九 州 大 学 大 学 院 総 合 理 工 学 報 告第27巻 第4号 355-360頁 平 成 18 年 3 月

Engineering Sciences Report, Kyushu University
Vol.27, No.4 pp.355-360, MAR. 2006

Spatio-Temporal Behavior of Bistable Density Transitionin Magnetized Plasma
Shunjiro SHINOHARA*1,† Katsuhisa SUGIMORI*2
Yasushi NAKAMURA*3 and Masatoshi YAGI*4
E-mail of corresponding author: sinohara@aees.kyushu-u.ac.jp†(Received January 31, 2006)
Self-excited bistable transition phenomena have been investigated by voltage biasing to an inserted electrode of a radio frequency (rf)-produced, magnetized plasma. Spatio-temporal behaviors ofglobal, density transitions and back ones between two states (flip-flop pattern) have been measured,
as to the ion saturation current Iis and floating potential Vf in the bulk plasma and near the electroderegions. Transition time Ttr between two states was dependent on the bulk region, and it was lessthan ms and ~ a few ms for Iis and Vf, respectively. On the other hand, Ttr was very small for the bias
current on the order of ~ µs, and it was also small for Iis and Vf, which have less than a few tens of µs
near the electrode region, where structural changes of plasma potential and density were observed at
the transition. These showed the importance of the sheath, electrode region to trigger the transition
coming from the two-dimensional particle balance and motion with sheath type instabilities.
Key words: Plasma, Transition, Bistability, Self-excitation, Biasing, Electrode, Electric field, Magnetic

field

1.

Introduction

Transition and bifurcation phenomena inplasmas have been supplying many various
interesting topics in the fields of basic nonlinear physics as well as the fundamental plasma
physics including fusion-oriented research.
The intrinsically nonlinear characteristics ofthe plasma exhibit various interesting phenomena 1-19) such as the self-organized structural formation including hystereses. However,there have been few experiments 5-9) from abasic viewpoint to study these transitions.
Recently, density transitions in bistablesystems were clearly found and reported 20,21),
by voltage biasing to electrodes inserted into
the rf-produced, cylindrical magnetizedplasma: density transitions and back ones
between two global states, accompanied bypotential changes. Control of the staying timeand staying probability in one of two states, by*1 Department of Energy Engineering Science*2 Department of Advanced Energy Engineering Science,
Graduate student (Present Address: Komatsu
Electronic Metals Co., Ltd.)*3 Department of Advanced Energy Engineering Science,
Graduate student (Present Address: Sharp Electronics
Corp.)*4 Research Institute for Applied Mechanics

changing the bias voltage, was tried, with alsoemphasizing hysteresis characteristics in astatistical sense. Although general features oftransitions were found in the previous papers
20,21), simultaneous spatio-temporal behaviors
were not obtained due to the limited channelsof the probes and the data acquisition system.
Furthermore, the structures near the electrodehave not been measured in spite of suggesting
its importance of triggering transitions.
Here, we have examined spatio-temporal
behaviors of global characteristics of aself-excited bistable system from a viewpoint of
the transition times of parameters such as ion
saturation current Iis, floating potential Vf, andbias current Ib, in order to have a clue of thetriggering / governing mechanisms of transitions. In addition to the bulk plasma region,
plasma behaviors in the sheath region (nearthe electrode) were investigated to understandthe short transition times such as Ib, since thepotential structure change in this region due tosome instabilities, e.g., sheath type instabilities, is considered to initiate the transitions.
Note that these measurements have beenpossible due to an introduction of the new dataacquisition system, multi-channel probe array,and three-dimensional moving system 22) located near the electrode.

356

Spatio-Temporal Behavior of Bistable Density Transition in Magnetized Plasma

2.

Experimental Results

2.1

Experimental setup

A typical argon pressure of P0 = 1-3 mTorr
with the continuous rf power and frequency of
Prf = 160 W and frf = 7 MHz, respectively, wereapplied to a linear device, 45 cm in outer diameter and 170 cm in axial length, with themagnetic field of 500 G, as shown in Fig.1(a).
Here, x (z) is taken along the radial (axial) direction. We used ten concentric rings as biased
electrodes 6,7,9), and the no. 3 electrode (innerand outer radii are 3.7 and 6 cm, respectively)
was used. In addition to the conventional
Langmuir probes, we newly installeda 24-channel probe array, as shown in Fig.1(b),and three-dimensional probe moving system 22).
Note that the frequency responses in measuring Iis and Vf were more than 50 kHz and lessthan 10 kHz, respectively.
Most of the data were stored in the datalogger with a sampling time of 10 µs. With theuse of the current probe and additional logger,
which has the faster sampling time of 50 ns,
we could observe the fast change of Ib. For

