Flow Shear Effects on Drift-Wave Instability in Multi-Ion Plasmas
T. Kaneko, R. Ichiki, K. Hayashi, and R. Hatakeyama
Department of Electronic Engineering, Tohoku University, Sendai 980-8579, Japan
Abstract. Parallel and perpendicular plasma flow velocity shears are independently controlled and superimposed in
magnetized plasmas using a modified plasma-synthesis method with concentrically three-segmented electron and ion
emitters. The parallel shear is observed to destabilize the drift-wave instability depending on the shear strength, while the
perpendicular shear superimposed on the parallel shear is demonstrated to suppress the instability even in the presence of
the parallel shear. When negative ions are introduced into this plasma, the range of shear strength which destabilizes the
drift-wave instability is found to extend to both the positive and negative values with increasing negative ion exchange
Keywords: Flow Shear, Drift-Wave Instability, Negative Ions
PACS: 52.35.Kt, 52.35.Qz
Sheared plasma flows in magnetized plasmas are very important issues not only in near-Earth space plasmas but
also in fusion oriented plasmas. In recent studies, the ion flow velocity shear parallel to the magnetic field lines has
been reported to enhance the ion-acoustic , ion-cyclotron , and drift-wave [3,4] instabilities, while the
perpendicular flow velocity shear has been confirmed to regulate not only the drift-wave but also ion-cyclotron
instabilities independent of the sign of the shear . In order to clarify the mechanisms of excitation and suppression
of these instabilities in the real situation of the space and fusion plasmas, it is necessary to realize the controlled
superposition of the parallel and perpendicular flow shears in multi-ion plasmas, i.e., the plasmas with a couple of
positive and/or negative ion species.
Thus, the aim of the present work is to independently control and superimpose the parallel and perpendicular
flow shears in the basic plasma device with concentrically three-segmented electron and ion emitters , and to
carry out laboratory experiments on the drift-wave instability excited and suppressed by the superimposed flow
shears in collisionless magnetized plasmas with negative ions as a first step of the multi-ion plasmas.
Experiments are performed in the QT-Upgrade machine of Tohoku University. We attempt to modify a plasmasynthesis
method with an electron (e−) emitter using a 10-cm-diameter tungsten (W) plate coated with a lanthanum
hexaboride (LaB6) and a potassium ion (K+) emitter using another W plate, which are oppositely located at the
machine ends as shown in Fig. 1. The collisionless plasma is produced when the surface-ionized potassium ions and
the thermionic electrons are generated by the spatially separated ion and electron emitters, respectively, and are
synthesized in the region between these emitters. Negative ions (SF6
−) are supplied by bleeding an SF6 gas into the
K+ − e− plasma and the negative ion exchange fraction (ε = n−/n+, n+: positive ion density, n−: negative ion density)
can be varied by changing the partial pressure of the gas. A negatively biased stainless (SUS) grid, the voltage of
which is typically Vg = −60 V, is installed at a distance of 10 cm from the ion emitter surface. Since the grid reflects
the electrons and the negative ions flowing from the electron emitter side, electron and negative-ion velocity
distribution functions 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, or radial electric field is
expected to be generated even in the fully-ionized collisionless plasma. This electric field causes the E ×B flows and
flow shears perpendicular to the magnetic-field lines. Voltages applied to the 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 is
individually biased (Vie1, Vie2, Vie3) at a positive value above the plasma potential that is determined by the bias
voltage of the electron emitter. Therefore, these parallel and perpendicular K+ flow velocity shears can be
superimposed by controlling the bias voltage of the ion and electron emitters independently. Here, Vee3 and 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 our conditions, the plasma density is 108 cm-3, the electron temperature is 0.2 eV, and the ion
temperature is almost the same as the electron temperature. A background gas pressure is less than 10-6 Torr.
FIGURE 1. Schematic of experimental setup.
