Observations of low frequency oscillations due to transverse sheared flowsEdward Thomas Jr., Jon David Jackson, Edwynn A. Wallace, and Gurudas Ganguli

Citation: Physics of Plasmas (1994-present) 10, 1191 (2003); doi: 10.1063/1.1567287 View online: http://dx.doi.org/10.1063/1.1567287 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/10/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The excitation of geodesic acoustic mode flows by a resonant magnetic field and by resonant heating Phys. Plasmas 20, 032508 (2013); 10.1063/1.4794837 Turbulent excitation of plasma oscillations in the acoustic frequency range Phys. Plasmas 14, 082304 (2007); 10.1063/1.2755944 Edge harmonic oscillations produced by toroidal velocity shear Phys. Plasmas 9, 2451 (2002); 10.1063/1.1472503 Low frequency oscillations in a plasma with spatially variable field-aligned flow Phys. Plasmas 9, 2321 (2002); 10.1063/1.1445181 Fast disruptions by ballooning mode ridges and fingers in high temperature, low resistivity toroidal plasmas Phys. Plasmas 8, 103 (2001); 10.1063/1.1331098

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PHYSICS OF PLASMAS VOLUME 10, NUMBER 5 MAY 2003

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Observations of low frequency oscillations due to transversesheared flows

Edward Thomas, Jr.,a) Jon David Jackson, and Edwynn A. WallaceDepartment of Physics, Auburn University, Auburn, Alabama 36849

Gurudas GanguliPlasma Physics Division, Naval Research Laboratory, Washington, DC 20375

~Received 31 January 2003; accepted 13 February 2003!

This Letter details observations of low frequency~i.e., v<V i , where V i is the ion cyclotronfrequency!, coherent instabilities in the Auburn Linear Experiment for Instability Studies~ALEXIS!. In the ALEXIS device, which is a 1.8-m long magnetized plasma column, the observedinstabilities are excited by the presence of sheared flows in the plasma that are transverse to the axialmagnetic field. The instabilities have long azimuthal wavelengths (m<2) and are localized in theplasma to regions where the sheared flow is maximized and are anticorrelated to both densitygradients and field aligned currents. ©2003 American Institute of Physics.@DOI: 10.1063/1.1567287#

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The role of transverse flow shear in magnetized plasmis a topic of much relevance to the plasma physics comnity. Here, flows are driven by the presence of an elecfield ~E! that is transverse to a magnetic field~B!, therebygiving rise to sheared flows in the direction ofEÃB. Withinthe fusion community, a great deal of excitement has bgenerated from studies of velocity shear stabilization of lfrequency modes in toroidal devices. Experiments in a nuber of toroidal devices have demonstrated that controthese sheared flows is an important mechanism for achiehigh performance conditions in fusion plasmas.1,2 Whilethese studies show promise, the exact mechanisms thatto stabilization and the resulting accessibility of enhancconfinement regimes~i.e., so-called H modes! are still beingdebated.3–5

Consequently, the primary objective of this experimeis to isolate and control the velocity shear in a simple linexperiment and to characterize the response of the plasmsheared flows. In these experiments, velocity shear is foto have a destabilizing effect on the plasma. This cleacontrasts with many of the observations of enhanced cfinement regimes in toroidal devices. Nonetheless, therevidence in both tokamak6 and stellarator7 devices thatEÃBdriven flows can be destabilizing. This raises the questionwhether shear flow is a cause or effect of H modes.

In space plasmas,EÃB driven flows are often associatewith satellite and sounding rocket observations of ion oflows from the ionosphere8,9 as well as low frequencywaves.10–12 Several mechanisms have been consideredthese phenomena, including magnetic field aligncurrents13,14 and Kelvin–Helmholtz instabilities,15,16 but nosingle mechanism appears to be completely adequate inplaining the observed phenomena. However, theoretwork at the Naval Research Laboratory~NRL! has shownthat shearedEÃB driven flows are an important and oftecritical component of the aforementioned phenomena.17–20

a!Electronic mail: etjr@physics.auburn.edu

1191070-664X/2003/10(5)/1191/4/$20.00

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Q-machines,21,22 linear plasma columns,23,24 low tem-perature toroidal devices,25 and large-volume experiments26

are used to explore the roles of velocity shear in both traverse and parallel flows on particle and wave transpormagnetized plasmas. While these experiments cannot acthe types of plasma parameters in either fusion or space pmas, important scalings are preserved. These experimcan provide valuable new insights into key plasma procesthat would be otherwise difficult to explore in devices wicomplex geometry such as tokamaks.

