J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

Plasma Acceleration in a Compact Helicon Source Using RF Antennae
Kyoichiro Toki,1Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei-city, Tokyo 184-8588 JAPANShunjiro Shinohara,2

Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, JAPANTakao Tanikawa,3Tokai University, 1117 Kitakaname, Hiratsuka, Kanagawa 259-1292, JAPAN

Tohru Hada,4Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, JAPANIkkoh Funaki,5Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, JAPANKostiantyn P. Shamrai6

Institute for Nuclear Research, National Academy of Sciences, 47 Prospect Nauki, Kiev 03680, UKRAINE

Yoshikazu Tanaka,7Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei-city, Tokyo 184-8588 JAPANandAkihiro Yamaguchi8
Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei-city, Tokyo 184-8588 JAPAN(Received: 31 August 2008 / Accepted: 6 December 2008)

The helicon wave excitation is one of the promising RF plasma production associated with a high density
plasma (~1013 cm-3) that enables electromagnetic acceleration. We newly employed an acceleration coil or 2 pairs ofcopper plates around the 2.5 cm o. d. glass tube. These methods are called a repetitious coil current acceleration anda continuous “Lissajous” acceleration, respectively. In case of the repetitious coil acceleration, the maximum
plasma velocity of 3.6 km/s was obtained with a 76% velocity increment with the absorbed plasma production +acceleration power of (400+180) W and the applied magnetic field strength of 1,450 gauss. As for the “Lissajous”
acceleration, the plasma velocity was 2.2 km/s with the absorbed plasma production + acceleration power of(290+200) W.
Keywords: electrodeless,

B
u
e
E
I
J
m
t

=
=
=
=
=
=
=
=
ν
=
ω
=
Subscripts
0
=
e
=
ela
=
i
=

electromagnetic acceleration,

Nomenclaturemagnetic field
velocityelectronic charge
electric fieldprobe current
current
ion, neutral and electron masstime
collision frequency
angular velocity

helicon,plasma production,

inela
para
perp
x
y
z

=
=
=
=
=
=

plasma acceleration

inelastic
pararell
perpendicularx direction
y direction
z direction

1. Introduction

Recently electric propulsions have attracted wider
attention with increasing opportunities in space
applications because of their capability to save more
propellant than the conventional chemical propulsions.
For this reason, the electric propulsions are employed forlong-term missions, such as interplanetary flight andsatellite attitude control. This implies that the electric

initialelectronelastic
ion

This work supported by Grant-in-Aid for Scientific Research (A), 17206084, Japan Society for the Promotion of Science
1. toki@cc.tuat.ac.jp, 2. sinohara@aees.kyushu-u.ac.jp, 3. tnth@keyaki.cc.u-tokai.ac.jp, 4. hada@esst.kyushu-u.ac.jp, 5. funaki@isas.jaxa.jp,
6. kshamrai@kinr.kiev.ua, 7. 50007643303@st.tuat.ac.jp, 8. 50004255119@st.tuat.ac.jp (The leading authour, Prof. Toki was deceased on May 26, 2009.)

25©2009 by The Japan Society of Plasma
Science and Nuclear Fusion Research

K. Toki et al., Plasma Acceleration in a Compact Helicon Source Using RF Antennae

direction with its amplitude proportional to the time
gradient of the applied magnetic field. The coil current
induced has a saw-tooth current waveform. When theLorentz force acts as an acceleration direction in a certain
period, the plasma is compressed and directly accelerated
toward downstream direction while the plasma isdecelerated during the reversed change of the coil current.
In order to prevent cancellation of acceleration with thisdeceleration phase, we took advantage of the differenceof the skin time between the acceleration and thedeceleration phases. The deceleration current decreases
rapidly, while the acceleration current increases slowly.
In this process, the deceleration force acts only theplasma periphery and the acceleration force acts the bulk
plasma. The ideal wave form is shown in Fig.1.