Superposition of Parallel and Perpendicular Flow Velocity Shears
At first, we demonstrate the independent control of the parallel and perpendicular K+ flow velocity shears and the
superposition of these shears in the absence of the negative ions. Figure 2 shows the plasma potential φ (closed
circles) and the K+ flow energy EK
+ (open circles) at the radial center r = 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 at constant 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
the parallel flow velocity shear can be generated in the boundary 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 that the 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 controlled by the bias voltages
of the electron emitter. Since the parallel and perpendicular shears are now able to be controlled independently, we
attempt to superimpose these shears. Figure 2(c) presents the plasma potential and the K+ flow energy as a function
of Vee1 at constant Vie1 = 5 V. In this case, the plasma potential is directly changed by Vee1, and the K+ flow energy
is also changed by Vee1, because the bias-voltage difference Vie1−Vee1 decreases with an increase in Vee1 for the fixed
Vie1. Based on these results, the superposition of the parallel and perpendicular flow velocity shears is realized by
controlling the Vie1 and Vee1 simultaneously.
These parallel and perpendicular shears are found 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 = 1.5 cm.
FIGURE 2. Plasma potential φ and positive ion flow energy EK
+ as functions of (a) Vie1, (b) Vie1 and Vee1, and (c) Vee1.
r = 0 cm, Vie2 = 5.0 V, Vee2 = −2.0 V.
Figure 3 shows contour views of normalized fluctuation amplitudes as functions of parallel Vie1 and
perpendicular Vee1 flow velocity shears for Vie2 = 1.0 V and Vee2 = −2.0 V, where horizontal and vertical dotted lines
in Fig. 3 denote the situations in the absence of the parallel and perpendicular shears, respectively.
In the case that the perpendicular shear is not generated at Vee1 = −2.2 V, the fluctuation amplitude of the driftwave
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. When the perpendicular shear is superimposed on the parallel shear, on the other hand, the drift-wave
instability is found to be suppressed by the perpendicular shear even in the presence of the parallel shear. The driftwave
instability excited by the parallel shear is rapidly suppressed for Vee1 > −2.2 V in any parallel shear strength.
For Vee1 < −2.2 V, on the other hand, the drift-wave is hard to be suppressed when the larger parallel shear is
generated. Based on these results, the sign of the perpendicular shear is found to be important in modifying the
parallel shear enhanced instability. The modification of the parallel-shear enhanced drift-wave instability by the
perpendicular shear is also observed for Vie1 > 1.0 V. In this case, however, the fluctuation amplitude has the
maximum value in the presence of the perpendicular shear at Vee1 = −1.9 V, which is different from the abovementioned
result for Vie1 < 1.0 V and is under investigation.
FIGURE 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.
Effects of Flow Velocity Shears in Negative Ion Plasmas
Figure 4 shows normalized fluctuation powers ~ 2 / 2
Iis Iis as functions of the parallel shear strength ΔVie and the
negative ion exchange fraction ε, where the perpendicular shear is not generated. The characteristics of the
fluctuations, attributed to the parallel-shear modified drift-wave instability, are found to change when the negative
−) are introduced into the plasma . The range of the parallel-shear strength that destabilizes the
fluctuations extends to both the positive and negative values. Furthermore, for large concentration of the negative
ions, the frequency spectrum makes a transition from sharp to broad as the shear strength is increased. These trends
may be related to negative-ion effects on the wave phase velocity which, in turn, modifies Landau damping and
growth. We are interested in possible applications of these results to structure formation in a turbulent plasma that
contain both the negative ions and the sheared positive-ion flow.
FIGURE 4. Normalized fluctuation powers ~ 2 / 2
Iis Iis as functions of the parallel shear strength ΔVie and the negative ion
exchange fraction ε, where the perpendicular shear is not generated. r = 1.5 cm.
The independent control of parallel and perpendicular flow velocity shears in magnetized plasmas is realized
using a modified plasma-synthesis method with segmented plasma sources. The positive-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, the perpendicular shear which is superimposed on the parallel shear is
demonstrated to suppress the drift-wave instability even in the presence of the parallel shear, and the suppression
characteristc is found to depend on the sign of the perpendicular shear.
The range of shear strength which destabilizes the drift-wave instability is found to extend to both the positive
and negative values with introducing the negative ions into the plasma. Moreover, the increase in the negative ion
exchange fraction gradually broadens the frequency spectrum of the fluctuation. This is likely to imply that the
introduction of the negative ions leads the fluctuation to a nonlinear regime.
The authors are indebted to H. Ishida for his technical assistance. We also express our gratitude to Professor M.
Koepke and Dr. G. Ganguli for their useful comments and discussion. This work was supported by a Grant-
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