(a)

2.2

Spatio-temporal behavior and transition
time

Figure 2 shows an example of the spatio-temporal behavior as to the global changeof radial Iis (proportional to plasma density)
and Vf profiles at z = 30 cm by the 24-channel
probe. Transition time Ttr was dependent onradial position, and there were some differences of this time between transitions fromstate I (Iis was large away from the No.3 electrode axially and in the outer radial region ofthis electrode) to state II (Iis was small in theabove mentioned regions) and from state II tostate I. For convenience, this time is defined as
the elapsed time to take the values from 20 %to 80 % of the difference between averaged
values in state I and state II.
Figure 3 shows Ttr of Iis and Vf for different
axial locations, taken at x = 9 cm (in the outerradial region of the electrode). Both Iis and Vf
Ar GasTen Concentric Rings(z = 95 cm)
To Pump44.5 cm (I.D.)

Langmuir Probe 24ch. Probe(z = 15 cm) (z = 30 cm)

controlling the state from I to II or vice versa
dynamically, a function generator and an amplifier were also used to change the bias voltage V3.

SpiralAntenna
RF (7 MHz)zx

Mach Probe(z = 30 cm)

2D Langmuir Probe 3D Langmuir Probe Magnetic Field
Coils(z = 90 cm)(z = 60 cm)
170 cmφ
W (0.1 cm , 0.3 cml)

ch. 3 ch.1

ch.23

ch.24

2.7 cm

(b)

ch.2

ch.22

2.8 cm26.7 cm
Macor
Fig.1

Schematic view of (a) experimental setup and (b) 24-channel probe array.

平成18年

九 州 大 学 大 学 院 総 合 理 工 学 報 告Transition Time (ms)

0.8

(a)

第27巻

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357

(a) Iis0.6

from State II to State I

0.4
0.2
0.0

from State I to State II
10 20 30 40 50 60 70 80 90 100

Transition Time (ms)z (cm)(b)8(b) Vf6

from State I to State II4
20from State II to State I

10 20 30 40 50 60 70 80 90 100

z (cm)

Spatio-temporal behaviors of (a) ion saturation
current Iis and (b) floating potential Vf (different
shots) at z = 30 cm with bias voltage V3 = 160 V
and fill pressure P0 = 2.1 mTorr, measured by
the 24-channel probe.

showed nearly constant Ttr regardless of theaxial position. Typical Ttr of Iis was less than
0.5 ms, and Ttr from state I to state II issmaller than that from state II to state I (seealso Fig.2). On the other hand, typical Ttr of Vf
was on the order of a few ms, and Ttr from state
I to state II is larger than that from state II tostate I (see also Fig.2). From this, transitions
occur globally at nearly the same rate regardless of the axial position.
Figure 4 shows Ttr of Iis and Vf for different
radial locations, by the 24-channel probe. Different transition times depending on radial
locations were found. There was a tendency
that Ttr, for both transitions of from state I tostate II and from state II to state I, wassmaller in the inner radial region of the electrode than that of in the outer region in bothcases of Iis and Vf. This may be related to thesmaller plasma volume, which can change theequilibrium in the shorter time if the phenomena between the inner and outer regions
are similar. Here, the case of the transition
from state I to state II in Iis is an exception: Ttr
was nearly constant of ~ 0.2 ms along the radial direction.

Transition times of (a) Iis and (b) Vf on different
axial locations. Here, data are taken at x = 9 cm
with V3 = 157 V and P0 = 1.8 mTorr.

1.8
Iis
1.6
from State II
1.4
to State I
1.2
1.0
0.8
from State I
0.6 to State II
0.4
0.2
0.0
-20-18-16-14-12-10 -8 -6 -4 -2 0(a)2x (cm)
8

Transition Time (ms)Fig.2

Transition Time (ms)Fig.3(b) Vffrom State I
to State II

64from State II
to State I2
0-20-18-16-14-12-10 -8 -6 -4 -2 0

2x (cm)
Fig.4

Transition times of (a) Iis and (b) Vf as a function ofradial position for the same condition as that inFig. 2. Radial position of no. 3 electrode is denoted
as a horizontal closed bar.