propulsion is required very long lifetime in order to keep
working for many years.
The electrodeless configuration is one of the long
lived electric propulsion solutions free from electrodeerosions [1-2], for example, VASIMR (Variable Specific
Impulse Magnetoplasma Rocket). This plasma source
based on the helicon plasma excitation which is one of
the RF plasma production methods [3-4]. The VASIMR
also employs a magnetic nozzle acceleration dependingon the ICRH (Ion Cyclotron Resonance Heating) as theplasma energisation, hence VASIMR can avoid
deterioration of the engine caused by electrode erosion[5]. However, the acceleration principle is based upon“plasma heating” and “passive nozzle expansion”
categorized into an electrothermal regime. Here, wewould like to propose an “electrodeless electromagnetic
acceleration” in smaller thrusters than VASIMR.
This paper describes a new type small electrodelesselectromagnetic thruster. A compact helicon plasma
source was prepared to produce high density plasma(~1013 cm-3) that enables the electromagnetic acceleration.
We already successfully established a helicon mode
plasma in a 2.5 cm i.d. glass tube [6-8]. The plasma
acceleration methods are divided into three categories.
They are electrostatic or electromagnetic acceleration in
addition to electrothermal acceleration such as VASIMR.
Our plasma acceleration is based on electromagnetic
principle [6], and employed two types of plasma methods
using a coil or an RF antenna.

B. Continuous “Lissajous” Acceleration of Plasma
Secondly, we proposed 2 pairs of deflection plates
around the glass tube to generate rotating electric field so
as to induce electron current continuously in azimuth
direction inside the cylindrical plasma. The ion current is
scarcely induced because of its larger inertia. This iscalled as “Lissajous” acceleration but this approachrequires important premises of the electric field
penetration into high density plasma. The analysis ofplasma acceleration is explained by using MHD
equations including j × B term and E must include thecollective plasma response.

dux= eEx − mν ux + euy Bz
dt
dum y = eEy − mνuy − eu x Bz
dtm

2. Principles of Electromagnetic Acceleration

A. Repetitious Coil Current Acceleration of Plasma
The first approach is the coil current acceleration thatinduces a diamagnetic electron current in the azimuth

Acceleration CoilAr gasxz
Ar Plasma exhaust
Glass tube SADDLE Antenna(a)Schematic of Coil acceleration device.

Jθ

J
(b)

J

S

eE 0
1
sin(ω t + φ )m (ω 0 − ω ) 2 + ν 2

uy =

eE0
m

1
(ω 0 − ω )2 + ν 2cos(ω t + φ )

(3)

(4)

ω0 − ων(5)

ν = ν ela + ν inela(6)

As far as the collision frequency ν remains in a
finite value, not the ions but the electrons due to theinertia difference, mainly contribute to rotational velocity
and current around z-axis by rotating applied electric

Sa Sb

J induced in plasma. (c) A saw-tooth current for the Coil.
Fig. 1.

ux =tan φ =

B
B×Jθ

(2)

Here, x, y, z are the coordinates depicted in Fig. 2 andω0 = eB/m. The solution of these differential equations
includes a general solution decaying exponentially by -ν t
and then only a special solution is valid and finallyremained as expressed below.

Electro Magnetic Coily(1)

Principle of a repetitious coil current acceleration.
26

K. Toki et al., Plasma Acceleration in a Compact Helicon Source Using RF Antennae

fields of Ex and Ey. The collision frequency must
involve elastic νela, inelastic νinela collisions and charge
exchange collisions νcex, if necessary.

Rotary Pump

RF-Amp. Signal Generator

Electro Magnetic Coil
RF Antenna
Ar gasOil Diffusion
Pump

Pirrani Vacuum Gauge
M.B.

y

x

Acceleration antenna

SADDLE ANTENNA

Mach Probez
Ar Plasma exhaust
Glass tube SADDLE Antenna(a)Electromagnetic coil

Schematic of “Lissajous” acceleration device.
yx z

Vy=V0cosωt Phase Shifter90°

Vacuum Chamber

M.B.

RF-Amp. Function Generator

Fig. 3. Experimental devices.

T020-5536A for 300 W acceleration amplifier withfrequency range of 1-16 MHz were used for RF powersource. In case of the continuous Lissajous acceleration,
two RF signals with external phasing each other are
amplified and input to the antennae via separate matchingboxes.

