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The ZaP Flow Z-Pinch Project

DOE GRANT #DE-FG03-98ER54460

Final Report

January 1, 1998 – December 31, 2004

U. Shumlak, B. A. Nelson,and the ZaP Group

University of WashingtonSeattle, Washington

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Contents

1 Introduction and Summary 41.1 ZaP Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Personnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Faculty and Scientific Staff . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Present Graduate Students . . . . . . . . . . . . . . . . . . . . . . . . 51.2.3 Previous Graduate Students . . . . . . . . . . . . . . . . . . . . . . . 51.2.4 Undergraduate Students . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Conferences and Publications . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Experimental Results 102.1 Velocity Profiles and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Velocity Dependence on Neutral Gas Injection . . . . . . . . . . . . . . . . . 122.3 Comparison to Theoretical Threshold for Stability . . . . . . . . . . . . . . . 122.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 The ZaP Experiment 153.1 Thomson Scattering System Design . . . . . . . . . . . . . . . . . . . . . . . 153.2 Larger Inner Electrode Design . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2

List of Figures

1 Upper: Contours showing the evolution of the velocity profiles in time nor-malized to the quiescent period. (The plot is constructed from data of manypulses.) Lower: Magnetic fluctuation levels for m=1, 2, & 3 for one plasmapulse. The quiescent period is 36.5 µs. . . . . . . . . . . . . . . . . . . . . . 11

2 Velocity shear data (from IDS) normalized by the theoretical threshold asfunction of time. The plenum pressure in the gas puff valves is varied. The(unnormalized) m=1 component of the magnetic field at the outer electrodeis also plotted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Schematic of the ZaP Thomson scattering design. . . . . . . . . . . . . . . . 154 Estimate of ZaP Thomson scattering system signal to noise ratio using mea-

sured bremsstrahlung data and the ZaP TS system design. . . . . . . . . . . 165 Schematic of the 15 cm inner electrode design. . . . . . . . . . . . . . . . . . 17

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1 Introduction and Summary

This is the Final Report covering the period of January 1, 1998 through December 31, 2004for the ZaP experiment at the University of Washington, Seattle, DOE Grant #DE-FG03-98ER54460.

1.1 ZaP Results

The ZaP experiment has achieved excellent results, maintaining a Z-pinch equilibrium forapproximately 2000 MHD growth times. This equilibrium has a flow shear in the rangepredicted by theory [1] to provide stabilization. These results are published in PhysicalReview Letters [2], Fusion Science and Technology [3] and Physics of Plasmas [4, 5], (includedin an Appendix) and presented at the meetings including the APS Division of Plasma Physics,AIAA, IEEE ICOPS, and the IAEA Fusion Energy Conferences (see Section 1.3).

1.2 Personnel

The ZaP group consists of faculty, staff, graduate students, and undergraduates, and benefitsfrom consulting and collaboration arrangements with several individuals and institutions.

1.2.1 Faculty and Scientific Staff

The ZaP experimental group is led by Prof. Uri Shumlak (Aeronautics and Astronautics—A& A) and Prof. Brian A. Nelson (Electrical Engineering) is Co-PI. Dr. Edward Crawford(Scientist A & A) assists in general project tasks, the holography system, and design of theThomson scattering system. Dr. Raymond P. Golingo (A & A) finished his PhD on ZaP inDecember 2003, and continues to work on the project as a Post Doctoral Research Associate.Dr. Golingo has published a journal article on his PhD studies.

Dr. Daniel J. Den Hartog of the University of Wisconsin–Madison consults with theZaP group. Dr. Den Hartog designed and built the intensified CCD (ICCD) multi-chordspectrometer, and is a major contributer to the Thomson scattering system design.

Charles Hartman of LLNL, consults with the ZaP group. Dr. Hartman helped designend loss analyzers and probes, and also performed simulations of ZaP and data analysis.

Masayoshi Nagata of the University of Hyogo, Himeji, Japan, has again loaned the ZaPgroup his ion Doppler spectrometer (IDS) to measure time-dependent ion velocity and tem-perature along a single chord. These results are reported at the 2004 IAEA Conference.

The University of Washington and the University of Hyogo have renewed and expandeda collaborative agreement between the UW College of Engineering and College of Arts andSciences, and the UH Faculty of Engineering and Faculty of Science. This agreement, signedby the Deans of the UW Colleges and the President of UH encourages more collaborationbetween these two institutions. Profs. Uyama, Nagata, Shumlak, and Nelson were instru-mental in achieving this collaborative agreement. The state of Washington and the HyogoPrefecture are ‘sister states’.

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1.2.2 Present Graduate Students

Stuart L. Jackson (A & A) is the senior ZaP graduate student, beginning his fifth yearof graduate school on the project. Mr. Jackson completed his Masters Degree thesis inDecember 2003. In addition to leading experimental operations, Mr. Jackson operates theholography diagnostic and analysis.

1.2.3 Previous Graduate Students

Adam M. Madson (A & A) wrote his masters thesis on the ZaP project. Mr. Madsondeployed two 32-channel photodiode arrays to provide visible light tomography.

Mike Beerman (Mat. Sci.) worked with the ZaP project for two quarters. He made high-frequency measurements of the ZaP voltage waveforms and performed a careful calibrationand error propagation of ZaP surface magnetic field probes.

Justin Bright (A & A) wrote his masters thesis on a neural network program to calculatethe position of the ZaP current channel.

1.2.4 Undergraduate Students

Undergraduate students make large contributions to the ZaP experiment by designing andbuilding equipment and participating in the data acquisition and analysis. They are: PeterNorgaard (now a graduate student in plasma physics at Princeton), Daniel Jackson (now agraduate student studying plasma opening switches at the University of New Mexico), KrisYirak (now a graduate student working on the Omega laser at the University of Rochester),Theodore Shreve, Jason Buller, Derek Schmuland, Colin Adams, David Banks, JonathanMorrow, Mary Attia, Sonca Nguyen, Bryan Munro, Brian Lee, and Emmett Lalish.

Other undergraduate students who worked on ZaP include: Melissa Senger, Joseph Ven-zon, Ray Marcilla, Apostolos Vlachos, Tuan Le, Daniel Lee, Daniel Choi, Eric Forbes,Richard Golob, Tammy Gordin, Steven Hentel, Autumn Lewis, William Litsch, KhahnNguyen, Matthew O’Brien, Graham Schelle, In Taek Song, and David Okada.

1.3 Conferences and Publications

ZaP results have been presented at program reviews, the IAEA meeting on Fusion EnergyResearch, the IEEE ICOPS meeting, the APS DPP meeting, AIAA meetings, and workshopson innovative confinement concepts. During this reporting period, the following presentationswere made:

• IAEA Meeting:

– “Evidence of Flow Stabilization in the ZaP Z Pinch Experiment,” U. Shumlak, E.Crawford, R. P. Golingo, B. A. Nelson, A. Zyrmpas, D. J. Den Hartog, and D. J.Holly, International Atomic Energy Agency Fusion Energy Conference, Sorrento,Italy, October 2000, presenter U. Shumlak.

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– “Evolution of Plasm Flow Shear in the ZaP Flow Z-Pinch”, U. Shumlak, C. S.Adams, R. P. Golingo, S. L. Jackson, B. A. Nelson, and T. L. Shreve, InternationalAtomic Energy Agency Fusion Energy Conference, Lyon, France, October 2002.

• Seminars:

– “The Flow Stabilized Z-Pinch Experiment: ZaP,” University of Wisconsin, Madi-son, Wisconsin, May 1998.

– “The Flow Stabilized Z-Pinch Thruster,” Weizmann Institute of Science, Rehovot,Israel, November 1998.

– “The ZaP Flow-Through Z-Pinch Experiment: Design and Initial Results,” U.Shumlak, B. A. Nelson, R. P. Golingo, D. Tang, E. Crawford, D. J. Den Hartog,and D. J. Holly, Fortieth Annual American Physical Society Meeting of the Di-vision of Plasma Physics, New Orleans, Louisiana, November 1998, presenter U.Shumlak.

• Invited Talks:

– Uri Shumlak, “Sheared Flow Stabilization Experiments in the ZaP Flow Z-Pinch”,Forty-Fourth Annual American Physical Society Meeting of the Division of PlasmaPhysics, Orlando, Florida, November 2002

• Contributed Posters:

– “End Loss Particle Flux as an Indicator of Quiescence in a Flowing Z-Pinch,” P.C.Norgaard, U. Shumlak, B.A. Nelson, R.P. Golingo, and S.L. Jackson, Forty-sixthAnnual American Physical Society Meeting of the Division of Plasma Physics,Savannah, GA, November 2004.

– “Two-Dimensional Z-Pinch Plasma Structure Measured using Photo Diode Ar-rays and Tomography,” A.M. Madson, U. Shumlak, B.A. Nelson, R.P. Golingo,K.T. Yirak, J.C. Morrow, and M.R. Attia, Forty-sixth Annual American Physi-cal Society Meeting of the Division of Plasma Physics, Savannah, GA, November2004.

– “Overview and Recent Results from the ZaP experiment,” R. P. Golingo, U.Shumlak, B. A. Nelson, S. L. Jackson, A. M. Madson, T. L. Shreve, D. J. DenHartog, and the ZaP Research Team, Forty-sixth Annual American Physical So-ciety Meeting of the Division of Plasma Physics, Savannah, GA, November 2004.