358

Spatio-Temporal Behavior of Bistable Density Transition in Magnetized Plasma

2.3

Plasma behavior near electrode

Since the importance of the transitions near
the electrode region was suggested, the spatio-temporal behaviors near this region were
investigated using the scanned Langmuirprobe in three-dimensional direction 22). Figure
5 shows the spatial profiles of Iis and Vf in state
I and state II. Mostly, this probe was moved
along the arc trajectory, as shown in the insetof this figure. The probe position at θ = 12o(15.5o) corresponds to the outer radial edge ofthe no.2 electrode (the surface of no.3 electrode). From this, Iis decreased slowly (did notchange so much) toward the electrode with θ =12o-15.5o in state I (state II). This Iis was larger
in state II than that in state I, which is the
opposite behavior in the bulk plasma region,
where Iis was larger in state I than that instate II.
No. 3
No. 2

x

There is a slight hump of Iis in state IIaround θ = 13.5o, which may correspond thehump of Vf (virtual anode-like) observed in Fig.
5(b). In state II, Vf was higher than that instate I by > 20 V. In state I, the value of Vf was
lower than that in the central region (along thez axis) with x = 5 cm by > 15 V, which showsthat the electrons can be trapped easily in thecentral region. This is consistent with the factthat in the bulk plasma region Iis in state I islarger than that in state II. On the other hand,
although the sampling time of 10 µs is notenough, Iis near the electrode region, regardless of θ, changed very fast (< 10 µs transitiontime) on the same order of the changing time ofIb, which is much faster than the change of Iis
in the bulk region. Here, Tr of Vf was also smallof less than a few tens of µs (this time is limited by the measuring system mentioned before). These also show the importance of density transition near the electrode region in addition to the fast Ib change written below.

z

0.10

●
●

0°

(a)

Trajectory of Probe

Ib (A)

0.8

(a)

●

12°
15.5°

0.05

0.00

State II

0.4
Main

0.2
0.0
9

40

-50

10

11

No. 2

(b)

V f (V)

13

14

15

θ (degree)

16

0.08

No. 3

0.06

State II

150

200

(b)

0.04
0.02

-0.02

Region

0
9

100

0.00
Main

10

Fig.5

12

50

time (µs)

State I30
20

0RegionIb (A)Iis (arb. units)

0.6State I

10

11

0

5

10

15

time (µs)

12

13

14

15

No. 2

θ (degree)

16
No. 3

Spatial profiles of (a) Iis and (b) Vf near the electrode with V3 = 177 V and P0 = 1.2 mTorr. Typicalvalues of Iis and Vf in the main region at the sameradial location of no. 3 electrode are shown as arrows, and inset shows a trajectory of the probe.

Fig.6

Time evolution of (a) Ib with P0 = 3.5 mTorr fromstate I to state II by the fast rise of V3 from 110 V
to 210 V. Here, Fig. (b) shows time change of Ib of
Fig. (a) in an expanding time scale.

This Ib change was carefully measured in acontrolled manner. As was described, the function generator and the amplifier were used inaddition to the fast logger with a sampling平成18年

九 州 大 学 大 学 院 総 合 理 工 学 報 告time of 50 ns. Note that this does not mean the
self-excited transition, but the forced transition. However, general characteristics such as
the Ttr of Iis and Vf were not changed. Figure 6
shows the time evolution of Ib by the fast rise of
V3. Here, the initial (final) voltage V3 = 110 V(210 V) corresponds to state I only (state IIonly). At t ~ 350 ns Ib had a sharp overshot
positive spike, as is shown as an arrow in
Fig.6(a), which can be clearly seen in Fig.6(b)in an expanding time scale for a different shot
(there was a drift of Ib: baseline of this current,
i.e. zero current, is -10 mA).
The real rise time of Ib is shorter, which isestimated to be less than several tens of ns, if
considering the rise time (~ 300 ns) of V3. Then,the fast decay (e-folding time was < 400 ns)
was observed, and after t = 1.2 µs [the second
chained vertical line in Fig. 6(b)], Ib became
steady with some fluctuations. Here, the oscillation period of 143 ns superimposed on thisIb corresponded to the 7 MHz frequency of therf power source. Sometimes we could see thefine different structures even in the same stateof “state II”, which was suggested from the
distribution function of Iis in Ref. 21: at t = 64
µs [a vertical dotted line in Fig. 6(a)], there
was the second jump of Ib and it occupied thisnew state steadily after that.

3.

