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

Characteristics of Large Diameter, High-Density
Helicon Plasma with Short Axial Length
Using a Flat Spiral Antenna
Taisei MOTOMURA, Kenji TANAKA, Shunjiro SHINOHARA,Takao TANIKAWA1) and Konstantin P. SHAMRAI2)
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
1)
Research Institute of Science and Technology, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan2)
Institute for Nuclear Research, National Academy of Sciences, Kiev 03680, Ukraine(Received: 1 September 2008 / Accepted: 14 October 2008)

A large diameter (up to 73.8 cm), high-density helicon plasma with short axial length (≤ 81 cm)
has been successfully produced using a ﬂat spiral antenna. The electron plasma density can reach up
to ∼ 1013 cm−3 with the input radio frequency (rf) power of < 4 kW for various axial lengths, and thedensity scaling as a function of the axial length is in good agreement with expectations. The stronger
the degree of magnetic ﬁeld convergence from the antenna to the bulk plasma region is, the lower
the minimum input rf power required to obtain a helicon plasma is. In the convergent magnetic ﬁeld
conﬁguration, radial proﬁles of the excited rf magnetic ﬁeld show the exicitation of higher order radialmode in addition to the component of the fundamental one. The manifestation of higher order mode isclosely related to the magnetic ﬁeld conﬁguration and the rf radiation pattern of the ﬂat spiral antenna.
Keywords: helicon plasma, density jump, high order radial mode, short axial length, ﬂat spiral antenna
diameter is 2.5 cm, resulting in A = 1.9 that is larger
than ours.

1. Introduction
High-density helicon plasmas [1-4] are potentiallyvery useful in various plasma applications, such as inplasma processing, fusion, basic science ﬁelds including space plasmas and the development of magnetoplasma rockets. Using a helicon wave for plasma production gives advantages of having an easy operationand having a wide range of operational parameters.
Developing a large volume plasma source with a large
diameter is also important, and a high-density helicon plasma with very large plasma volume (up to 2.1m3 ) has been obtained using a device at ISAS/JAXA(Institute of Space and Astronautical Science/JapanAerospace eXploration Agency) [5-8].
However, having a shorter axial length with alarge diameter (or a lower aspect ratio A, where A
is the ratio of the axial length to the diameter) is often desirable in some of the above applications, e.g.,
the plasma processing and a magnetoplasma rocket.
Therefore, using the same device at ISAS/JAXA, wehave attempted to eﬀectively shorten the plasma column length from 486 cm to as short as 12.5 cm byinstalling a termination plate inside the chamber [Fig.
1 (a)], reducing A from 6.6 to 0.17.
Here, we report the successful production of ahigh-density helicon plasma with 0.17 ≤ A ≤ 1.1,
which is much smaller than the aspect ratio of plasmas produced in conventional helicon sources. Notethat although the axial length of the shortest helicon
plasma ever produced is a mere 4.7 cm [9], the plasma

2. Experimental Setup
Langmuir Probe

Magnetic Probe(a)
Termination PlatePlasma
ArI.D.
73.8 cm

Flat-SpiralAntenna
Separate CoilTurboPump

14 Magnetic Field Coils
Permanent Magnets

z = 0 cm(b)z = 486 cm

I s = 100 A
80 A
60 A

40 A
20 A0AFig. 1 (a) Schematic drawing of plasma device. (b) Axial
magnetic ﬁeld conﬁgurations for various values ofthe separate coil current Is at radial position r = 0cm.

In our device at ISAS/JAXA [5-8] [Fig. 1 (a)],the size of vacuum chamber is 73.8 cm in inner diameter and 486 cm in axial length. The magnetic ﬁeld

author’s e-mail: tmoto@aees.kyushu-u.ac.jp

6©2009 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchT. Motomura et al., Characteristics of Large Diameter, High-Density Helicon Plasma with Short Axial Length Using a Flat Spiral Antennais produced by 14 main coils and a newly installed
separate coil which is located at the axial positionof z = 0 cm. The magnetic ﬁeld conﬁguration near
the antenna can be more ﬂexibly controlled using thisseparate coil than using the old one used in the previous experiments [5-8], as shown in Fig.1 (b) (the 14main coils generate the uniform axial ﬁeld of 140 G in
the central region). A 4-turn ﬂat spiral antenna, 43
cm in diameter, is connected to the rf power supply(maximum power of 5 kW with 7 MHz excitation frequency) through a matching circuit. The rf radiation
pattern from the antenna can be varied by changing
the number of spiral turns used for plasma production
as discussed in the previous papers [5-8]. The termination plate placed at zE = 12.5 - 81 cm is made ofa stainless steel punching plate, 0.5 mm thick, witha transparency of ∼ 35 %, and is electrically ﬂoating (zE is the axial position of the termination plate).
Permanent magnets (the ﬁeld strength at the surface
is 1 kG) are installed at one end of the chamber toform a multi-mirror surface ﬁeld inside the chamber[7]. A Langmuir probe and a magnetic probe are used
to measure the spatial proﬁles of ion saturation current and the z-component of the excited rf magnetic
ﬁeld, respectively. The working gas is argon with a ﬁllpressure of 0.75 mTorr.