– “Overview and Recent Results from the ZaP Flow Z-Pinch”, U. Shumlak, B. A.Nelson, R. P. Golingo, S. L. Jackson, J. Buller, D. Jackson, J. Kim, P. Norgaard,T. Shreve, K. Yirak, and D. J. Den Hartog, Forty-Fifth Annual American PhysicalSociety Meeting of the Division of Plasma Physics, Albuquerque, NM, October2003.

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– “Sustainment of a Sheared Flow in a Z-pinch”, R. P. Golingo, U. Shumlak, B. A.Nelson, S. L. Jackson, K. T. Yirak, and D. J. Den Hartog, Forty-Fifth AnnualAmerican Physical Society Meeting of the Division of Plasma Physics, Albu-querque, NM, October 2003.

– “Electron Density Characteristics of the ZaP Flow Z-Pinch”, S. L. Jackson, U.Shumlak, B. A. Nelson, E. A. Crawford, R. P. Golingo, and T. L. Shreve, Forty-Fifth Annual American Physical Society Meeting of the Division of Plasma Physics,Albuquerque, NM, October 2003.

– “Holographic Interferometry on the ZaP Flow Z-Pinch Experiment,” S. L. Jack-son, E. A. Crawford, R. P. Golingo, B. A. Nelson, U. Shumlak, Forty-FourthAnnual American Physical Society Meeting of the Division of Plasma Physics,Orlando, Florida, November 2002.

– “Formation and Sustainment of a Sheared Flow in a Z-pinch,” R. P. Golingo, S. L.Jackson, B. A. Nelson, U. Shumlak, and D. J. Den Hartog, Forty-Fourth AnnualAmerican Physical Society Meeting of the Division of Plasma Physics, Orlando,Florida, November 2002.

– “The ZaP Flow Z-Pinch Project: Investigations of Flow Shear on MHD Stability,”B. A. Nelson, U. Shumlak, R. P. Golingo, S. L. Jackson, J. Bright, and D. J. DenHartog, Forty-Fourth Annual American Physical Society Meeting of the Divisionof Plasma Physics, Orlando, Florida, November 2002.

– “A New Velocity Inversion Method for the ZaP Flow Z-Pinch Project”, R. P.Golingo, U. Shumlak, B. A. Nelson, E. A. Crawford, S. L. Jackson, and D. J. DenHartog, Forty-Third Annual American Physical Society Meeting of the Divisionof Plasma Physics, Long Beach, California, November 2001.

– “Holographic Interferometry on the ZaP Flow Z-Pinch”, S. L. Jackson, U. Shum-lak, E. A. Crawford, B. A. Nelson, and R. P. Golingo, Forty-Third Annual Amer-ican Physical Society Meeting of the Division of Plasma Physics, Long Beach,California, November 2001.

– “Magnetic Mode Data and Plasma Location in the Zap Experiment”, J. E. Bright,U. Shumlak, and B. A. Nelson, Forty-Third Annual American Physical SocietyMeeting of the Division of Plasma Physics, Long Beach, California, November2001.

– “A New Velocity Inversion Method for the ZaP Flow Z-Pinch Project”, R. P.Golingo, U. Shumlak, B. A. Nelson, E. A. Crawford, S. L. Jackson, and D. J. DenHartog, Forty-Third Annual American Physical Society Meeting of the Divisionof Plasma Physics, Long Beach, California, November 2001.

– “Holographic Interferometry on the ZaP Flow Z-Pinch”, S. L. Jackson, U. Shum-lak, E. A. Crawford, B. A. Nelson, and R. P. Golingo, Forty-Third Annual Amer-ican Physical Society Meeting of the Division of Plasma Physics, Long Beach,California, November 2001.

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– “Magnetic Mode Data and Plasma Location in the Zap Experiment”, J. E. Bright,U. Shumlak, and B. A. Nelson, Forty-Third Annual American Physical SocietyMeeting of the Division of Plasma Physics, Long Beach, California, November2001.

– “Formation of a Sheared Flow Z-Pinch Plasma,” R. P. Golingo, U. Shumlak, andB. A. Nelson, Thirty-Ninth AIAA Aerospace Sciences Meeting, Reno, Nevada,January 2001, presenter R. P. Golingo.

– “A Near-Term, Z-Pinch Fusion Space Thruster,” U. Shumlak, Thirty-Sixth AIAA-/ASME/SAE/ASEE Joint Propulsion Conference, Huntsville, Alabama, July 2000,presenter U. Shumlak.

– “The ZaP Flow Z-Pinch Project,” U. Shumlak, R. P. Golingo, B. A. Nelson, E.Crawford, E. T. Forbes, D. J. Den Hartog, D. J. Holly, and M. Nagata, Forty-Second Annual American Physical Society Meeting of the Division of PlasmaPhysics, Quebec City, Canada, October 2000, presenter U. Shumlak.

– “Spectroscopic Studies of the ZaP Experiment,” R. P. Golingo, B. A. Nelson, U.Shumlak, E. Crawford, D. J. Den Hartog, D. J. Holly, and M. Nagata, Forty-Second Annual American Physical Society Meeting of the Division of PlasmaPhysics, Quebec City, Canada, October 2000, presenter R. P. Golingo.

– “Magnetic Studies of Symmetry and Stability in the ZaP Flow Z-Pinch,” B. A.Nelson, R. P. Golingo, U. Shumlak, E. Crawford, D. J. Den Hartog, and D. J.Holly, Forty-Second Annual American Physical Society Meeting of the Divisionof Plasma Physics, Quebec City, Canada, October 2000, presenter B. A. Nelson.

– “Symmetry and Stability of the ZaP Flow-Through Z-Pinch,” B. A. Nelson, R. P.Golingo, U. Shumlak, D. Tang, E. Crawford, D. J. Den Hartog, and D. J. Holly,Forty-First Annual American Physical Society Meeting of the Division of PlasmaPhysics, Seattle, Washington, November 1999, presenter B. A. Nelson. DiscreteWavelet Transform Based Magnetic Probe Calibration

– “The Flow-Stabilized Z-Pinch Experiment: ZaP,” U. Shumlak, B. A. Nelson, R.P. Golingo, D. Tang, E. Crawford, D. J. Den Hartog, and D. J. Holly, Forty-FirstAnnual American Physical Society Meeting of the Division of Plasma Physics,Seattle, Washington, November 1999, presenter U. Shumlak.

– “The ZaP Flow-Through Z-Pinch Experiment: Design and Initial Results” U.Shumlak, B.A. Nelson, R.P. Golingo, D. Tang, E. Crawford, D.J. Den Hartog, andD.J. Holly, Fortieth Annual American Physical Society Meeting of theDivision ofPlasma Physics, November 1998, New Orleans, LA

• Workshops:

– Contributed talk: “Formation and Sustainment of a Sheared Flow Z-Pinch”, In-novative Confinement Concepts Workshop, Madison, WI, May 2004. Presentedby Dr. R. P. Golingo.

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– “The Flow Stabilized Z-Pinch Experiment: ZaP,” U. Shumlak, R. P. Golingo, S.L. Jackson, B. A. Nelson, E. A. Crawford, and D. J. Den Hartog, Innovative Con-finement Concepts Workshop, College Park, Maryland, February 2002, presenterU. Shumlak.

– “Flow Stabilization in a Z Pinch,” U. Shumlak, B. A. Nelson, R. P. Golingo,E. Crawford, D. J. Den Hartog, and D. J. Holly, Workshop on Stability andConfinement of Alternative Concepts, Varenna, Italy, October 2000, presenter U.Shumlak.

– Innovative Confinement Concepts, LBNL and LLNL, Berkeley CA (US Feb. 2000)

– The 3rd Workshop on Active MHD Mode Control in Innovative Confinement Con-cepts, Seattle WA, U. Shumlak presenter, B. A. Nelson, local organizer, Nov. 2000.

1.3.1 Publications

• Published:

D. J. Den Hartog and R. P. Golingo “Telecentric Viewing System for LightCollection from a Z-Pinch Plasma” Review of Scientific Instruments 72, 2224(2001).

U. Shumlak, R. P. Golingo, B. A. Nelson, and D. J. Den Hartog “Evidence ofStabilization in the Z-Pinch” Physical Review Letters 87, (2001).

U. Shumlak, B. A. Nelson, R. P. Golingo, S. L. Jackson, E. A. Crawford and D.J. Den Hartog, “Sheared flow stabilization experiments in the ZaP flow Z pinch”Physics of Plasmas, 10(5):1683–1693, May 2003.

R. P. Golingo and U. Shumlak, “Spatial deconvolution technique to obtain ve-locity profiles from chord integrated spectra” Review of Scientific Instruments,74(4):2332–2337, April 2003.

D. J. Den Hartog, R. P. Golingo, S. L. Jackson, B. A. Nelson, and U. Shumlak.“The zap flow Z-pinch: plasma flow shear and stability” Fusion Science andTechnology, 47(1T):134 – 7, 2005.

R. P. Golingo, U. Shumlak, and B. A. Nelson. “Formation of a sheared flow Zpinch” Physics of Plasmas, 12(6):62505 – 1, June 2005.

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2 Experimental Results

ZaP has continued to increase the stable quiescent period and has collected more dataconsistent with the concept of sheared-flow stabilization.