~

Vx=V0sinωt(b)~Concept of Rotation Electric field.

B. Probe for Measuring Plasma Velocity
We used a Mach probe shown in Fig. 4. [7] The Machprobe comprises two tips facing parallel andperpendicular to the plasma flow. Our Mach probe wasmade from 1.5 mm diam. copper rods with 45 degrees
tapered surfaces, the one parallel and the otherperpendicular to the flow. These rods are covered by 2
mm in diam. ceramic tubes. Here, ion acoustic Mach
number Mi is defined by ratio of plasma velocity to theion acoustic velocity Cs.
(7)
UU

Fig. 2. Principle of Continuous “Lissajous” Acceleration.

3. Experimental Procedures

A. Experimental Devices
Our compact helicon source consists of plasma
production portion, plasma acceleration portion and avacuum system. A 2.5 cm i.d. with totally about 30 cm
long pyrex glass tube connected to a vacuum chamber(Fig. 3). Ar gas is supplied from a metallic end plate witha gas port to the glass tube. The RF power for plasma
production and acceleration are applied during the Ar gas
flow along the glass tube toward the vacuum chamber. A
double saddle type (Boswell type) antenna is used forplasma production, and a 47 turn acceleration coil or apair of acceleration antennae downstream are used foracceleration. The vacuum chamber is evacuated down to
0.1 Pa (1 mTorr) or lower, and the Ar gas is fed by amass flow controller Brooks 5850E at a predeterminedmass flow rate, 0.5 mg/s corresponding to the backgroundpressures of 0.1 Pa (1 mTorr). A 489 turn coil magnet
produces 38 gauss/A up to 1,450 gauss maximum in the
midst of coil bobbin. A signal generator of HP-8657A
and a 500 Wmax amplifier of Thamway T145-5768A
with a matching box T020-5558A at the frequency 27.12
MHz for plasma production, and T145-5536 withMi =Plasma flowCs=

γ eTe + γ iTi

Iperp, Sb

Ipara, Sb

Iperp, Sa

Ipara, Sa
Mach Probe
Angle 0ﾟFig. 4miAngle 90ﾟ

Mach probe rotates around the centerline of the plasma.

The ion acoustic Mach number Mi is expressed as the27

K. Toki et al., Plasma Acceleration in a Compact Helicon Source Using RF Antennae

ratio of ion saturation currents collected by two probe
tips.

I paraI perpI paraI perp

=

Mi

(8)

κ

(

= exp aM i

1/ a), a = − ln κ

(9)Where, κ is dependent on the ratio of Ti/Te. In a
supersonic flow (Mi>1), Eq.(8) is used. But, in a subsonicflow (Mi<1), Eq.(9) is used.
To minimize the probe interactions with the plasma
ignition, the ceramic insulator as thin as 2 mm o.d. diam.
tube was used. The probe voltage was applied by abattery from -60 to +60 V. The probe current wasmeasured by a simple resistor. Both the probe voltage andcurrent traces are recorded by an Omniace RA1200
digital recorder and then analyzed by a personal computer.
The electron temperature was evaluated from the gradientof probe curve near the floating potential and the plasma
density was calculated from the ion saturation current.
To improve measurement accuracy, we developed aprobe assembly driver rotatable around the edge of Machprobe and making 2 positions at the angle of 0o or 90o
degrees. It enables to estimate the ratio of probe tips
area with sheath layer. Thus, we can obtain the tip area
ratio by using this assembly. If the ratio of ion saturation
currents at the angle of 0o is equal to that of 90o , theirrelationship is expressed below.

I para S a⋅= I 90I perp S b

I para S b⋅= I0
I perp S a

Fig. 5. Plasma velocity measurement of a repetitious
coil current acceleration at each absorbed RF
power (0o and 90o are the angles in Fig. 4).

(10)Here, Sa and Sb are the area of probe tip a and b,
respectively. Consequently, the ratio of probe tips area isexpressed as the following.

