Proceedings of ITC/ISHW2007

Eﬀects of Superimposed Parallel and Perpendicular
Flow Velocity Shears on Drift-Wave Instabilities
in Magnetized Plasmas
Toshiro KANEKO, Shuichi TAMURA and Rikizo HATAKEYAMA
Department of Electronic Engineering, Tohoku University, Sendai 980-8579, Japan
Plasma ﬂow velocity shears parallel and perpendicular to magnetic ﬁeld lines are independently controlled and superimposed using a modiﬁed plasma-synthesis method with concentrically three-segmented
electron and ion emitters. The ﬂuctuation amplitude of the drift wave which has an azimuthal modenumber m = 3 is observed to increase with increasing the parallel shear strength in the absence of theperpendicular shear. When the perpendicular shear is superimposed on the parallel shear, the drift
wave of m = 3 is found to change into that of m = 2. Furthermore, the parallel shear strength required
for the excitation of the drift wave becomes large with a decrease in the azimuthal mode number. Basedon these results, the superposition of the parallel and perpendicular shears can aﬀect the characteristicsof the drift wave through the variation of the azimuthal mode number.
Keywords: plasma ﬂow velocity shear, drift wave, azimuthal mode number, plasma-synthesis method

1 Introduction
Plasma ﬂows and their velocity shears in magnetizedplasmas have attracted much attention not only infusion oriented plasmas but also in space plasmas,
because the ion ﬂow velocity shear parallel to themagnetic ﬁeld lines has been reported to enhance theion-acoustic [1, 2], ion-cyclotron [3, 4], and drift-wave[5, 6] instabilities, while the perpendicular ﬂow velocity shear has been conﬁrmed to regulate not only thedrift-wave but also ion-cyclotron instabilities independent of the sign of the shear [7]. In order to clarify themechanisms of excitation and suppression of these instabilities in the real situation of the fusion and spaceplasmas, it is necessary to realize the controlled superposition of the parallel and perpendicular ﬂow shears
in magnetized plasmas.
Thus, the aim of the present work is to independently control and superimpose the parallel and perpendicular ﬂow shears in the basic plasma device withconcentrically three-segmented electron and ion emitters [8], and to carry out laboratory experiments on
the drift-wave instability excited and suppressed by
the superimposed ﬂow shears in collisionless magnetized plasmas.

2 Experimental Setup
Experiments are performed in the QT -Upgrade machine of Tohoku University. We attempt to modify a plasma-synthesis method with an electron (e− )author’s e-mail: kaneko@ecei.tohoku.ac.jp

emitter using a 10-cm-diameter tungsten (W) plate
and a potassium ion (K+ ) emitter using another W
plate, which are oppositely located at the machineends as shown in Fig. 1. The collisionless plasma isproduced when the surface-ionized potassium ions andthe thermionic electrons are generated by the spatiallyseparated ion and electron emitters, respectively, andare synthesized in the region between these emitters.
A negatively biased stainless (SUS) grid, the voltageof which is typically Vg = −60 V, is installed at a distance of 10 cm from the ion emitter surface. Since thegrid reﬂects the electrons ﬂowing from the electron
emitter side, the electron velocity distribution function parallel to the magnetic ﬁelds are considered to
become Maxwellian.
Both the emitters are concentrically segmented
into three sections with the outer diameters of 2 cm
(ﬁrst electrode), 5.2 cm (second electrode), and 10 cm(third electrode), each of which is electrically isolated.
When each section of the electron emitter is individually biased, the radially-diﬀerent plasma potential, orradial electric ﬁeld is expected to be generated evenin the fully-ionized collisionless plasma. This electricﬁeld causes the E×B ﬂows and ﬂow shears perpendicular to the magnetic-ﬁeld lines. Voltages applied tothe electrodes set in order from the center to the outside are deﬁned as Vee1 , Vee2 , Vee3 , respectively. On
the other hand, the parallel K+ ﬂow with radially different energy, i.e., the parallel K+ ﬂow shear, is generated when each section of the segmented ion emitter isindividually biased (Vie1 , Vie2 , Vie3 ) at a positive value
above the plasma potential that is determined by thebias voltage of the electron emitter. Therefore, theseProceedings of ITC/ISHW2007

BElectron Emitter

K OvenIon Emitter
W HeaterW HeaterGGrid
Vee1 Vee2Vee3Vg

Vie3 Vie2 Vie1−510−105φ (V)15−1524680

Vie1 (V)Vie1 (V)0246815−510−105−15−4−20

EK+ (eV)(b)

0Vee1 (V)(c)