The goal of experiments at Auburn University is to dvelop a more complete understanding of the role of bstabilizing and destabilizing effects ofEÃB driven flows.Experiments described in this letter are performed usinsimple experimental geometry—a cylindrical plasmcolumn—to facilitate exploration of the basic physics witout the difficulties associated with more complex experimtal configurations.

This Letter summarizes the initial results of an expemental investigation of low frequency instabilities, at or blow the ion cyclotron frequency, which arise due to the prence of shearedEÃB flows in the plasma. Descriptions wilbe given of the experimental hardware and diagnostics ufor this investigation. This will be followed by a discussioof the experimental measurements. Finally, a discussionthe physical mechanisms that may be responsible forobserved instability will be presented.

Experiments are performed in the ALEXIS device—the Auburn Linear Experiment for Instability StudieALEXIS is 180 cm long, 10 cm diameter stainless stevacuum vessel. The chamber consists of a water-cooledtion, followed by a six-way cross section, a 100 cm losection that has numerous QF 40~‘‘quick flange’’ style 240mm diameter! diagnostic ports, and a final six-way crossection.

Experiments in ALEXIS are generally performed usinhelium gas. Plasmas are generated using an array of th0.25 mm diameter tungsten filaments that are heated w

1 © 2003 American Institute of Physics

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currents up to 7 A into thermionic emission. The plasmagenerated by allowing the filaments to emit electrons incurrent-limited mode ranging from 100 to 300 mA. Thplasma then passes through a grounded electrode andinto the main experimental volume. The plasma potenremains within 5 V of the laboratory electrical ground. Thconfiguration allows ALEXIS to operate under reproducibplasma conditions. Plasma parameters are measuredsingle27 and triple28 Langmuir probes. Typical operating conditions and plasma parameters for ALEXIS are listedTable I.

The key element of this experiment is a seriesfour concentric rings at the end of ALEXIS. These rinare mounted on a Macor block and oriented perpendiculto the axial magnetic field. Each ring can be independebiased to establish a desired radial potential structurethe plasma. In the experiments described in this Letter, R1, 2, and 4 are held at fixed bias voltages while the bvoltage on Ring 3 is varied. Rings 1 and 2 are set atsame bias voltage,V15V252120 V. Ring 4 is grounded aV450 V.

In these experiments, a low frequency instability is oserved to grow in the plasma as the bias voltage on Ringvaried. At a positive bias voltage, there is a significant mnetic field aligned current of up to 100 mA due to electrcollection. At negative bias voltages, field aligned curreare uI 3u<5 mA. A fast Fourier transform~FFT! spectrum ofthe floating potential on a Langmuir probe is shown in Fig.The FFT traces show the peak frequency of the instabilitybe nearf 5v/2p'30 kHz orv;0.8V i for these conditions.

Furthermore, the FFT traces show that the amplitudethe instability is anticorrelated with the current. This sugests that these modes may not be related to current-drphenomena. To confirm this, a comparison is made betwthe phase velocity of the instability and the parallel~i.e., fieldaligned! electron drift velocity.

In order for the mode to be a current-driven instability,is expected that the phase velocity of the wave,vw5(v2kyvE)/kz , should be comparable to the parallel electrdrift velocity, v i . Here, ky and kz are the azimuthal andlongitudinal wave numbers, respectively,v is the measuredangular frequency of the instability andvE is theEÃB driftspeed. The electron drift speed isv i5 j /n0e; where j is thecurrent density collected on Ring 3, which has a collectarea of 7.231024 m2, n0 is the electron density, ande is theelectron charge. Preliminary measurements show that for

TABLE I. Operating conditions in ALEXIS.

