Proceedings of ITC/ISHW2007

Generation of supersonic and super-Alfvénic flowby using ICRF heating and a magnetic nozzle
Akira Ando1, Tatsuya Hagiwara1, Toshihiro Komagome1,Kunihiko Hattori2, Masaaki Inutake3
1

Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan
2
Nippon Institute of Technology, Saitama, 345-8501 Japan.
3
Research Institute of Electrical Communication, Tohoku University, Sendai, 980-8577, Japan(Received/ Accepted)

Fast-flowing plasmas in supersonic and super-Alfvénic regime are generated in combined experiments of ioncyclotron resonance heating (ICRH) and acceleration in a magnetic nozzle. During radio-frequency (RF) wave
excitation in a fast-flowing plasma produced by a magnet-plasma-dynamic arcjet (MPDA), strong ion cyclotron
heating is clearly observed. Thermal energy in the heated plasma is converted into flow energy in a diverging
magnetic nozzle, where the magnetic moment μ is nearly kept at constant. Plasma flow energy can be controlled bychanging the input RF power and/or modifying the magnetic nozzle configuration. In a strongly diverging magneticnozzle, an Alfvén Mach number as well as an ion acoustic Mach number attains to more than unity, that is,supersonic and super-Alfvénic plasma flow is realized.
Keywords: supersonic plasma flow, super-Alfvenic plasma flow, ion cyclotron heating, magnetic nozzle, advanced
plasma thruster

1. Introduction
Recently, the production and control of fast-flowing
plasma are of growing significance for clarifying various
MHD phenomena observed in space and fusion plasmas,
for developing advanced electric propulsion systems andfor applying in various industrial researches.
In cosmic plasmas, astrophysical jet from a fast
rotating star is one of the most interesting phenomena [1].
Helical structure is often observed in the jet, and thephysical mechanism of the jet formation is still underinvestigation. In fusion plasmas such as in multiple
mirror [2]. and toroidal devices [3, 4], dynamics of a fastflowing plasma in magnetic fields are important from theview point of stabilizing and improving the plasma
confinement.
As for future space exploration projects, an electric
propulsion system is one of the inevitable technologies tobe urgently developed. In an advanced space propulsion
system for a manned interplanetary space flight, not only
a high power density plasma thruster generating higher
thrust, but also a thruster which has capability of varying
a specific impulse are requisite to improve propellant
utilization and thrust performance.
A magneto-plasma-dynamic arcjet (MPDA) is one ofthe plasma sources which can generate high density plasma
with high exhaust plasma velocity. It is utilized not only as
one of the representative devices for electric propulsion
author’s e-mail: akira@ecei.tohoku.ac.jp

systems but also as a supersonic plasma flow source.
Recently, intensive researches to develop an
advanced space thruster named as Variable SpecificImpulse Magnetoplasma Rocket (VASIMR) have been
performed for the purpose of manned Mars exploration.
The thruster can control a ratio of specific impulse tothrust at constant power. The exhausting plasma flow canbe controlled by a combined system of the ion cyclotron
heating and the magnetic nozzle [5]. A flowing plasma isheated by ion cyclotron range of frequency (ICRF)
heating and thermal energy of the heated plasma isconverted to flow energy in a magnetic nozzle.
We have demonstrated for the first time both the ion
cyclotron resonance heating and the acceleration of ionsin a magnetic nozzle [6]. Plasma flow was produced by
an MPDA installed in the HITOP (HIgh density TohokuPlasma) device in Tohoku University. Strong ion heating
was observed and the conversion of thermal energy toflow energy in a magnetic nozzle was confirmed. This
technology can be applied for production and control offast-flowing plasma in various applications.
In this paper we report experimental studies of afast-flowing plasma heated by ICRH and accelerated by adiverging magnetic nozzle in the HITOP device, Tohoku
University. We also obtained a fast-flowing plasma insupersonic and super-Alfvénic regime at the end of astrongly diverging magnetic nozzle.

Proceedings of ITC/ISHW2007

2. Experimental setup

3. Experimental results
3-1. Combined experiments of ICRH and a magneticnozzle
Experiments were performed with both amagnetic-beach and a diverging nozzle magnetic field
configurations. In Fig.1 the magnetic field configurationis also shown with a constant BU (=0.1T) at the antenna
position, a variable BD (corresponding to ion cyclotron
resonance condition) at the diamagnetic coil position, anda variable BN (corresponding to the EEA position ofdownstream region).
Figure 2 shows the typical waveforms of thedischarge current Id of the MPDA and the diamagnetic
coil signal W⊥. When radio-frequency (RF) waves werelaunched by a helically-wound antenna in a plasma
passing through a magnetic beach configuration, strong
increase of plasma thermal energy was observed, asshown in Fig.2 (b). We have confirmed that the strong
increase of W⊥ occurred when the magnetic field BD wasslightly lower than that of the ion cyclotron resonanceBB

BFig.1

Schematic of the HITOP device. Magnetic
field with magnetic beach and diverging
nozzle configuration is also shown.