015−510−105−15−4−20

EK+ (eV)At ﬁrst, we demonstrate the independent control ofthe parallel and perpendicular K+ ﬂow velocity shears
and the superposition of these shears. Figure 2 shows
the plasma potential φ (closed circles) and the K+ﬂow energy EK+ (open circles) at the radial centerr = 0 cm of the plasma column as functions of Vie1
and/or Vee1 , where Vie2 and Vee2 are ﬁxed at 5.0 V
and −2.0 V, respectively. When Vie1 is changed atconstant Vee1 = −2.2 V [Fig. 2(a)], the K+ ﬂow energy is found to increase in proportion to Vie1 , while
the plasma potential is almost constant at φ = −5.5 V.
Since the K+ ﬂow energy and the plasma potential in
the second electrode region are conﬁrmed to have constant values of 7 eV and −5.5 V, respectively, only theparallel ﬂow velocity shear can be generated in theboundary region between the ﬁrst and second electrodes by changing Vie1 .
When Vie1 and Vee1 are simultaneously changed
keeping the bias-voltage diﬀerence Vie1 −Vee1 constant[Fig. 2(b)], on the other hand, the K+ ﬂow energy does
not change, while the plasma potential is found to increase in proportion to Vee1 . This result denotes thatthe parallel shear does not change as far as Vie1 − Vee1
is constant, and the radial plasma potential diﬀerence,i.e., the perpendicular ﬂow velocity shear can be con-0

φ (V)3 Experimental Results(a)φ (V)parallel and perpendicular K+ ﬂow velocity shears canbe superimposed by controlling the bias voltage of theion and electron emitters independently. Here, Vee3and Vie3 are always kept at 0 V. A small radially movable Langmuir probe and an electrostatic energy analyzer are used to measure radial proﬁles of plasma
parameters and ion energy distribution functions parallel to the magnetic ﬁelds, respectively. Under ourconditions, the plasma density is 109 cm−3 , the electron temperature is 0.2 eV, and the ion temperatureis almost the same as the electron temperature. A
background gas pressure is less than 10−6 Torr.

EK+ (eV)Fig. 1 Schematic of experimental setup.

0Vee1 (V)Fig. 2 Plasma potential φ (closed circles) and K+ flow energy EK + (open circles) as functions of (a) Vie1 , (b)Vie1 and Vee1 , and (c) Vee1 . r = 0 cm, Vie2 = 5.0 V,
Vee2 = −2.0 V.

Proceedings of ITC/ISHW2007

(a)

2.4

䌾 䋭 (%)
Ies/Ies(a) 21.020.0㪇㪍㪈㪇㪉㪍

1.6

1Vie1 (V)

0.8
10.0

0.0
-0.8y (cm)

15.0

-1.6
-1.88

-1.80

-1.72

㪙㫓㫓㩷㫊㪿㪼㪸㫉A-2(b)-10x (cm)1.5y (cm)

(b)

-20

Vee1 (V)

0-1

5.0

-1.96

0

12061110

0.0

-1.0

1.00

B
-1.5
-1.5

0.0

1.5

-1.0x (cm)㪙㼠㩷㫊㪿㪼㪸㫉
Fig. 3 Contour views of normalized fluctuation amplitudes as functions of Vie1 and Vee1 . r = 1.5 cm,
Vie2 = 1.0 V, Vee2 = −2.0 V.

trolled by the bias voltages of the electron emitter.
Since the parallel and perpendicular shears are now
able to be controlled independently, we attempt tosuperimpose these shears.
Figure 2(c) presents the plasma potential and theK+ ﬂow energy as a function of Vee1 at constantVie1 = 5 V. In this case, the plasma potential is directly changed by Vee1 , and the K+ ﬂow energy is alsochanged by Vee1 , because the bias-voltage diﬀerence
Vie1 − Vee1 decreases with an increase in Vee1 for theﬁxed Vie1 . Based on these results, the superpositionof the parallel and perpendicular ﬂow velocity shears
is realized by controlling the Vie1 and Vee1 simultaneously. These parallel and perpendicular shears arefound to give rise to several types of low-frequency
instabilities. Here, we concentrate on the drift-wave
instability which is excited in the density gradient region around r = 1.0 ∼ 1.5 cm.
Figure 3(a) shows a contour view of normalized ﬂuctuation amplitudes Ies /I¯es obtained from frequency spectra of an electron saturation current Ies ofthe probe as functions of Vie1 and Vee1 for Vie2 = 1.0 V
and Vee2 = −2.0 V. Schematic model of the par-Fig. 4 2-dimensional profile of fluctuation phase θ whichis plotted as sin θ for (a) fluctuation A (Vee1 −1.90 V) and (b) fluctuation B (Vee1  −1.78 V).
Vie1 = −1.0 V, Vie2 = 1.0 V, Vee2 = −2.0 V.