2.1 Velocity Profiles and Stability

Extensive studies using the ICCD Doppler spectrometer have provided a mapping of theZaP velocity profile onto a radius - normalized quiescent time plane, Fig. 1. Plasma flowvelocity profiles are determined by measuring the Doppler shift of plasma impurity linesusing an imaging spectrometer with an intensified CCD camera (ICCD) operated with a100 ns gate. The spectrometer images 20 spatial chords spaced 1.78 mm apart through theplasma pinch at a 35◦ angle to the plasma axis providing a measurement of the axial velocityprofile. The collected data are chord-integrated and are deconvolved to determine the axialvelocity profile.[6] The velocity profile is measured at one time during a pulse. Varying theICCD trigger time between pulses provides a measure of the plasma flow time-dependentevolution throughout the plasma pulse. The upper plot of Fig. 1 shows the evolution ofthe axial velocity profile of the plasma pinch as a function of time τ normalized by theplasma quiescent period. Profiles are shown during the pinch assembly (τ < 0), through thequiescent period (defined as τ = [0, 1]), and through transition from quiescence to instability(τ > 1). The velocity profile evolves from a large uniform flow for τ < 0 to one that issheared with a higher velocity at the edge. Late in the quiescent period, τ ∼ 0.8, the edgevelocity decreases towards zero. At the end of the quiescent period, τ=1, the center velocityquickly decays, resulting in a plasma flow profile that is low and uniform.

Plasma stability is diagnosed with the azimuthal array of magnetic probes described inearlier Progress Reports. The measurements from the probe array determine the plasma’smagnetic structure. Data from these probes are Fourier analyzed to determine the time-dependent evolution of the low order azimuthal modes (m=1, 2, 3). The lower plot of Fig. 1shows the evolution of the m=1, 2, 3 Fourier modes of the magnetic field Bm (t) normalized bythe average magnetic field B0 (t). Large magnetic fluctuations occur during pinch assembly,after which the amplitude and frequency of the magnetic fluctuations diminish. This stablebehavior continues for 35 – 45 µs and defines the quiescent period. At the end of thequiescent period, the fluctuation levels then again change character, increase in magnitudeand frequency, and remain until the end of the plasma pulse. The time scale in Fig. 1 isnormalized by the duration of the quiescent period to allow data comparison among pulses.The quiescent period defines τ = [0, 1]. Data from other diagnostics are consistent withthis description of the plasma behavior. Visible emission from the pinch is recorded with afast framing camera and a photodiode array. The data show a stable pinch that becomesunstable. The timing of the stable period corresponds to the stable time shown in themagnetic mode data.

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τ

r(m

m)

-0.5 0 0.5 1 1.5-20

-10

0

10

20

1.2E+05

1.1E+05

1.0E+05

9.0E+04

8.0E+04

7.0E+04

6.0E+04

5.0E+04

4.0E+04

3.0E+04

2.0E+04

1.0E+04

0.0E+00

τ

-0.5 0.0 0.5 1.0 1.5

Bm/B

0

0.0

0.2

0.4

0.6

0.8

1.0

m=1

m=2

m=3

Pulse 40108045

Figure 1: Upper: Contours showing the evolution of the velocity profiles in time normalizedto the quiescent period. (The plot is constructed from data of many pulses.) Lower: Magneticfluctuation levels for m=1, 2, & 3 for one plasma pulse. The quiescent period is 36.5 µs.

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2.2 Velocity Dependence on Neutral Gas Injection

Time-dependent plasma flow velocities are measured during a single pulse with an IonDoppler Spectrometer (IDS) instrument. The instrument consists of a sixteen-anode PMTdetector connected to a 1 m spectrometer that views the plasma pinch along a single 35◦

chord. The spectrometer is tuned to plasma impurity lines. The sixteen signals from thePMT are fit with a Doppler shifted and broadened Gaussian distribution to provide a mea-sure of the chord-averaged plasma velocity and temperature as a function of time.

Further insight into the Z-pinch stabilization is obtained by varying the plenum pressureof the gas puff valves and, thereby, controlling the amount of injected neutral gas in a pulse.(The ZaP gas puff valves are described in Ref. [7].) The plenum pressure is varied between2150 and 4650 Torr and a series of pulses are performed. On each pulse the plasma velocityand temperature are determined from the IDS instrument data. The instrument only recordsvelocity and not velocity shear. However, if we assume the shear length is approximatelythe pinch radius, a ∼ 1 cm, and the mode of interest has ka = π, the theoretical stabilitythreshold (dVz/dr > 0.1kVA) can be expressed as Vz/ (0.1πVA) > 1. The time-dependentAlfven speed in the Z-pinch is computed using the instantaneous density measured fromthe two-chord interferometer and the instantaneous B0 measured from the magnetic probes.Figure 2 shows the velocity shear normalized by the theoretical threshold as a functionof time for three different plenum pressures. The m=1 component of the magnetic fieldmeasured at the outer electrode is also shown. For the plenum pressures of 3650 and 4650Torr, a period of time exists when the normalized velocity shear is above unity. Duringthis quiescent period the asymmetric magnetic fluctuations are lower and have a differentcharacter compared to before and after the quiescent period. The fluctuations during thequiescent period are characterized by low amplitude and low frequency. This characterchanges at approximately the same time that the normalized velocity shear drops belowunity. For the case with a plenum pressure of 2650 Torr, the normalized velocity shear neverexceeds unity and only briefly approaches unity. The magnetic fluctuations have a highamplitude and high frequency except when the velocity shear approaches the threshold.

2.3 Comparison to Theoretical Threshold for Stability

The measured axial flow shear is compared to the required threshold predicted by lineartheory. Using the experimental data, VA = 1.5 × 105 m/s. The theoretical growth timefor a static Z-pinch is approximately (kVA)−1 which for the experimental values obtained inthe ZaP experiment gives τgrowth = 21 ns for ka = π. The axial velocity shear required forstability according to the theory is 4.7 × 106 s−1. The experimental results show a stableperiod of more than 40 µs, almost 2000 growth times. The experimentally measured axialvelocity shear is between 6.5 – 12×106 s−1 during the stable period τ = [0, 0.9], the valuedrops to 3 – 6×106 s−1 at the end of the quiescent period τ ∼ 0.95 and below 3×106 s−1 afterthe quiescent period τ > 1 when the magnetic mode fluctuations are high. The correlationof the experimental stability data with the plasma flow measurements is consistent with theshear flow stabilization theory.[2, 4]

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Time ( s)

0 20 40 60 80 100

Vz/

0.1

VA

0

1

2

3

B1 (T

)

0.00

0.02

0.04

0.06

Velocity Ratio

m = 1

4650 torr

Pulse 40824005

Time ( s)

0 20 40 60 80 100

Vz/

0.1

VA

0

1

2

3

B1 (T

)

0.00

0.02

0.04

0.06

Velocity Ratio

m = 1

3650 torr

Pulse 40824028

Time ( s)

0 20 40 60 80 100

Vz/

0.1

VA

0

1

2

3

B1 (T

)

0.00

0.02

0.04

0.06

Velocity Ratio

m = 1

2650 torr

Pulse 40825014

Figure 2: Velocity shear data (from IDS) normalized by the theoretical threshold as functionof time. The plenum pressure in the gas puff valves is varied. The (unnormalized) m=1component of the magnetic field at the outer electrode is also plotted.

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2.4 Discussion

If it is assumed that velocity shear is playing the critical role of providing stability forthe otherwise unstable Z-pinch, then two possible mechanisms that limit the lifetime ofthe plasma confinement are: 1) decay of plasma current, and 2) loss of plasma flow or flowshear. These two mechanisms may not be completely independent. However, the experimentsconducted with different plenum pressures in the puff valves appear to discount the decay ofplasma current as the lifetime limiting mechanism. The bank configuration is identical for theexperiments. Different neutral gas injection alters the plasma dynamics and, thereby, altersthe plasma current. However, the plasma current pulse is generally similar. The currentpulse length is approximately 100 µs and the peak current varies between 160 – 200 kA.

Loss of plasma flow is a more likely mechanism that limits the plasma lifetime. Previousexperimental measurements indicate a decrease of plasma acceleration in the accelerationregion of the experiment that is approximately coincident with the end of the quiescentperiod in the Z-pinch plasma.[4] Specifically, the azimuthal magnetic field values measuredat several axial locations converge to the same value indicating a decrease of radial currentin the acceleration region. Plasma density in the acceleration region is also observed todecrease during these same experiments.[4] While not conclusive, the experimental resultssuggest the loss of plasma flow may be caused by a depletion of the injected neutral gas. Theexperimental results presented here further support this conjecture. The results presented inFig. 2 show shorter quiescent periods for less injected neutral gas. A distinct quiescent periodis not observed when the gas puff valve plenum pressure is lowered to 2650 Torr. Experimentsare on-going to further investigate the dependence of the plasma lifetime on injected neutralgas. Future experimental modifications include additional gas puffing capacity to approacha quasi steady-state operation of the ZaP Flow Z-Pinch experiment. True steady state is notlikely to be possible with gas puff valves; however, using plasma injectors may be feasible.

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Figure 3: Schematic of the ZaP Thomson scattering design.

3 The ZaP Experiment

Several hardware updates and modifications started during this reporting period are ongoing.

3.1 Thomson Scattering System Design

With help from Drs. Daniel Den Hartog and Ed Crawford, we are designing a (multi-pointcapable) Thomson scattering system for ZaP, Fig. 3. (Initial operation will be to mea-sure single point Te.) This system uses a Korad 10 J ruby laser (from the HIT project),a Hibshman spectrometer (from ZT-40), and an MCP detector (from ZT-40). Appropriatedata recording equipment is being sought. This system will be capable of measuring severalpoints across the plasma diameter at a single time. Calculations of signal to noise (and back-ground) lead us to expect excellent statistics, as seen in Fig. 4. The Korad laser beam andthe spectrometer have been characterized, and dark current measurements have successfullyperformed on the MCP. Design work is continuing on the input/output optics, beam path,beam dump, detector mount, and electronics.