Fig. 2 Electron density ne as a function of the rf input
power Pin with 486 cm axial length for diﬀerent
values of the separate coil current Is : (a) 0 A, (b)20 A, (c) 40 A, (d) 60 A,(e) 80 A and (f) 100 A,respectively. A Langmuir probe is at radial position
rp = 7.5 cm and axial position zp = 31.5 cm.

3. Experimental Results
First, we show the case with full plasma axial
length of 486 cm to estimate the eﬀect of the shortaxial length. Figure 2 shows the electron density ne
as a function of the rf input power Pin for six diﬀerent magnetic ﬁeld conﬁgurations realized by changing
the separate coil current Is [see Fig. 1(b)]. The vertical bars show the threshold power Pth , at which thedensity jump from an inductively coupled plasma to ahelicon plasma occurs. Typical values of ne in helicon
plasma discharge are ∼ 1013 cm−3 in all cases. With
the increase in the magnetic ﬁeld near the antenna,i.e., with the increase in Is , the position of Pth becomes clearer and the value of Pth increases. Further
increase in Is (to 100 A) shows no density jump for
Pin ≤ 4 kW.
Figure 3 shows ne as a function of Pin for two different axial lengths: zE = (a) 54.5 cm and (b) 34.5cm. Similar to the 486 cm length case ([5-8] and Fig.
2), the position of Pth becomes clearer and the valueof Pth increases even for the shorter axial length caseswith the increase in Is . These results are also consistent with the general tendency that the higher magnetic ﬁeld (uniform ﬁeld case) needs more rf power tohave helicon jumps [10]. Note that the plasma production eﬃciency, Ne /Pin (Ne : total number of electrons)of ∼ 3 × 1013 W−1 , is by more than one order of magnitude smaller than that of the 486 cm axial length

case: ∼ 1015 W−1 . This is due to the fact that shortening the axial length results in the enhancement of
the axial ion loss relative to the radial one [8].
Figure 4 shows helicon plasma production eﬃciency Ne /Pin as a function of the axial plasma length
L with Is = 20 A and 60 A. For the case of a shorter
axial length, the axial ion loss is much larger than theradial loss and is dominant. Therefore, Ne /Pin is expected to be proportional to L [8], which predicts thedotted line in Fig. 4 with a proportionality coeﬃcient
being roughly a factor of two lower than expected values [8]. From this, we can see a good agreement between the measurement and the prediction. We notethat the values of Ne /Pin for our shorter axial length
cases are still comparable or higher than those for theother small helicon devices (see Fig. 8 in [8]).
Figures 5(a) and 5(b) show the measurement of
the radial and axial proﬁles of B̃z /|I˜A |, the ratio of
excited rf magnetic ﬁeld to rf antenna current amplitude, respectively. Proﬁles at twelve phases during

7T. Motomura et al., Characteristics of Large Diameter, High-Density Helicon Plasma with Short Axial Length Using a Flat Spiral Antenna

Fig. 3 Electron density ne as a function of the rf input
power Pin for diﬀerent axial lengths: (a) zE = 54.5cm and (b) zE = 34.5 cm. The open circles andblack circles show the data taken at Is = 20 A and
Is = 60 A, respectively. Here, the position of Langmuir probe is at rp = 0 cm and (a) zp = 25 cm and(b) zp = 15 cm.

Fig. 5 (a) Radial and (b) axial proﬁles of the ratio of theexcited rf magnetic ﬁeld to the rf antenna current,B̃z /|I˜A |, with Is = 60 A, Pin ∼ 1.9 kW , zE =81 cm and the use of 2 turns (measurement). The
magnetic probe is located at zp = 51.5 cm for (a).
Thick lines are used for an eye-guide.

lation results in Fig. 6(a) are in good agreement withthe experimental ones in Fig. 5(a). In the calculation,
the following parameters are used: the amplitude ratioof J0 (k⊥2 r) to J0 (k⊥1 r) terms is 0.51, and the phase
diﬀerence at measurement position between the twowaves of the fundamental and the 2nd order modes is-6.5 degree.
Generally, a pure standing wave is represented
by the summation of propagating and reﬂected waves
without the damping eﬀect, meaning that their amplitudes are the same. Figure 6(b) shows the result of
the calculation in which a damping propagating wave
and partially reﬂected wave by the termination plate
are summed up. In our calculation, the eﬀects of thewave damping, the 2nd order radial mode, and theaxial boundary (the termination plate with the reﬂection coeﬃcient of 50 % is located at zE = 81 cm) areincluded. It can be seen that the wave pattern as wellas the parallel wave number obtained in the calculation [Fig. 6(b)] is nearly equal to that obtained in ourexperiment [Fig. 5 (b)].
Note that in the shortest case of zE = 12.5 cm, theaxial mode number of ∼ 3/4 is excited, which can beunderstood from the free (ﬁxed) boundary condition