Peak magnetic field (Bmax) 1000 GaussTypical magnetic field (Btyp) 70–100 GaussPlasma density (ne) 831015 m23

Electron temperature (Te) 5–10 eVIon temperature (Ti) ,0.05 eVOperating pressure~helium! ,0.8 mTorrIon cyclotron frequency (f ci) ;25 to 40 kHzMean free path 9 cmIon gyroradius/Chamber radius (r i /a) 0.1–0.2

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observed instabilitiesky;70 m21 andkz;8 m21; this givesthe ratiokz /ky;0.11.

At a current ofI 3'2 mA, the ratio of the parallel electron drift speed to the phase speed isuv i /vwu50.02. Bycontrast, a key requirement to establish the current driinstability is that uv i /vwu;1. Thus, the experimental measurements suggest that for the parameters in ALEXIS, iunlikely that this mode is a current driven mode.

In an additional attempt to characterize the instabilityLangmuir probe located 8 cm upstream from the ringsmoved radially through the plasma. The amplitude of tinstability, obtained from the FFT spectrum, is recorded afunction of position. This is done for several different curents ~i.e., bias voltages! on Ring 3. The results of thesmeasurements are shown in Fig. 2. Here, the instabilityshown to be localized to the region in the plasma that cocides with the radial position of Ring 3. It is also noted ththe data in Fig. 2 shows that the amplitude of the instabiincreases with decreasing collection current on Ring 3; thiconsistent with the measurement shown in Fig. 1.

Additionally, it is shown in Fig. 3 that this region of thplasma where the instability reaches its maximum amplitualso corresponds to the region where the electric fistrength as a function of the radial position is strongly vaing. This gives rise to a region of the plasma with a sheaEÃB flow. This provides good evidence that the observinstabilities may be related to the presence of sheared trverse flows in the plasma.

Of particular concern in this study is the presencedensity gradients in the plasma. These gradients couldvide a source of free energy to drive drift waves. A careanalysis of experimental measurements is required to demine whether drift waves are likely to grow for the condtions in ALEXIS. Figure 4 shows that the density gradient

FIG. 1. FFT spectra of the floating potential on a Langmuir probe indicatthe growth of the instability as a function of the current collected/bias vage on Ring 3. The measurements show that the growth of the instabilianticorrelated with the current. The vertical axis represents the amplitudthe FFT in arbitrary units~a.u.!.

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1193Phys. Plasmas, Vol. 10, No. 5, May 2003 Observations of low frequency oscillations . . .

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a minimum under the conditions when the instability hasmaximum amplitude~i.e., for minimum electron current onRing 3!. This provides an initial suggestion that the instabity may not be correlated to the density gradient. Howevemore detailed analysis is required to substantiate this msurement.

This is accomplished by computing an estimate forgrowth rate of drift waves in the presence of a sheared traverse flow following methods in Refs. 20 and 29. Thisshown in Eq.~1!,

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FIG. 2. Localization of the observed instability to the region near RingThe thick black lines labeled R1–R4 indicate the spatial extent of eacthe ring electrodes. This measurement is consistent with Fig. 2 in shothat the amplitude of the instability increases as the current collectedRing 3 decreases.

FIG. 3. Measurement of the plasma potential~solid squares! and computedelectric field~dashed line!. The plasma potential is measured using an emsive probe. The solid line is a fourth-order polynomial fit to the plaspotential measurements. The electric field is computed from the negderivative of the potential curve fit. This measurement is taken when Rinis drawing a low electron current.

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2kyvE# is the Doppler shifted frequency of the wave. Thtermv* e is the diamagnetic drift frequency and is computusing

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The drift frequency is estimated to bev* e;800 rad/s. Bycontrast, the Doppler shifted wave frequency isuv1Ru51.13106 rad/s@uv* eu. Using this fact in Eq.~1! with theknowledge that all of the remaining terms are positive denite leads to the result that, for the parameters used inALEXIS device for this investigation, the growth rate of driwaves is negative. This suggests that the instability obserin the ALEXIS device is not a drift wave.