3.2 Larger Inner Electrode Design

A new 15 cm diameter inner electrode, Fig. 5, is being built to replace the present 10 cmdiameter inner electrode. This will provide more adiabatic heating to increase the ion tem-perature by a factor of approximately 1.7. The present single gas puff valve on the smaller

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Figure 4: Estimate of ZaP Thomson scattering system signal to noise ratio using measuredbremsstrahlung data and the ZaP TS system design.

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Figure 5: Schematic of the 15 cm inner electrode design.

inner electrode will be replaced by eight azimuthally spaced gas puff valves in the larger elec-trode. This will help avoid depleting plasma in the acceleration region, which is correlatedwith the end of the quiescent period (see Section 2.4). Contoured termination “nose cones”can be interchanged to further control the flow profile.

The design has been completed and final machine drawings are being prepared. Thecopper electrode material has been purchased and is being prepared for machining.

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References

[1] U. Shumlak and C. W. Hartman. Sheared flow stabilization of the m=1 kink mode in Zpinches. Physical Review Letters, 75(18):3285–3288, October 1995.

[2] U. Shumlak, R. P. Golingo, B. A. Nelson, and D. J. Den Hartog. Evidence of stabilizationin the Z-pinch. Physical Review Letters, 87(20):205005/1–4, November 2001.

[3] D. J. Den Hartog, R. P. Golingo, S. L. Jackson, B. A. Nelson, and U. Shumlak. The zapflow z-pinch: plasma flow shear and stability. Fusion Science and Technology, 47(1T):134– 7, 2005.

[4] U. Shumlak, B. A. Nelson, R. P. Golingo, S. L. Jackson, E. A. Crawford, and D. J. DenHartog. Sheared Flow Stabilization Experiments in the ZaP Flow Z-Pinch. Physics ofPlasmas, 10(5):1683–1690, May 2003.

[5] R. P. Golingo, U. Shumlak, and B. A. Nelson. Formation of a sheared flow z pinch.Physics of Plasmas, 12(6):62505 – 1, June 2005.

[6] R. P. Golingo and U. Shumlak. A spatial devonvolution technique to obtain velocityprofiles from chord integrated spectra. Review of Scientific Instruments, 74(4):2332–2337, April 2003.

[7] T. Shreve. University of Washington Aerospace & Energetics Research Program ReportUWAERP/20030527:62-7316, University of Washington, Seattle, WA 98195, 2003.

18

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 72, NUMBER 4 APRIL 2001

Telecentric viewing system for light collection from a z-pinch plasmaD. J. Den Hartoga)

Sterling Scientific, 2310 Van Hise Avenue, Madison, Wisconsin 53705

R. P. GolingoDepartment of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195

~Received 24 August 2000; accepted for publication 8 January 2001!

As part of a Doppler spectroscopy system to measure the radial variation of ion flow andtemperature, a pair of telecentric viewing telescopes has been installed on the ZaPz-pinch plasmadevice. Each telescope simultaneously collects 20 chords of light~200–1200 nm! emitted byimpurities in the plasma, and images the chords on a fiber optic bundle for transport to aspectrometer. The center-to-center spacing of adjacent chords in the plasma is 1.24 mm, thus radialvariation across ther 510– 15 mm ZaP plasma is completely recorded. In this telecentric imagingsystem, all object chords and image points, including those laterally displaced from the optical axis,are formed by ray bundles whose chief ray is parallel to the optical axis. Thus all 20 light collectionchords passing through the ZaP plasma are parallel, and all 20 image points fill the optical fiberswith an identical cone. This maximizes system efficiency and measurement precision, and simplifiescalibration and data analysis. ©2001 American Institute of Physics.@DOI: 10.1063/1.1353188#

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The ZaPz-pinch plasma device1 at the University ofWashington produces a small diameter~20–30 mm! densez-pinch plasma with typical electron density 1022– 1023m23

and ion plus electron temperature 100–200 eV. The plais stable, with relatively low magnetic mode activity, for teof microseconds.2 This is orders of magnitude longer thapredicted by a simple ideal magnetohydrodynamic calcution. Radial shear in the axial plasma flow has been propoas a potential stabilizing mechanism,3–5 thus accurate measurement of the magnitude and radial variation of the aflow will provide critical input to theory.

Plasma flow is being passively measured in ZaP bycording the Doppler shift of UV and visible lines emitted bintrinsic carbon and oxygen impurities in the majority hydrgen plasma.6 Useful lines are CIII at 229.687 nm and OV at278.101 nm, similar to what has been observed in a gas-z pinch.7,8 To obtain radially resolved profiles of the axiflow velocity in ZaP, the plasma is viewed through two tescopes~Fig. 1!. The radial telescope views perpendicularthe axis of the ZaP plasma, and thus provides the nDoppler-shifted reference spectra~radial and poloidal flowsare small relative to axial flow!. The oblique telescope view35° off the ZaP axis, and is sensitive to Doppler shiftsduced by axial flows. These viewing telescopestelecentric9 ~Fig. 2!, meaning that the object and imaglenses are separated by the sum of their focal lengths, witaperture stop at the conjugate focal plane to place the puof the two lenses at infinity. This insures that all objechords in the plasma and image points on the fiber bunincluding those laterally displaced from the optical axis, aformed by ray bundles whose chief ray is parallel to toptical axis. Two advantages result from this: First, alllight collection chords passing through the ZaP plasma

a!Present address: Department of Physics, University of Wisconsin-MadMadison, WI 53706; electronic mail: [email protected]

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parallel and equally spaced, simplifying calibration and dreduction, particularly inversion of the chord-average proto local flow velocities.10,11 Second, all 20 image points othe fiber bundle are formed by identical cones whose chray is perpendicular to the fiber face; thus each individoptical fiber is efficiently filled at an identicalf /7.

The 20 image points from the telescope collectichords are formed on 20 individual fused silica core/cmultimode fibers. These 400mm core diameter fibers armounted in a line, 0.62 mm center-to-center spacing, in ctom fixtures that preserve one-to-one mapping. Light froeach collection chord is mapped to a specific vertical lotion on the entrance slit by simply butting the fiber bundfixture ~and thus the fiber faces! directly to the slit face, witha typical slit width of 25mm. If not bent in an excessivelytight radius, the 4 m long large core optical fibers effectivepreserve thef /7 cone with which they were filled, so nmatching optics are necessary to fill thef /7 acceptance of the

n,FIG. 1. Side view of the ZaP device and two viewing telescopes in scmatic form.

4 © 2001 American Institute of Physics

P license or copyright, see http://rsi.aip.org/rsi/copyright.jsp

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2225Rev. Sci. Instrum., Vol. 72, No. 4, April 2001 Notes

FIG. 2. Top view of radial viewing telescope, illustrating the telecentricity of the object chords and image points. Only central and extreme edge rabundlesare shown.

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0.5 m spectrometer~Acton Research SpectraPro 500i!. Thisspectrometer is corrected for astigmatism, thus the imageach of the fibers butted up to the entrance slit is preseand light from each fiber is dispersed across a distinct hzontal strip of the spectrometer exit plane. Each horizonstrip then contains the Doppler broadened and shifted spefrom a specific collection chord in the plasma. All 20these spectra are simultaneously recorded by a gated~>100ns! intensified CCD camera~Roper Scientific PI-MAX! andare stripped out of the two-dimensional camera image byanalysis program. Thus the entire radial profile of the plasflow velocity is captured at a specific timepoint during tZaP discharge; temporal development of the profile iscorded by firing reproducible discharges and moving the gtime.

In order to simplify telescope design, the lenses wfixed in place, but the fiber bundle fixture is mounted on ttranslation stages to provide fine adjustability both paraand perpendicular to the optical axis. The radial teleschas two lenses of 175 and 350 mm focal length, whileoblique telescope has lenses of 250 and 500 mm focal lenBoth telescopes magnify the plasma light collection choby a factor of20.5 onto the fiber bundle faces. The centto-center spacing of adjacent chords in the plasma is 1mm. Therefore, the 23.6 mm wide line of chords in tplasma appears as an 11.8 mm line of image points onbundle face, and the line image is inverted. The linechords in the plasma does not need to be centered onplasmar 50, as the perpendicular translation stage allothe edge chord to move out tor 520 mm for the radial tele-scope and tor 517 mm for the oblique telescope~these lim-its are determined by the diameter of the viewing hole inZaP outer electrode!. Thus it is possible to position the edgchords outside the edge of the ZaP plasma (r 510– 15 mm)

FIG. 3. Sample Doppler-broadened spectra~C III line at 229.687 nm! fromthe 20 chords through the radial viewing telescope.

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and clearly record the behavior of the edge plasma, anportant requirement for successful inversion of the chointegrated profiles.

During design, the telecentricity of the viewing telescopes was optimized for the 200–250 nm wavelength ranRefractive power of the lenses falls at longer wavelengtbut this is partially compensated by installing a slighlarger aperture stop and moving it toward the longer folength lens, and translating the face of the fiber bundleture away from the shorter focal length lens~see Fig. 2!.With these adjustments, degradation of image quality isnor, and magnification changes by only a few percent. Sithe windows, telescope lenses, and optical fibers are Ugrade fused silica, the system is useful from 200 to 1200

Although the ability to record spectra from the two telscopes simultaneously would be ideal, doing so wouldquire two separate spectrometers. As a cost effective altetive, each of the viewing telescopes is connected toseparate entrance slit on the spectrometer, designated‘‘side’’ and ‘‘front’’ slits. The front slit looks directly at thecollimating mirror, while the side slit is remotely engagedprecisely flipping a mirror driven by a stepper motor into toptical path. When this mirror is engaged, light is blockfrom the front slit, therefore data can be recorded from oone slit~and one telescope! during a ZaP shot. Therefore, thusual operating procedure requires a shot to obtain spefrom the radial view to provide the baseline calibration of tnon-Doppler-shifted emission line~typical data shown inFig. 3! then spectra are recorded from the oblique telescto measure the radial variation of the plasma flow profile

ACKNOWLEDGMENTS

The authors acknowledge close collaboration with DHolly, B. A. Nelson, and U. Shumlak. This work was suported by the U. S. Department of Energy under a Subctract from the University of Washington.

