beam and the electron pressure downstream of thesource tube are compared with the upstream
electron pressure.
2. Experiment Setup
Experiments are performed in Permanent
Magnets expanding Plasma machine at Iwate
University (PMPI) shown in Fig.1. The machine
has a 20-cm-long and 6.6-cm-diameter source tube
contiguously connected to a 30-cm-long and26-cm-diameter stainless steel diffusion chamber,where z = 0 cm is defined as the source exit.
Permanent magnet arrays surrounding the source
tube provide a constant magnetic field of about 100
G inside the source and an expanding field
decreasing to 10 G at the middle of the diffusion
chamber. A double-turn rf loop antenna winding theTe pressure  2  n p r k BTe rdr ,Ti beam  2 

0

np-up

-3

Density (cm )101210

11

10

10

100

2

4r (cm)6810

11

np-down
nbeam

(b)

1010

10

910

80

24r (cm)

6810…（1）0rbeam13(a)-3

3. Experimental results
Fig. 2(a) shows the radial profile of the upstreamplasma density np-up at z = -11.5 cm for an rf powerof 250 W. This axial position gives the maximum
electron pressure along z, and the previous
experiments have shown the thrust from the DL
source can be given by the maximum pressure [6,7].
Fig. 2(b) shows the radial profiles of thedownstream plasma density np-down and ion beam
density nbeam measured at z = 3 cm. It is found thatboth nbeam and np-down are radially non-uniform. The
momentums from the electron pressure and thedrifting ion beam can be described by theintegration in the cross section as

10Density (cm )source tube at z = -9 cm is powered from a 13.56
MHz rf power supply, and an argon plasma isproduced by an inductively-coupled mode
discharge. The rf power is varied in the range of
100-800 W. The flow rate of the argon gas ischosen as 4.5 sccm giving the argon gas pressure ofabout 0.75 mTorr, where the gas pressure ismeasured by an ionization gauge connected to aside port of diffusion chamber. Then the DLstructure is formed near the plasma source exit, andthe supersonic ion beam is generated downstreamof the source exit [3].

mi nbeam r vbeam r rdr ,…（2）At the axial position of the maximum electronpressure, it is assumed that the ions are notaccelerated and its drift velocity is zero. Then thetotal momentum at this position corresponds to theelectron pressure; it can be obtained as ~0.75 mN.
On the other hand, the downstream momentum isdue to both the thermal electrons and the driftingions. The total momentum downstream of thesource exit (z = 3 cm) can be estimated as ~0.2 mN,where Te(pressure_down) and Ti(beam) are ~0.1 mN and~0.09 mN, respectively. Even if the contribution
from the neutral beams produced through thecharge-exchange collisions, it is still ~0.3 mN. Now
the electron temperature is assumed to be uniform
in the system. However, the previous studies haveshown the presence of the energetic electrons both
inside and outside the source. These energetic
electrons would also contribute to the total
momentum. Detailed measurements will bereported in the presentation.

Fig.2. Radial profiles of (a) the plasma density at z =-11.5 cm, and (b) the plasma density and ion beam
density at z = 3 cm.

4. Conclusion
The total momentums both inside and outside thesource tube are experimentally investigated in thepermanent-magnet plasma source. The results show
a significant disagreement and discussed from theviewpoint of the charge-exchange collisions and theradially non-uniform electron energy distributions.
References[1] O. V. Batishchev, IEEE Trans. Plasma Sci., 37, 1563
(2009).
[2] C. Charles, J. Phys. D: Appl. Phys., 42, 163001(2009).
[3] K. Takahashi, T. Fujiwara, Appl. Phys. Lett., 94,061502 (2009).
[4] A. Fruchtman, Phys. Rev. Lett., 96, 065002 (2006).
[5] E. Ahedo, M. Merino, Phys. Plasmas., 17, 073501(2010).
[6] K. Takahashi, et al., Appl. Phys. Lett., 98, 141503(2011).
[7] T. Lafleur, et al., Phys. Plasmas., 18, 080701 (2011).