RF on
2(a)

103

Thermal energy ,J/m Discharge current ,kA

Experiments were performed in the HITOP device inTohoku University [7,8]. Schematic view is shown inFig.1. The diameter of a cylindrical vacuum chamber is0.8m, and length is 3.3m. An external magnetic field canbe produced up to 0.1T with magnetic coils surroundingaround the vacuum chamber. An MPDA is installed at
one end port of the HITOP, which consists of coaxial pairof electrodes. A rod cathode is made of tungsten (10mmin diameter), and an annular anode is made ofmolybdenum (30mm in diameter). A quasi-steady plasma
was formed during 1ms by a high power MPDA withhelium as a working gas. The plasma was heated by RFwaves launched by a right-handed helically-woundantenna set at Z=0.6m downstream of the MPDA. RFfrequency fRF can be varied from 0.2MHz to 0.5MHz
with a RF power PRF up to 20kW.
Diamagnetic coil is set at Z=2.3m to measure theplasma thermal energy. Electrostatic energy analyzers(EEAs) are set at Z=2.33m and Z=3.13m to measure ion
energy distribution and ion temperature Ti⊥ and Ti//. Here,the suffix ⊥ and // indicate perpendicular and parallel
components to the axial magnetic field, respectively.
In the region far downstream of the MPDA, weevaluated ion acoustic Mach number Mi by a Mach probe.
The Mach probe has two plane surfaces, one of which
faced the flow upstream while the other faced
downstream. The ion Mach number could be derived as afunction of the ratio of two ion saturation current
densities, Jup and Jdown, The relationship between Mi and
Jup/Jdown was calibrated with the spectroscopic
measurements [9,10]

Fig.2

(b)

0.06
0.04

RF ON
RF OFFΔW

⊥

0.02

W⊥

000.5

11.5

2Time ,msTime evolutions of (a) Id and (b) W⊥ .
He plasma. fRF=0.24MHz.

condition, ω / ωci = 1. This shift was caused by theDoppler effect. Here, ω and ωci are the angular frequencyof excited RF wave and ion cyclotron motion,
respectively, and ωci is expressed as ωci = eB/mi withelectron charge e and ion mass mi.
The plasma thermal energy was converted to flowenergy in a diverging magnetic nozzle. We measured ion
temperatures by the EEAs in three types of magnetic
nozzle configurations. Figure 3 shows typical EEA
signals obtained before and after the nozzle with BD(Z=2.33m) = 57.5mT and BN (Z=3.13m) = 6.9mT. Strong
increase of ion temperature, especially in theperpendicular direction was occurred before the magneticBB

i⊥

T =18.9eVi//

w/o RF

10(a)
1-50

050
100 150Retarding voltage, V200

T =22.6eVi⊥

T =93.2eVi//

80
60
40
200(a)
22.5
3Axial position Z, m

3.5Fig. 4 Axial profile of Ti⊥ in the three magnetic
nozzle configurations. Lines are calculated
ones assuming μ =const. Closed triangles :BN=28.1mT, closed circles : BN=17.2mT,closed diamonds : BN=6.9mT.
B10B

1-50i⊥(b)

Ion temperature T , eVB

050100 150
Retarding voltage, V200Fig. 3
Electrostatic energy analyzer signals
measured at (a) Z=2.33m and (b) Z=3.13m.
He plasma. PRF=19kW, fRF=0.24MHz,
ne=1.0×1017m-3, BD=57.5mT, and BN=6.9mT.
B

100
T80i⊥
i//

60
40
2000Bnozzle. Ti⊥ increased from 5eV to 89eV with the RF input
power of 19kW.
The EEA signal decreased above the retarding voltageof 100V as shown in Fig.3 (a). The Larmor radius ofhelium ions becomes 5cm with Ti⊥ = 100eV and B =57.5mT, which almost equals to the plasma radius. The
highly-heated ions expanded to outer region and thesignal measured at the center position decreased above
the retarding voltage of 100V.
By passing through the diverging magnetic nozzle,
increase of Ti// and decrease of Ti⊥ were clearly observedin the analyzer signals shown in Fig.3 (b). This energy
conversion was occurred due to the conservation law of
the magnetic moment, μ (=W⊥/B).
Figure 4 shows an axial profiles of measured Ti⊥ inthe three magnetic fields. Profiles of Ti⊥ calculated byassuming μ =const. are also shown in the figure. It isconfirmed that Ti⊥ varied so as to keep the magnetic
moment constant but some discrepancy was observed inlarger gradient of the magnetic field. It should be caused
by a particle motion along a weak magnetic field.
We also measured axial profile of plasma potential
Vs by an electrostatic Langmuir probe and an emissive
probe. When RF wave was excited and ion heating wasoccurred, the potential decreased along the field line andaxial electric field was formed. The electric field(a) Z=2.33m