allel and perpendicular shears introduction is shownin Fig. 3(b), where black arrows described at ordinate axis mean the parallel ion ﬂow velocity and solid
curves described at abscissa axis mean the radial potential proﬁles, which are controlled by Vie1 and Vee1 ,respectively, corresponding to the variation of the parallel and perpendicular ﬂow velocity shears. Here, horizontal and vertical dotted lines in Fig. 3 denote thesituations in the absence of the parallel and perpendicular shears, respectively, which are conﬁrmed by
the actual measurements of the ion ﬂow energy andthe space potential.
In the case that the perpendicular shear is not
generated at Vee1 = −1.8 V, the ﬂuctuation amplitudeof the drift-wave instability is observed to increase
with increasing the parallel shear strength by changing
Vie1 to the negative value from 1.0 V, but the instability is found to be gradually stabilized when the shear
strength exceeds the critical value. The destabilizing and stabilizing mechanisms are well explained bya plasma kinetic theory including the eﬀect of radial
density gradient [5]. When the perpendicular shear
is superimposed on the parallel shear, the drift wave
excited by the parallel shear is found to be suppressedProceedings of ITC/ISHW2007
by the perpendicular shear independently of the signof the perpendicular shear. Furthermore, we can observe two characteristic ﬂuctuation peaks dependingon the perpendicular shear strength as presented in
the contour views [Fig. 3(a)], which are deﬁned as
ﬂuctuations A and B as described in the schematic
model [Fig. 3(b)].
To readily identify the azimuthal componentof each ﬂuctuation’s wavevector, we measure 2dimensional (x, y) proﬁles of ﬂuctuation phase in theplasma-column cross section. The phase is measured
with reference to a spatially ﬁxed Langmuir probe
located at an axial distance of 26 cm from the 2dimensionally translatable probe. Figure 4 presents
the 2-dimensional phase proﬁles for (a) ﬂuctuation Aand (b) ﬂuctuation B. Since the phase diﬀerence θ between the 2-dimensional probe and the reference probe
is plotted as sin θ, red (1.0) and blue (−1.0) indicate
the phase of +π/2 and −π/2, respectively, relative tothe reference probe. Green corresponds to zero andπ relative phase. In the case of the small perpendicular shear strength, i.e., ﬂuctuation B [Fig. 4(b)], theazimuthal mode is found to be m = 3. On the other
hand, in the presence of the relatively large perpendicular shear, i.e., ﬂuctuation A [Fig. 4(a)], the azimuthalmode changes into m = 2. The perpendicular shear
can modify the azimuthal mode number depending on
its strength.
For these two kinds of drift waves, we measure
the dependence of ﬂuctuation amplitudes on the parallel shear strength, which are obtained from Fig. 3(a).
As a result, with an increase in the parallel shear
strength, it is found that m = 3 mode (Vee1 −1.78 V) ﬁrst excited and m = 2 mode (Vee1 −1.90 V) needs strong parallel shear strength to excite the mode. These phenomena can be explained by
the theoretical calculation that the growth rate of theparallel-shear excited drift wave sensitively depends
on the azimuthal wave number, i.e., mode number[6]. Therefore, the superposition of the parallel andperpendicular shears can aﬀect the characteristics ofthe drift wave through the variation of the azimuthalmode number.

4 Conclusions
The independent control of parallel and perpendicular ﬂow velocity shears in magnetized plasmas is realized using a modiﬁed plasma-synthesis method withsegmented plasma sources. The ion ﬂow velocity
shear parallel to the magnetic-ﬁeld lines is observed
to destabilize the drift-wave instability depending on
the strength of the parallel shear. On the other hand,when the perpendicular shear is superimposed on theparallel shear, the drift wave of m = 3 is found tochange into that of m = 2, and the instability is suppressed for strong perpendicular shears. The superposition of these shears can aﬀect the characteristics ofthe drift wave through the variation of the azimuthalmode number.

Acknowledgments
The authors are indebted to H. Ishida for his technicalassistance. We also express our gratitude to Professor
M. Koepke and Dr. G. Ganguli for their useful comments and discussion. This work was supported by aGrant-in-Aid for Scientiﬁc Research from the Ministryof Education, Culture, Sports, Science and Technology, Japan.

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