Fig. 4 Plasma production eﬃciency Ne /Pin (Ne : total
number of electrons) in the helicon discharge as afunction of the plasma length L. The dotted line isa predicted curve of Ne /Pin ∝ L to ﬁt the experimental data. Typical error bar is also shown.

one rf period at Is = 60 A and zE = 81 cm are shown.
For comparison, Figs. 6(a) and 6(b) show the calculation of the radial and axial proﬁles of B̃z , respectively,based on ref. [11] and the following discussions using
the experimental values. Note that the vertical axis isnormalized by the amplitude of the fundamental mode
expressed as J0 (k⊥1 r), which will be described later.
Contrary to the expectations, the observed radial
proﬁle is not a simple fundamental mode of the Bessel
function J0 (k⊥1 r) with m (azimuthal mode number)= 0, where, k⊥j a is the jth zero of the J1 Bessel function (a: eﬀective plasma radius). Our data can be
expressed as a combination of at least two Bessel functions: J0 (k⊥j r) with n = 1 and 2 [12, 13]; the calcu8

T. Motomura et al., Characteristics of Large Diameter, High-Density Helicon Plasma with Short Axial Length Using a Flat Spiral Antenna

Fig. 6 (a) Radial and (b) axial proﬁles of B̃z (calculation).
The amplitude ratio, (1st radial mode) / (2nd radial mode), is 1 / 0.51 and the phase diﬀerence
between two modes at z = 51.5 cm is -6.5 degree.
The wave reﬂection coeﬃcient at the termination
plate is 50% for the calculation of axial proﬁle.

Fig. 7 Radial proﬁles of B̃z /|I˜A | for two diﬀerent magnetic
ﬁeld conﬁgurations by changing the separate coilcurrent Is and two antenna radiation patterns measured at zE = 81 cm and zp = 51.5 cm for three
diﬀerent cases. The separate coil current Is , thenumber of antenna turns used, and the input rf
power Pin , respectively, are: (a) 60 A, 2 turns and∼ 1.9 kW, (b) 60 A, 4 turns and ∼ 3.4 kW, and (c)20 A, 4 turns and ∼ 1.7 kW.

at the antenna side (termination plate) of z = 0 (12.5)
cm, i.e., the axial mode number n = 1/4 + p/2 (pis the integer more than zero and here p = 2) can be
excited from this boundary condition.
Figure 7 shows the axial proﬁles of B̃z /|I˜A | for different magnetic ﬁeld conﬁgurations (by changing Is )and the diﬀerent antenna radiation patterns. The contribution of the higher order radial modes becomes
more important as Is is reduced (i.e., the degree ofthe magnetic ﬁeld convergence is stronger) and thenumber of antenna turns used is increased. It appears
that the magnetic ﬁeld conﬁguration [14] and the radial density proﬁle play very important roles in theexcitation of the higher order radial modes. Preliminary theoretical results indicate that the excitationof the higher order radial modes is more signiﬁcantwith the peaked radial density proﬁle. The next stepis to fully understand the excitation mechanism of thehigher order radial modes.

(12.5-81 cm), high-density helicon plasma (up to ∼1013 cm−3 ) with an rf power of < 4 kW, showing
the m = 0 helicon wave structure. The magnetic
ﬁeld conﬁguration near the antenna critically inﬂuences the plasma production. In the higher magnetic ﬁeld strength near the antenna, the higher rf
input power is necessary to achieve a helicon density jump. The plasma production eﬃciency Ne /Pinis ∼ 4 × 1012 − 3 × 1013 W−1 , which agrees with theexpectations and is higher than that in the other small
diameter machines. The exicitation of higher order radial modes is considered to be related to the magnetic
ﬁeld conﬁguration and the radial density proﬁle.

4. Conclusions
To summarize, we have successfully produced alarge diameter (up to 73.8 cm), short axial length9T. Motomura et al., Characteristics of Large Diameter, High-Density Helicon Plasma with Short Axial Length Using a Flat Spiral Antenna

5. Acknowledgements
Our experiments were performed at ISAS/JAXA
under their research collaboration program. We thankDr. I. Funaki, Dr. S. Sato, Dr. T. Takeda andProf. K. Yamagiwa for their assistance in carryingout the experiments. The research was partially supported by the Grants-in-Aid for Scientiﬁc Research(A) 17206084, (B) 20340163 and (C) 19540524 fromthe Japan Society for the Promotion of Science.
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