1U. Shumlaket al., Bull. Am. Phys. Soc.44 ~7!, 113 ~1999!.2B. A. Nelsonet al., Bull. Am. Phys. Soc.45 ~7!, 210 ~2000!.3U. Shumlak and C. W. Hartman, Phys. Rev. Lett.75, 3285~1995!; T. D.Arber and D. F. Howell,ibid. 76, 2198 ~1996!; U. Shumlak and C. W.Hartman,ibid. 76, 2199~1996!.

4T. D. Arber and D. F. Howell, Phys. Plasmas3, 554 ~1996!.5A. B. Hassam, Phys. Plasmas6, 3772~1999!.6I. H. Hutchinson,Principles of Plasma Diagnostics~Cambridge Univer-sity Press, Cambridge, 1987!, p. 230.

7R. Aradet al., Rev. Sci. Instrum.63, 5127~1992!.8M. E. Foordet al., Phys. Rev. Lett.72, 3827~1994!; 73, 1190~E! ~1994!.9W. J. Smith,Modern Optical Engineering: The Design of Optical System,2nd ed.~McGraw-Hill, New York, 1990!, p. 142.

10R. E. Bell, Rev. Sci. Instrum.68, 1273~1997!.11J. Howard, Plasma Phys. Controlled Fusion38, 489 ~1996!.


VOLUME 87, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 12 NOVEMBER 2001

205005-1

Evidence of Stabilization in the Z-Pinch

U. Shumlak, R. P. Golingo, and B. A. NelsonUniversity of Washington, Aerospace and Energetics Research Program, Seattle, Washington 98195-2250

D. J. Den Hartog*Sterling Scientific, Inc., Madison, Wisconsin

(Received 11 June 2001; published 29 October 2001)

Theoretical studies have predicted that the Z-pinch can be stabilized with a sufficiently sheared axialflow [U. Shumlak and C. W. Hartman, Phys. Rev. Lett. 75, 3285 (1995)]. A Z-pinch experiment isdesigned to generate a plasma which contains a large axial flow. Magnetic fluctuations and velocityprofiles in the plasma pinch are measured. Experimental results show a stable period which is over 700times the expected instability growth time in a static Z-pinch. The experimentally measured axial velocityshear is greater than the theoretical threshold during the stable period and approximately zero afterwardswhen the magnetic mode fluctuations are high.

DOI: 10.1103/PhysRevLett.87.205005 PACS numbers: 52.58.Lq, 52.30.–q, 52.35.Py

The Z-pinch plasma configuration has been studiedsince the beginning of the pursuit of magnetic plasmaconfinement fusion [1–3]. The Z-pinch was largely aban-doned as a magnetic confinement configuration due toviolent magnetohydrodynamic (MHD) instabilities (grossm � 0 “sausage” and m � 1 “kink” modes) demonstratedboth theoretically and experimentally [4]. However, ex-periments have generated Z-pinch plasmas with inherentaxial plasma flows exhibiting stable confinement for timesmuch longer than the predicted growth times [5,6]. Astable, high-density Z-pinch configuration would haveprofound implications for magnetic confinement thermo-nuclear fusion [7–9].

Theoretical studies have demonstrated that the Z-pinchcan be stabilized with a sufficiently sheared axial flow [10].Experimental results presented here show a stable periodwhich is over 700 times the expected instability growthtime in a static Z-pinch. The experimentally measured ax-ial velocity shear is greater than the theoretical thresholdduring the stable period and approximately zero afterwardswhen the magnetic mode fluctuations are high. The cor-relation of the experimental stability data with the plasmaflow measurements is consistent with the shear flow sta-bilization theory presented in Ref. [10]. However, at thispoint causality cannot be determined.

The role of plasma flow on the MHD instabilities in aZ-pinch has been examined theoretically using linear sta-bility analysis [10,11]. The fundamental result from bothof these studies is the Z-pinch can be stabilized by applyinga sheared axial flow though the required magnitude of theplasma flow differs for these two studies. Reference [10]concludes that an axial plasma flow with a linear shearof yz�a . 0.1kVA is required for stability of the m � 1mode where k is the axial wave number. Reference [11]concludes that an axial plasma flow of yz . 2 2 4VA isrequired for stability of all modes with ka � 10. Both ofthese results are for a conducting wall placed far enough

0031-9007�01�87(20)�205005(4)$15.00

from the plasma boundary that it has no effect. Nonlinearresults for the m � 0 mode are presented in Fig. 1. The re-sults are generated using Mach2 [12,13], a time-dependent,resistive MHD code. An equilibrium is initialized witha sheared axial plasma flow and an axially periodic den-sity perturbation. The figure shows the pressure contoursfor the case of (a) no flow and (b) yz�a � 0.2kVA at thesame simulation time. Figure 1(a) shows a well-developedm � 0 instability in a static Z-pinch plasma. Figure 1(b)shows a substantially less developed m � 0 instability ina Z-pinch plasma with a sheared axial flow.

The ZaP (Z-pinch) experiment at the University ofWashington has been used to investigate the effect ofplasma flow on the stability of a Z-pinch. The experimentis designed to generate a Z-pinch plasma which containsa large axial flow. The experimental device is depicted inFig. 2. The flow Z-pinch configuration is generated byusing a coaxial accelerator to initiate the hydrogen plasma

(b)(a)

FIG. 1. Nonlinear simulation results showing the pressure con-tours in a Z-pinch at the same simulation time (a) for the de-veloped m � 0 mode with no equilibrium axial flow and (b) forthe stabilized m � 0 mode with yz�a � 0.2kVA.

© 2001 The American Physical Society 205005-1


FIG. 2. Side view drawing of the ZaP experiment showing the relevant features. The solid lines indicate the electrodes and thedotted lines indicate the vacuum vessel. The top and bottom ports in the assembly region are used for spectroscopy, and the sideports are used for obtaining images from the fast framing camera and measuring density.

from puff injected neutral gas and to accelerate the plasmaaxially in the “acceleration region.” When the plasmareaches the end of the inner electrode of the accelerator, theplasma assembles along the axis in the “assembly region.”The plasma in contact with the outer electrode continues tomove axially until it reaches the electrode end wall wherethe plasma moves radially inward to complete the pinchformation. The axial plasma flow is maintained in thepinch by inertia. Plasma is accelerated and incorporatedinto the pinch continually by current in the acceleration re-gion. The plasma accelerator operates in a “quasi-steady-state” mode that has been described previously [14].

The Z-pinch plasma has a 50 cm length and an approxi-mately 1 cm radius when assembled. The peak plasmacurrent supplied from a 46 kJ capacitor bank is 275 kAand has a quarter cycle time of 30 msec. The experimentalmeasurements presented in this paper are obtained at thepinch midplane as identified in Fig. 2.

The electron number density in the plasma pinch is de-termined from a two chord He-Ne heterodyne quadratureinterferometer. One chord traverses the plasma midplanealong the geometric diameter, and a second chord is paral-lel to and 2 cm above the first chord. The plasma densityis assumed to have spatially uniform values outside andinside the pinch radius determined from optical emissionand spectroscopic data. The plasma electron number den-sity is determined to be 1016 1017 cm23 inside the pinch.

The magnetic field measured at the outer electrode atthe pinch midplane with surface mounted magnetic probesis 0.15–0.25 T. The magnetic field at the pinch radiusis then 1.5–2.5 T assuming no plasma current outside ofthe pinch radius. The total plasma temperature �Te 1 Ti�is estimated from force balance to be 150–200 eV. Theion temperature is calculated from Doppler broadening ofimpurity lines to be 50–80 eV.

Eight surface magnetic probes are equally spaced aroundthe azimuth at the pinch midplane. The probes measurethe azimuthal magnetic field at the surface of the outerelectrode. Data from these probes are Fourier analyzed to

205005-2

determine the time-dependent evolution of the low orderazimuthal modes �m � 1, 2, 3�. Figure 3 shows the timeevolution of the m � 1 and m � 2 Fourier modes of themagnetic field. The average magnetic field B0�t� of alleight probes is used to normalize the Fourier mode data atthe pinch midplane. The m � 3 mode (not shown in thefigure) is also analyzed and is lower than the m � 2 levelat all times. The figure also shows the evolution of thetotal plasma current for reference.

The plasma arrives at the pinch midplane at approxi-mately 18 msec. Magnetic mode fluctuation data beforethis time can be ignored and are caused by small signalnoise which is amplified in the normalization procedure.After the pinch has formed the initially large fluctuationlevels for both m � 1 and m � 2 change character for ap-proximately 17 msec. The change in character is identifiedby lower levels and decreased frequency. The fluctuationlevels then again change character, increase in magnitudeand frequency, and remain until the end of the plasmapulse.

Optical emission images of the pinch midplane are ob-tained with a fast framing camera every 1 msec. The im-ages show a stable pinch that becomes unstable to a kink

FIG. 3. Time evolution of Fourier components of the magneticfield fluctuation at the pinch midplane for m � 1 and m � 2showing the quiescent period from 21 to 38 msec. The valuesare normalized to the average magnetic field value at the pinchmidplane. The evolution of the total plasma current (dashedcurve) is included for reference.