T51015RF input power P , kW20RF100Ti⊥

EEA signal, μA

100100i⊥

T =88.8eV

Ion temperature T , eV

EEA signal, μA

100

Ion temperature T , eV

Proceedings of ITC/ISHW2007i⊥

80(b) Z=3.13m

Ti//

60
40200051015RF input power P , kW

20RFFig. 5 Dependence of Ti⊥ (closed circles) and Ti//(open circles) on RF input power measured at(a) Z=2.33m and (b) Z=3.13m. fRF=0.24MHz,
ne=1.0×1017m-3, BD=57.5mT, and BN=17.2mT.
BB

appeared in a magnetic nozzle accelerates ions to thedownstream direction. The ion velocity distribution inparallel direction to the magnetic field was determined by
the energy conversion from the increased thermal energy
and the acceleration by the electric field. The formationof the electric field is probably due to the ambipolarelectric field, but further study is necessary to understandthis phenomena.
The ion acoustic Mach number Mi is one of theimportant parameters of an accelerated flow, which isdefined as the following equation

Proceedings of ITC/ISHW2007

UzUz=Csk B (γ eTe + γ iTi ) mi(1)0.12(a)Here, Cs is the ion acoustic wave velocity, Uz is ion
flow velocity, kB is the Boltzmann constant, mi is the ion
mass, and γ i and γ e are the specific heat ratios of the ionsand electrons, respectively. The square of Mi is relatedwith the ratio of flow energy to thermal energy of theflowing plasma. At the end of the magnetic nozzle region,
this ratio attained to more than 4, which corresponds toMi > 2, that is supersonic plasma flow was formed.
The parallel energy of exhausting plasma can bechanged by controlling the input RF power PRF. Figure 5
shows dependences of Ti⊥ and Ti// on PRF measured at
Z=2.33m (before the magnetic nozzle) and Z=3.13m(after the magnetic nozzle). As shown in Fig.5 (a),Ti⊥ increased linearly with the increase of PRF, whereas
Ti// slightly increased with PRF in the ion heating region(Z=2.33m). After the energy conversion in the magneticnozzle, Ti// strongly increased linearly with the increase of
PRF as shown in Fig.5 (b).
These experimental data clearly show that parallel
energy of exhausting plasma, thus also the ion Mach
number of the plasma flow, can be controlled bychanging the input RF power and/or modifying themagnetic nozzle configuration.

B (T)

Mi =

3-2. Supersonic and super-Alfvénic plasma flow in astrongly diverging magnetic nozzle
In order to realize super-Alfvénic flow, plasma flow
should exceed the Alfvén velocity VA. The Alfvén Mach
number MA is defined as the following equation.

[1] D.L. Meier, S. Koide,Y. Uchida, Science, 291, 84 (2001) ;M. Nakamura, Y. Uchida, S. Hirose, New Astronomy, 6,61 (2001)..
[2] V.V. Mirnov and A.J. Lichtenberg, Rev. of Plasma Physics(Consultant Bureau, New York-London, 1996), Vol.19,p.53.
[3] L.C. Steinhauer and A. Ishida, Phys. Rev. Lett., 79, 3423
(1997).
[4] S.M. Mahajan and Z. Yoshida, Phys. Rev. Lett., 81, 4863
(1998).
[5] F.R.ChangDiaz, et.al., Proc. of 36th Joint Propulsion Conf.,(Huntsville, 2000), AIAA-2000-3756, pp.1-8.
[6] A.Ando, et.al., Phys. Plasmas. 13, 057103 (2006).
[7] M. Inutake, et al., Trans. of Fusion Technology, 43, 118(2002).
[8] M. Inutake, et al., Plasma Phys. Control. Fusion, 49, A121
(2007).
[9] A.Ando, et al., Thin Solid Films, 506-507C, 601 (2006).
[10] A.Ando, et al., Contrib. to Plasma Physics, 46, 335 (2006).

Mi =Uz=VA BzUz

μ 0 ni mi(2)Here, VA is the Alfvén velocity, μ0 is permeability, niis the ion density.
We have measured ion Mach number by a Machprobe and ion density by Langmuir probe and obtained
axial profiles of Mi and MA in the diverging magnetic
field as shown in Fig.6. Here, no ICRF heating wasapplied. As is shown in the figure, both of Mi and MA
attained to more than unity, that is, supersonic andsuper-Alfvénic plasma flow was realized in a laboratory
plasma. Further experiments should be necessary with thecombination of ICRF heating.

Acknowledgments
This work was supported in part by Grant-in-Aid for
Scientific Researches from Japan Society for thePromotion of Science, and under the auspices of the NIFS
Collaborative Research Program (NIFS07KKMB001 andNIFS06KUGM018).

z0.08
0.04

A0i

Mach number M , M

B2M
1.5(b)

i

1
0.5
00.8

MA

1.2

1.6

2

2.4Z (m)Fig. 6 Axial profile of (a) magnetic field and (b)ion Mach number Mi and Alfvén Mach
number MA in the diverging magnetic nozzle
configurations.

References