With the aforementioned experimental results, it is posible to draw the following conclusions. First, the observinstability is not related to current driven phenomena. In fathe amplitude of the instability grows with decreasing curent. Second, the observed instability is not a drift wave. Tfrequency of the instability is much higher than the drfrequency. Third, the instability is localized to a region of tplasma in which the electric field strength is strongvarying—suggesting the presence of sheared flows.

To characterize the observed instability, consider thesponse of the plasma to both a field aligned current antransverse flow. This response is parametrized by the tR5kyvE /kzv i . Using the preliminary values for the ratio otransverse and parallel wave numbers given earlier giveestimated value ofR;70. For casesR@1, it has been shownthat ion cyclotron waves can be driven unstable by velocshear even in the absence of a field aligned current.17,18,34

These shear driven ion cyclotron modes prefer long amuthal wavelengths30 ~i.e., low m numbers!, which is thespectral characteristic of the observed instability.

At a radiusr 52 cm, the measured azimuthal wave number ky5m/r ~where,m is the azimuthal mode number andris the radius! suggests a mode number between 1 and

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FIG. 4. Scaling of the density gradient (dn/dr) in the vicinity of Ring 3with the magnitude of the electron currents~bias voltage! collected on Ring3. As the current collected by the ring is decreased, the density profilALEXIS flattens.

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Thus, another possible mechanism for this instability cobe the Kelvin–Helmholtz~KH! mode. However, KH modesprefer highm-numbers31–33and have no growth form51. Inaddition, they are strongly Landau damped19 unlesskz /ky

;0. Since the experimental observations givekz /ky;0.11and have lowm numbers, it appears unlikely that the oserved modes are due to the KH instability.

Considering this initial evidence, the results suggest tthe observed instabilities are related to the presence ofsheared flow in the plasma. These measurements are cotent with prior observations of the inhomogenous enedensity driven~IEDD! instability.34,35The IEDD instability isa velocity shear driven instability in the ion cyclotron frquency range.

At present, the IEDD instability has been observedtwo experiments, a Q-machine35 and a large volume plasmchamber.34 This experiment, therefore, expands the rangeexperimental environments in which this new classplasma instability has been observed. Given the recentportance of velocity shear driven phenomena to a wide vety of plasma systems, it is critical to develop both a thretical and experimental base in which to explore manythese phenomena. The results reported in this letter proevidence for the formation of the IEDD instability iALEXIS. Upcoming experiments will seek to obtain mohighly resolved measurements of the potential structuremake use of optical techniques to directly measure ion floin the plasma.

In summary, low frequency waves in the ion cyclotroregime have been identified in a magnetized helium plascolumn. The radial potential structure in the plasma is ctrolled using an array of four ring electrodes that are orienperpendicularly to the axial magnetic field. An instabilityobserved in the plasma that is spatially localized at the raposition corresponding to Ring 3 and is correlated to the bvoltage~collected current! on that electrode. The preliminarevidence suggests that the instability is a transverse veloshear driven ion cyclotron wave.

These measurements are contrary to results oftentained from toroidal fusion energy experiments in which floshear is a signature of the transition to enhanced confinemregimes and a corresponding stabilization of low frequemodes even though shear represents a source of free enThis indicates that there may be conditions under whichlocity shear is a stabilizing agent as opposed to a destabing agent. Whether these conditions are specific to expmental devices or more general remains an outstanding isClearly, additional physical mechanisms associated withoidal plasma systems may play an important role and reqfurther scrutiny.36

ACKNOWLEDGMENTS

The authors would like to extend their thanks to DWilliam Amatucci of the Naval Research Laboratory and

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Dr. Robert Merlino of the University of Iowa for valuabldiscussions on plasma diagnostics and data interpretatio

This work is supported by U.S. Department of EnerGrant No. DE-FG02-00ER54577. G.G. is supported byNaval Research Laboratory.

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