205005-2


mode. The timing of the stable period corresponds to thestable time shown in the magnetic data.

Plasma flow velocity profiles are determined by mea-suring the Doppler shift of plasma impurity lines usinga 0.5 m imaging spectrometer with an intensified charge-coupled device (ICCD) detector. The ICCD camera is setto a gating time of 1 msec and the trigger time is var-ied between plasma pulses. The spectrometer images 20spatial chords through the plasma onto the ICCD camerausing telecentric viewing telescopes [15]. The telescopesare connected to the spectrometer with a fiber bundle com-posed of twenty fused silica fibers. The chords image 20points spaced 1.24 mm apart along a diameter through thepinch. Optical access to the midplane is provided throughradial viewports and oblique viewports positioned at a 35±

angle to the plasma column, as shown in Fig. 2.Doppler shifts are calculated by viewing the plasma

through the radial viewport to locate the unshifted impu-rity line and then viewing the plasma through the obliqueviewport. The oblique view has a directional componentalong the axis and, therefore, is sensitive to Doppler shiftsfrom axial flows. Figure 4 shows the output from the ICCDspectrometer tuned to the C-III line at 229.7 nm and view-ing the plasma through the oblique viewport. The triggertime for the ICCD is 30 msec which is during the quies-cent period. (This pulse is the same presented in Fig. 3.)The data show a shift of the C-III line being emitted fromthe chords of the inner core of the pinch and a lesser shiftof the line being emitted from the edge of the pinch.

The data are deconvolved to resolve the spatial depen-dence of the Doppler shift of the impurity line. The rawdata are corrected to remove instrument distortions andbinned into 20 nonoverlapping spatial chords. The binneddata are deconvolved by assuming the plasma is uniformwithin 10 concentric shells. The spectral line shapes ateach chord location are fit with Gaussians modified by the

FIG. 4. Chord-integrated C-III line (229.7 nm) emission at30 msec with a 1 msec gate obtained with the ICCD spectrome-ter showing the Doppler shift of the impurity line in the core ofthe pinch and a smaller shift towards the edge of the plasma.The solid line is positioned at 229.7 nm for reference. (The peaksignal to noise ratio of the lowest intensity chord is 15.5.)

205005-3

instrument function and account for the chord-integratedview through outer shells. The procedure is repeated be-ginning from each edge of the plasma. Fit parameters arethe location of the plasma edge, the plasma axis location,and the emissivity, Doppler shift, and Doppler width of theemitted light at each chord location. The deconvolved ve-locity profile for the data shown in Fig. 4 is presented inFig. 5. The lack of symmetry in the fitted profiles indicatesa lack of symmetry in this plasma pulse. The symmetryof the deconvolved fit is sensitive to the plasma axis lo-cation. The emissivity profile (not shown) indicates theplasma has a characteristic pinch radius of approximately1 cm and is centered in the horizontal plane with respect tothe experimental geometry. The velocity profile in Fig. 5shows a large axial velocity in the inner core of the pinchof 105 m�s and a lower value of 4 3 104 m�s towards theedge of the pinch.

After the quiescent time the plasma flow velocity is sig-nificantly reduced. Figure 6 shows the ICCD output forthe same setup as previous with a trigger time of 38 msecwhich is after the quiescent period and when the magneticmode activity is high. The spectra for all of the spatial lo-cations are centered on the 229.7 nm reference line in thefigure. A maximum limit to the velocity is determined byfitting the chord integrated data with two Gaussian func-tions having equal widths which overestimates the veloc-ity. (An accurate deconvolution is not possible withoutsimultaneous data to identify the edge and center of theplasma.) The peaks are broader indicating random plasmamotion and plasma heating due to flow stagnation on theelectrode end wall, identified in Fig. 2. At a velocity of105 m�s the plasma flows through the 50 cm assembly re-gion in 5 msec.

The experimental data from the plasma optical emissionand surface magnetic probes indicate the plasma, which isinitially unstable during assembly, forms a stable plasma

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205005-3


FIG. 6. Chord-integrated C-III line (229.7 nm) emission at38 msec with a 1 msec gate obtained with the ICCD spectrome-ter showing a negligible Doppler shift of the impurity line. Thesolid line is positioned at 229.7 nm for reference.

pinch. The plasma remains stable during a 15 20 msecquiescent period. During the quiescent period the plasmaflow is organized into a profile that has a large shear of theaxial velocity and is maximum close to the plasma edge.After the quiescent period the plasma becomes unstableas evidenced by an increase in magnetic fluctuation levelsand a disappearance of the pinch from the field of viewof the optical camera. After the quiescent period the flowvelocity is mostly uniform with a maximum considerablyless than during the quiescent period.

The measured axial flow shear can be compared to therequired threshold predicted by linear theory. The mag-netic field at the outer electrode is measured to be 0.18 Tfor a magnetic field value at the characteristic pinch ra-dius Ba � 1.8 T assuming zero plasma current densityfor r . a. The electron number density in the pinch ismeasured to be n � 9 3 1016 cm23. The Alfvén veloc-ity is VA � Ba�

pmoMin � 1.3 3 105 m�s, where Mi is

the mass of a hydrogen ion. The theoretical growth ratesfor a static plasma are approximately kVA for the m � 1mode and VA�a for the m � 0 mode. For a typical valueof ka � p the shortest growth time would be 24 nsec fora static Z-pinch plasma with the magnetic field strength,density, and radius measured on the ZaP experiment. Therequired axial velocity shear for stability according to theshear flow stabilization theory presented in Ref. [10] is4.2 3 106 s21.

The experimental results show a stable period of17 msec which is over 700 growth times. The experi-mentally measured axial velocity shear is 1.9 3 107 s21

during the stable period and approximately zero after-wards when the magnetic mode fluctuations are high.The correlation of the experimental stability data with theplasma flow measurements is consistent with the shearflow stabilization theory presented in Ref. [10].

205005-4

The presence of a sheared axial plasma velocity is co-incident with low magnetic fluctuations; however, it hasnot been determined that the decrease in the plasma veloc-ity shear leads to the increase in the magnetic fluctuations.Therefore, at this point causality cannot be determined.

Axial plasma velocity profiles with a radial shear havebeen measured in a Z-pinch plasma. Significant reductionsin the magnetic fluctuations are coincident with the pres-ence of the sheared sub-Alfvénic plasma flows. The ex-perimental evidence is consistent with the theory that grossMHD modes can be stabilized with sufficiently shearedaxial plasma flow. Nonlinear simulations also supportthis theory. The sheared flow stabilization of the disrup-tion modes in Z-pinches has important implications forthe flow-through Z-pinch and other magnetic confinementconfigurations.

This work is supported through a grant from the Depart-ment of Energy. The authors wish to acknowledge E. A.Crawford and T. R. Jarboe for valuable discussions.

*Present address: Department of Physics, University ofWisconsin-Madison, 1150 University Avenue, Madison,Wisconsin 53706.

[1] W. H. Bennett, Phys. Rev. 45, 890 (1934).[2] A. S. Bishop, Project Sherwood (Addison-Wesley, Read-

ing, MA, 1958).[3] W. A. Newcomb, Ann. Phys. (N.Y.) 10, 232 (1960).[4] A. A. Ware, Nucl. Fusion Suppl. 3, 869 (1962).[5] A. A. Newton, J. Marshall, and R. L. Morse, in Proceedings

of the Third European Conference on Controlled Fusionand Plasma Physics, Utrecht, 1969 (Wolters-Noordhoff,Groningen, 1969), p.119.

[6] V. G. Belan, S. P. Zolotarev, V. F. Levahov, V. S. Mainashev,A. I. Morozov, V. L. Podkovyrov, and Yu. V. Skvortsov,Sov. J. Plasma. Phys. 16, 96 (1990).

[7] C. W. Hartman, G. Carlson, M. Hoffman, R. Werner, andD. Y. Cheng, Nucl. Fusion 17, 909 (1977).

[8] C. W. Hartman, J. L. Eddleman, R. Moir, and U. Shumlak,Fusion Technol. 26, 1203 (1994).

[9] C. W. Hartman, J. L. Eddleman, A. A. Newton, L. J.Perkins, and U. Shumlak, Comments Plasma Phys. Con-trol. Fusion 17, 267 (1996).

[10] U. Shumlak and C. W. Hartman, Phys. Rev. Lett. 75, 3285(1995).

[11] T. D. Arber and D. F. Howell, Phys. Plasmas 3, 554 (1996).[12] R. E. Peterkin, Jr., M. H. Frese, and C. R. Sovinec, J. Com-

put. Phys. 140, 148 (1998).[13] U. Shumlak, T. W. Hussey, and R. E. Peterkin, Jr., IEEE

Trans. Plasma Sci. 23, 83 (1995).[14] K. F. Schoenberg, R. A. Gerwin, R. W. Moses, Jr., J. T.

Scheuer, and H. P. Wagner, Phys. Plasmas 5, 2090 (1998);A. I. Morozov, Sov. J. Plasma Phys. 16, 69 (1990).

[15] D. J. Den Hartog and R. P. Golingo, Rev. Sci. Instrum. 72,2224 (2001).

205005-4

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 74, NUMBER 4 APRIL 2003

Spatial deconvolution technique to obtain velocity profiles from chordintegrated spectra

R. P. Golingoa) and U. ShumlakUniversity of Washington, Aerospace and Energetics Research Program, Seattle, Washington 98195-2250

~Received 16 July 2002; accepted 20 December 2002!