Sa
=
Sb

I 90
I0

Fig. 6. Electron temperature of a repetitious coil current
acceleration at each absorbed RF power (0o and
90o are the angles in Fig. 4).
were placed along the centerline of glass tube about 6.5
cm downstream position from the edge of theacceleration coil. The 47 turn coil for plasma acceleration
was wound around the 2.5 cm glass tube. The repetitious
coil current acceleration is done under the chamberpressure of 0.10 Pa, Ar gas flow rate of 0.4 mg/s, theforward plasma production power of 400 W at afrequency of 27.12 MHz, a plasma acceleration frequency
for the coil of 6 MHz, and the applied magnetic fieldstrength of 1,450 gauss. The applied saw-tooth waveform
exhibited the rise-time of 170 ns and the fall-time of 17
ns, actually not so sharp as shown in Fig. 1 (c).
The plasma velocity, electron temperature and plasma
density are shown in Fig. 5- Fig. 7. Here, “net absorbed
acceleration power” means the forward power minus
reflection power. The diamond and square plots are thedata for the probe angle of 0o and 90o degrees,(11)

By applying Eq.(11), we obtain the ratio of Ipara andIperp with high precision.

4. Experimental Results

Firstly, the axial and radial magnetic field intensity
were measured by gauss meter. The axial distance of 0
mm is the edge of double saddle type antenna set-up
point and axial distance of 20 mm is in the midst of coilbobbin. The magnetic field intensity at the acceleration
point (90 mm) was 800 gauss. The maximum of radial
magnetic field intensity was 330 gauss.
A. Repetitious Coil Current Acceleration Results
The measurement for various acceleration powers up
to 180 W were conducted. The tips of the Mach probe28

K. Toki et al., Plasma Acceleration in a Compact Helicon Source Using RF Antennae

continuous “Lissajous” acceleration under the conditionsof the chamber pressure of 0.13 Pa, Ar gas flow rate ofrespectively. The solid line implies the averaged data at
0o and 90o. Figure 5 shows plasma velocity increases, as

Fig. 7. Plasma density of a repetitious coil current
acceleration at each absorbed RF power(0o and 90o
are the angles in Fig. 4).

Fig. 8 Plasma velocity at each phase difference in“Lissajou”acceleration (0o and 90o are the angles

in Fig. 4).
0.5 mg/s, the absorbed plasma production power of 290
W at frequency of 13.56 MHz, the absorbed plasma

the applied acceleration power increases. The velocity
was increased by 76 % compared with the value before
acceleration at the max power of 180 W. Similarly, themore the applied acceleration power increases, the more
the electron temperature increases. At the maximum
power of 180 W, it indicates about 2.2 times increase
compared with before acceleration. This implies that theplasma velocity increase was brought about by thermal
acceleration process. On the other hand, the plasma
density is decreased as the plasma is accelerated. Thus,
the product of density × electron temperature seems to beconstant with RF power. When we adopted a repetitious
coil current acceleration method, the RF power wasabsorbed into electrons to raise the electron temperatureand this results in the electrothermal acceleration. Our
final goal is to have plasma electromagneticallyaccelerated. At present, we have found that one of thereasons of insufficient electromagnetic acceleration is dueto the incomplete formation of the saw-tooth waveform.
The required steep gradient of the deceleration period ismoderated by the filter of the matching box. The coilcurrent through the matching box, the saw-tooth
waveform tends to change into a sinusoidal waveform.
We should solve this problem in the next step.

Fig. 9

Electron temperature at each phase difference in“Lissajous” acceleration (0o and 90o are theangles in Fig. 4).
acceleration power of 200 W at frequency of 15 MHz andthe applied magnetic field strength of 1,450 gauss.
The diamond and square plots are the data which
represent the probe angle of 0o and 90o degrees,
respectively. The solid line in the figures is average ofmeasuring data at 0o and 90o probe positions and dottedline denotes the case applied only plasma production
power. In Fig. 8, it was recognized that the plasma
velocity was increased by 50% compared to the before
acceleration and resulted in 2.2 km/s. This is notsatisfactory result because our goal in this power level is
14 km/s corresponding to 50% thrust efficiency. This
result implies that only a little amount of the acceleration