Discussion and Conclusion

The spatio-temporal characteristics of bistable system in a magnetized plasma are discussed, focusing on the triggering/governing
mechanisms. This mechanism, which will be
described later in detail, can be considered asfollows as a promising candidate: a kind of thesheath type instabilities to change the potential structure near the electrode causes the fastchange of Ib by the electron motion along thefield on the order of less than several tens of ns.
Next, due to the balance of the ambipolarity,
ions moves slowly along the field with a timescale of the ion transit time followed by theperpendicular ion motion across the field. Final, another stable equilibrium, i.e., different,
global potential and density profiles, in thebulk region is reached on a transport timescale (the ion classical transport across themagnetic field) of a few ms.
Now, detailed characteristics on transition
phenomena in the initial phase are discussed.
As was mentioned, the behavior near the electrode region is important, since during transitions Ib, Iis, and Vf changed very fast. Furthermore, there were some events with notransitions even though spikes of Ib were ob-

第27巻

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359

served. The changing time scale of Ib was estimated to be less than several tens of ns,
which is close to the characteristic time scale ofthe time-dependent sheath, e.g., Refs. 23
and 24, in the range of ns (1 / ωpe range). The
decay time of Ib and the time necessary to havethe steady condition after the transition forabout a few µs are comparable to the ion transit time through the sheath region. The above
behaviors may be related to the sheath and theion acoustic type instabilities 25).
The next phase of transitions is considered.
Due to a change of Ib, keeping the total ambipolarity leads to a change of the perpendicularion flow due to enhanced diffusion by, e.g.,change of some instabilities or turbulent states.
Then, the slow change of plasma parameters inthe bulk region are expected on a transport
time scale. Note that the physical picture of
the ion motion across the magnetic field issimilar to the one in potential-driven ion cyclotron oscillations in a Q machine 26), although
the time scale of ~ µs in our experiments ismuch shorter than the inverses of the ion cyclotron frequency of ~ 50 µs. Here, in a Q machine, the cyclotron oscillations were observed
when the electrode half radius is larger than
the ion Larmor radius. In our case, the transition effect fades out when the number of biased
rings was increased, where the radial width of
one ring was a few times of the ion Larmor
radius.
In order to simulate the observed results,
which suggest the sheath type instabilities,
two-dimensional particle-in-cell simulations ofa magnetized plasma have been carried out 27).
Preliminary results show that there is anautonomous oscillation: the main oscillation
region is limited to the zone in which magnetic
field lines are connected with the positively
charged electrostatic plate. This is a kind of
bifurcation phenomenon and appears with thepotential of the plate being less than a criticalvalue. The size of the plate must be finite
across the magnetic field, because the electron
and ion motions, which are mainly parallel andperpendicular to the magnetic field, respectively, influence the negative sheath facing theplate. The oscillation of the sheath width parallel to the magnetic field is synchronized withthat of the amplitude of the potential, and a
periodic ion bunching is also observed near theplate. The oscillation period is determined by
the transit time of ions, which pass throughthe sheath region. These behaviors suggest akind of two-dimensional sheath instability.
This should be investigated in detail, andchanging gas species may also give additional

360

Spatio-Temporal Behavior of Bistable Density Transition in Magnetized Plasma

information.
For further investigation, it is necessary tohave a comparative study between experimental and stimulation results, noting the
dynamic change of the two-dimensional sheathstructure (local density and potential in asmall area) followed by the bulk plasma one.
An ion velocity distribution function may bealso a key to understand this mechanism aswell as the probalistic transition with hystereses 20,21).
To summarize, detailed behaviors of theself-excited bistable transition phenomena
have been investigated in the bulk as well as
electrode regions. Depending on the spatial
region, transition time of Ttr was different.
Near the electrode, where structural changesof the potential and the density were observedat the transition, Ttr was much shorter thanthat in the bulk region. These showed the important role of the structural changes to trigger the transitions due to the sheath type instabilities near the electrode. Next process isthe ion motion along and across the field,
which follows the fast change of Ib, and final,
another stable equilibrium in the bulk plasma
is obtained on a transport time scale.
Acknowledgments
We would like to thank Professor H. Naito
for fruitful discussions and to Professor
Emeritus Y. Kawai for his continuous encouragement. This work has been partly supportedby the Grants-in-Aid for Scientific Research(C)(2), No.14580519, from the Japan Society
for the Promotion of Science, and by the
Grant-in-Aid for Encouragement of Young Researchers of the Faculty of Engineering Sciences, Kyushu University.

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