Passive spectroscopy is used to measure the plasma parameters on the ZaP experiment at theUniversity of Washington. Twenty spectral intensities, which are functions of the plasma’s density,velocity, and temperature along the viewing chord, are recorded on a charged coupled device. Theinstrument function is different for each viewing chord. A deconvolution technique based on a shellmodel, which includes the effects of the instrument function, is developed to deduce the localplasma parameters. The error analysis for this technique is also developed. The technique is able tomodel complicated plasma parameter profiles and is able to deduce the local plasma parameters andposition of the plasma. ©2003 American Institute of Physics.@DOI: 10.1063/1.1556956#

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I. INTRODUCTION

Passive spectroscopy of impurity ion line radiationoften used to study the density, velocity, and temperaturplasmas. Profile information can be determined by viewthe plasma along multiple chords through the plasmadeconvolving the spectral intensities.1–5An Abel inversion ofeach wavelength is inappropriate when the spectral intenis a function of the radius and viewing chord. This happewhen the instrument function changes across the chordthe velocity direction at a given radius changes betweenlines of sight, such as the poloidal velocity when viewfrom one side of the machine. A method based on a smodel is described to deconvolve the plasma parameterfiles measured by passive spectroscopy on the ZaP~Z Pinch!experiment at the University of Washington.6 The methodtakes into account the instrument function and can be uwhen the local spectral intensity changes as a function ofline of sight. The method is capable of deconvolving radiavarying spectra even when multiple overlapping linespresent.

The effect of a sheared axial velocity on plasma insbilities in a Z pinch is studied on the ZaP experiment.coaxial accelerator coupled to a pinch assemble regionduces Z pinches that are approximately 50 cm long withcm radius. Typically the Z pinch has an electron numbdensity of 1016– 1017cm23, an edge magnetic field of 1.52.5 T, total temperatures of 150–200 eV, and axial velociof 0 – 1.23105 m/s. These parameters are measured withagnostics that include a two chord interferometer, hographic interferometer, surface magnetic probes, a fast fring camera, and passive spectroscopy.

Passive spectroscopy is used to measure the plasmlocity profile. Light emitted by impurity ions entrained in thplasma is collected with two telecentric telescopes.7 Eachtelescope collects light from 20 parallel chords, spaced 1mm apart, that view through the plasma. One telesc

a!Author to whom correspondence should be addressed; [email protected]

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views the plasma 90° to thez axis, while the other views theplasma 35° to thez axis as shown in Fig. 1. All optics anfibers in this system are UV compatible. A swing out mirrin the 0.5 m spectrometer, Action Research Spectra Pro 5is used to select the 90° or 35° view. The spectra arecorded with an intensified charge coupled device~ICCD!,Roper Scientific PI-MAX, with a typical gating time o0.5–1ms. Calibration data are used to remove the curvatbefore multiple rows are binned which reduces the widththe instrument function, the spectral intensity measuredthe spectrometer of an infinitesimally thin line of unit emisivity. The full width at half maximum~FWHM! of the in-strument function varies from 5 pixels for the edge chords3.5 pixels for the center chords. The instrument functionsthree chords are shown in Fig. 2.

Since the instrument function is neither a Gaussian noLorentzian and varies across the chords, a different metfor obtaining the local ion velocity in the plasma is deveoped. Section II introduces the deconvolution techniquediscusses the variables that affect the spectra measuredeach chord. A shell model is assumed to find the plasparameters. A detailed error analysis is also describedfully account for the uncertainties in the measurementsassumed plasma geometry necessary for the deconvolutechnique. Section III presents the deconvolution of synthtest spectra to demonstrate robustness of the techniquethe deconvolution of real spectra measured on the ZaPperiment.

II. DECONVOLUTION TECHNIQUE

A different deconvolution technique, which includes thinstrument function, is developed to calculate the plasmarameters when the position of the plasma is unknown. Ofdeconvolution techniques begin by removing the instrumfunction8 or assume the Doppler broadening is givenDl25Dlobs

2 2Dl ins2 whereDl is the FWHM due to Doppler

broadening,Dlobs is the observed FWHM, andDl ins is theFWHM in the instrument function.9 These methods do nowork when the spectral intensity has multiple peaks oril:



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2333Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 Spatial deconvolution technique

instrument function is not Gaussian or Lorentzian. Individuparameter profiles using moments of the spectral intensare then found3,4 or assumptions about the profile shapemade.5 These methods rely on other diagnostics to definegeometry of the plasma. The technique which is develohere finds the plasma parameters and geometry in aconsistent technique using the measured spectral intenswithout intermediate steps.

A. Shell model

A shell model is assumed to represent the plasma.plasma is partitioned into discrete shells where the localplitude of the emissivityAj , ion temperatureTj , and veloc-ity vj are constant in each shell.3 The spectral intensity fromshell j along the line of sight of chordi is then described by

ei j ~l!5Aj

A2pwj

expF2~l2l02usi "vj ul0 /c!2

2wj2 G1Bj ,

~1!

where l0 is the unshifted wavelength of the emitted linradiation,si is a unit vector in the direction of the line osight,wj is proportional to the FWHM of the spectral inten

FIG. 1. Diagram of the ZaP vacuum chamber showing the major comnents of the tank. The 90° telescope views the plasma through the bomidplane port. The 35° telescope views the plasma through the bottom aport. Both telescopes are focused in the center of the machine at themidplane.

FIG. 2. The instrument function varies across the chords. Shown aremeasured instrument functions of chord 1~solid line!, chord 5~dotted line!,and chord 10~dashed line! using the Cd I line at 228.8 nm. The width of thinstrument function decreases for the central chords.


leseedlf-ies

e-

sity, and Bj is an offset of the spectra due to broadbaradiation. The temperature is related towj by

wj25

kTjl02

mic2 , ~2!

wherek is Boltzmann’s constant andmi is the ion mass. Theshells are assumed to be concentric circles, where the axthe plasma coincides with the center of the shells. The sgeometry for the 35° telescope is shown in Fig. 3. The ouradius of shell j is given by r j5xchord( j )1dDr wherexchord( j ) is the impact parameter of chordj, Dr is the spacingbetween chords and shells, andd is the relative position ofthe viewing chord in each shell. The outer radius of shell 1set by the extrapolated zero crossing of the measured esivity, usuallyr 15r 212Dr . The radiation measured by eacchord is the sum of the contributions from each shell thatchord intersects, Fig. 3. The collected spectral intensitychord i is given by

Ei~l!5(j

ei j ~l!Li j , ~3!

whereLi j is the length of chordi through shellj. The col-lected spectral intensity is broadened by the instrument fution

Mi~l!5E2Dl

Dl

Ei~l2l8!Fi~l8!dl8, ~4!

whereMi is the instrument broadened spectral intensity,Fi isthe instrument function of chordi measured during the calibration of the ICCD spectrometer, and 2Dl is the span of themeasured instrument function. Coma in the spectromcauses the instrument function to be asymmetric as showFig. 2. The FWHM of the instrument function, measurwith the Cd I line at 228.8 nm, varies from 0.030 nm for thcenter chords to 0.047 nm for the edge chord. The inclusof the instrument function in the analysis causes the specintensities to be a function of the impact parameter and

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FIG. 3. The 35° view of a quarter of the plasma showing the chord and slocations when the plasma is centered in the machine. The dashed linethe sightlines of the 35° viewing telescope. The ovals are the outer edgeach shell when viewed from the 35° viewing telescope.


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2334 Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 R. P. Golingo and U. Shumlak

viewing chord even when the angle between the velovector and the lines of sight of the chords does not chan

B. Deconvolution procedure

The plasma parameter profiles cannot accuratelyfound by simply reversing the steps of the previous secbecause of difficulties with the removal of the instrumefunction. This difficulty precludes the use of Abel or matrmethods because the instrument function must be remobefore using these methods. Instead, an instrument brened Gaussian10 is defined for each shell

mi j ~l!5E2Dl

Dl

ei j ~l2l8!Fi~l8!dl8. ~5!

An equation similar to Eq.~4! can be written as

Mi~l!5(j

mi j ~l!Li j . ~6!

Since the length matrixLi j is triangular, back substitutioncan be used to find the plasma parameters.

By viewing the plasma with telecentric telescopes othe horizontal location of the plasma affects the impactrameter of each viewing chord. The location is founditeratively deconvolving the data. Guesses for the centerthe edge of the pinch are made, which sets the geometry.length matrixLi j is calculated. The plasma parameter pfiles for this geometry are then found.

The edge chord measures only the emission fromoutermost shell. Leti 51 be the outermost chord andj 51the outermost shell. All of the termsL1 j are zero except forj 51. The measured spectral intensity of the outer chordgiven by

M1~l!5L11E2Dl

Dl

e11~l2l8!F1~l8!dl85L11m11~l!.

~7!

The plasma parameters for the outer shell are found wileast squares fit of an instrument broadened GaussiaM1(l)/L11 using a Marquardt method with equal weighgiven to each point.

The plasma parameters of the inner shells are determby removing the contribution from the outer shells and fittian instrument broadened Gaussian to the remaining datachord i be a chord in the plasma and shellj be the corre-sponding shell in the plasma. An instrument broadenGaussian for the outer shells, 1 toj 21, contribution to themeasured spectral intensityMi

outer is found with

Miouter~l!5 (

j 8, j

mi j 8~l!Li j 8 , ~8!

wheremi j 8 is calculated using the plasma parameters frthe previous shells and Eq.~5!. The emission from the sheis given by removing the outer shells’ contribution

mi j ~l!5maxS Mi~l!2Miouter~l!

Li j,0D . ~9!