B. Continuous “Lissajous” Acceleration Results
Figures 8-10 exhibit the results of measured plasma
velocity, electron temperature and plasma density for“Lissajous” acceleration. The tips of the Mach probe areplaced 6.5 cm downstream location from the edge of theantennae and rotated at the position. We tried a29

K. Toki et al., Plasma Acceleration in a Compact Helicon Source Using RF Antennae

power was absorbed by plasma and the rest of the power
was dissipated as circuit loss or vacuum loading.
The electron temperature revealed small decrease at
all phase differences. This indicated that the power for
acceleration was not absorbed by electrons. On thecontrary, the plasma density showed slight increase at allphase differences. This result implies that the plasma wascreated by applying RF power of acceleration, or otherfactors like plasma space potential have some effects on
this measurement. The principle of continuous“Lissajous” acceleration is based on electrons rotational
drift motion. The RF electric field penetrating radiallyinto plasma was not measured but predicted by Shamrai

collision between electrons and neutrals under thispressure is nearly equal to the acceleration frequency. To
avoid this problem, we should maintain the acceleration
region at higher vacuum condition than ever. Thissituation would be realized to lower the Ar gas flow rate,
to place whole the device inside the vacuum chamber, orto increase the acceleration frequency of the amplifier.
We need to ascertain the best shape of RF antenna for theplasma electromagnetic acceleration attempting various
RF matching conditions for higher absorption efficiency.
Figure 11 is an experiment of a repetitious coil current
acceleration. In the interior of the magnetic coil of thebottom picture, the plasma emits blue light. This shows aso-called “blue mode” of helicon wave excited plasma.

5. Conclusion

Fig. 10For the repetitious coil current acceleration method,
the maximum plasma velocity was 3.6 km/s. It was 76 %velocity increment compared with the value before
acceleration under the chamber pressure of 0.10 Pa, Ar
gas flow rate of 0.4 mg/s, the absorbed plasma production
and acceleration power of (400+180) W, the coil of 47
turns and the applied magnetic field strength of 1,450
gauss. However, the electron temperature was raised up
to about 2.2 times higher than the value before
acceleration. This implies that the increment of plasma
velocity is done by thermal process.
For the continuous “Lissajous” acceleration method,
the plasma velocity was 2.2 km/s under the chamberpressure of 0.13 Pa, Ar gas flow rate of 0.5 mg/s, theabsorbed plasma production and acceleration power of(290+200) W, the coil of 47 turns and the appliedmagnetic field strength of 1,450 gauss.

Plasma density at each phase difference (0o and 90o

are the angles in Fig. 4).
about 10 V/cm at the plasma center and this value
increases toward the plasma periphery [8]. The
acceleration profile in radial direction is similar to thiselectric field distribution. However, as shown in Fig. 8,
the plasma velocity did not reveal remarkable
acceleration / deceleration corresponding to the signchange of electron motion with the phase difference. The
electromagnetic acceleration may not fully take place but
the electrothermal acceleration is dominant because the6. References[1] K. P. Shamrai, et al., J. Physics IV, France 7, C4, pp.
365-381 (1997).
[2] K. Toki, et al., IEPC 03-0168, Proc. of the 28th International
Electric Propulsion Conference, Toulouse (2003).
[3] S. Shinohara, J. of Plasma and Fusion Research, 78, 1, pp.
5-18 (2002).
[4] C. Charles, R. Boswell, et al., AIAA-2006-4838, 42nd
AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Exhibit, Sacramento (2006).
[5] J. P. Squire, F. R. Chang Diaz, et al., AIAA 2000-3752,
36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference,
Huntsville (2000).
[6] K. Toki, S. Shinohara, T. Tanikawa and K. P. Shamrai,
ELSEVIER, Thin Solid Films, 506-507, pp. 597-600 (2005).
[7] A. Ando, et al., J. of Plasma and Fusion Res., 81, 6, pp.
451-457 (2005).
[8] K. Toki, et al., AIAA 2004-3935, 40th AIAA/ASME /SAE
/ASEE Joint Propulsion Conference, Huntsville (2004).

Fig. 11. Experiment of a repetitious coil current acceleration.

30