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The plasma parameters for shellj are found with a Marquardmethod. This procedure is repeated for each successive cuntil the shell axis is crossed. Once the axis is crossedplasma parameters for the inner two shells are also fousing the spectral intensities measured by the nextchords. The deconvolution procedure is also repeated stafrom the other side, by beginning at chord 20 and decreasthe chord index.

The two deconvolution procedures yield two profilesthe emissivity, ion temperature, and ion velocity for the asumed geometry. The center of the plasma is found byjusting the guess of the pinch center until the emissivity athe velocity of the inner two shells from the left and rigdeconvolutions converge.

C. Error analysis

The deconvolution of the plasma profiles relies on taccuracy of the experimental measurements and of thesumed plasma model which includes the center and elocations of the plasma. To properly account for the cobined effect of the inaccuracies a detailed error analysiperformed. The data are fit with a Marquardt method wequal weights given to each point. The actual uncertaintyeach spectral intensity is proportional to the intensity. Whthe actual uncertainties are used as weights the fitted sphad a lower amplitude at the maximum measured specintensity and fit the wings of the spectra. The agreembetween the measured and fitted spectral intensities is shin Fig. 4. Once the plasma parameters are found the errothe parameters are calculated.

The errors in the plasma parameters are found for esource of uncertainty. The uncertainty of the measured sptra sMi(l) is given by

sMi2 ~l!5@b iAMi~l!#21@AMBi#

2, ~10!

FIG. 4. The deconvolution technique is able to recreate the spectral insities. Shown are the measured spectral intensities~squares! and the spectralintensities from the deconvolution technique~solid line!.


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whereb i is a multiplier for each chord found by measurinthe standard deviation of the spectra where there is noradiation11 and MBi is the level of the background of eacchord. The error in the spectral intensities of the inner shsNmi j(l) due to noise in the measured spectral intensitiegiven by

sNmi j2 ~l!5FsMi~l!

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, ~11!

wheresNouter(l) is the uncertainty fromMiouter(l) which is

given by

sNouter2 ~l!5 (

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,F]mi j 8~l!

]aj 8,sN j8,

a Li j 8G2J , ~12!

whereaj 8, is parameter, of shell j 8 andsN j8,a is the error of

aj 8, due to the uncertainty in the measured spectral inteties. Once the uncertainties at each wavelength are founderror of each parametersN j,

a can be found by taking theinverse of the curvature matrix as described in Ref. 12.

The uncertainties in the length matrixsGi j are calculatedusing the uncertainty in the center location, maximum shradius, and the location of the chord through each shell.error sGmi j(l) due to the uncertainties in the geometrythe pinch is given by

sGmi j2 ~l!5FsGouter~l!

Li jG2

1H @Mi~l!2Miouter~l!#2sGi j

Li j2 J 2

, ~13!

where the uncertainty in the spectral intensity from the oushellssGouter(l) is given by

sGouter2 ~l!5 (

j 8, jH @mi j 8~l!sGi j 8#

2

1(,

F]mi j 8~l!2

]aj 8,sG j8,

a Li j 8G2J , ~14!

wheresG j8,a is the error of each parameter due to the unc

tainty in the geometry. The error of each parameter due touncertainties in the geometry are found with the samethod as withsN j,

a . The total error in each parameters j ,a

is

s j ,a 5A~sN j,

a !21~sG j,a !2. ~15!

This method of finding the errors shows the influence of euncertainty on the fitted profiles.

III. RESULTS OF DECONVOLUTION TECHNIQUE

The deconvolution process is tested using various sthetic profiles of emissivity, velocity, and temperature. Tsynthetic spectral intensities are generated without usingshell assumption. The local spectral intensity along eachof sight,e(r ,l), is found using Eq.~1!. The chord integratedspectral intensity for each wavelength,E(x,l), is given by


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E(x,l) is then broadened with the instrument function usiEq. ~4!. This process of generating synthetic spectral intsities tests the assumption that the plasma parametersconstant in each shell. Random noise, with a mean of zand standard deviation of 1, is multiplied bysMi

(l), calcu-lated using Eq.~10!, and added to the synthetic spectral itensities. The spectra are then deconvolved using the prdure described.

A variety of synthetic profiles of emissivity, velocity, antemperature are used to verify the robustness of the devolution technique. Two profile sets are presented here.has a peaked emissivity profile and a hollow velocity profiand the other has a hollow emissivity profile and peakvelocity profile more typical of real data. Figure 5 shows tpeaked emissivity synthetic profile and the results fromdeconvolution technique applied to the spectral intensiwith noise, consistent with that of measured spectra, addLarge gradients of parameters within each shell are usetest the ability of the constant parameter assumption to arately resolve the profiles. The errors due to the geometrytested by positioning the profiles off axis. Figure 6 showshollow synthetic profile with large gradients. The deconvlution technique is able to calculate the gradients. Errorsthe center location have the largest effect on the plasmarameters in the central shells and justifies using the inshell parameters to set the pinch geometry. The value ofparameters for the edge shells changes by a small amoThe appropriated is a function of the gradients in the profiles. When there is a large gradient in the velocity the msured temperature increases because a velocity grawithin a shell will broaden the spectral intensity. The errcalculation is verified by applying different sets of rando

FIG. 5. Results of the deconvolution technique~diamonds! applied to syn-thetic profiles~dashed lines!. The profiles are centered between chord 10 achord 11 which is the center of the machine. Random noise has been ato the integrated, instrument broadened data at levels consistent withexperimental noise.


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2336 Rev. Sci. Instrum., Vol. 74, No. 4, April 2003 R. P. Golingo and U. Shumlak

noise to the spectral intensities calculated with this profiapplying the deconvolution technique with geometries witthe uncertainties of the pinch geometry, and finding theerage and standard deviation of the plasma parameters.calculated error bars of the plasma parameters are sliglarger than the standard deviation found with the multideconvolutions.

The deconvolution technique is used to determine veity profiles in the ZaP experiment which generates axiaflowing plasmas. The C III line at 229.7 nm representsbulk of the hot plasma and is well separated from other linThe spectral intensities from three of the chords of this lare shown in Fig. 7. The plasma profiles of the C III line

FIG. 6. Results of the deconvolution technique~diamonds! applied to syn-thetic profiles~dashed lines!. The profiles are centered between chord 11 achord 12 to simulate a pinch which is not centered in the machine. Rannoise has been added to the integrated, instrument broadened data atconsistent with the experimental noise.

FIG. 7. The measured C III spectral intensities for ZaP pulse 726 025.vertical line is at the unshifted wavelength of 229.7 nm. The solid curvthe spectral intensities of chord 1, the dotted line is from chord 5, anddashed line is from chord 10. The centroid of the intensities for each chdecreases for the center chords, showing the velocity is increasing foinner chords.


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229.7 nm are shown in Fig. 8. The wavelength span showthe figure corresponds to 44 pixels. The minimum measuDoppler shift is 3 pixels which is well within the resolutioof the instrument. The chord spacing is 1.24 mm in tplasma and provides a limit to the spatial resolution ofdeconvolved profiles. The technique was able to determthe geometry of the pinch as can be seen in the peakedfiles of the emissivity and the offset. The center locationthe Z pinch measured with the magnetic probes is consiswith position measured with the deconvolution techniquThe magnetic probes are located in the outer electrodecan locate the position of the pinch to within a centimetThe size of the Z pinch from the deconvolution techniqagrees with the size measured with the holographic interometer and the fast framing camera. The velocity proshows a large axial velocity in the center with a gradientthe outer shells. The temperature in the edge shells is lathan the temperature from pressure balance. A velocity shbeyond the view of the telescopes will cause the temperaof the edge chords to appear high. The slight asymmetrthe left and right deconvolutions shown in Fig. 8 implyslight asymmetry in the plasma. The quality of the deconlution is determined by chord integrating the deconvolvprofiles and comparing the results to the measured speintensities. The results are shown as lines in Fig. 4.

The deconvolution technique described is able to callate the profiles of the plasma parameters. The techniworks for many different profiles and accounts for the effeof the instrument function. The technique is able to detmine the geometry of the pinch independent of other dinostics. The technique is being used to measure the plaprofiles for C III triplet at 465 nm and the C IV line at 465.nm.

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FIG. 8. The deconvolved emissivity~a!, velocity ~b!, temperature~c!, andoffset ~d! of the C III line for ZaP pulse 726 025 showing a pinch withsheared velocity profile. The parameters with negative impact paramwere calculated using chords 1–10 and the parameters with positive imparameters were calculated using chords 11–20. The profiles are siwhen calculated from both sides of the pinch.


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ACKNOWLEDGMENTS

The authors would like to acknowledge D. J. Den Hartfor his work designing and assembling the instrument andA. Nelson and W. Litsch for useful discussions on the decvolution technique. This work is supported through a grfrom the U.S. Department of Energy Grant No. DE-FG098ER54460.

1I. H. Hutchinson,Principles of Plasma Diagnostics~Cambridge Univer-sity Press, Cambridge, 1987!, p. 230.

2A. Chelouah, E. Marode, and G. Hartmann, J. Phys. D27, 770 ~1994!.3R. E. Bell, Rev. Sci. Instrum.68, 1273~1997!.


.-t-

4I. Condrea, E. Haddad, B. C. Gergory, and G. Abel, Phys. Plasmas7, 3641~2000!.

5N. J. Conway, P. G. Carlon, and M. R. Tournianski, Rev. Sci. Instrum.70,934 ~1999!.

6U. Shumlak, R. P. Golingo, and B. A. Nelson, Phys. Rev. Lett.87, 205005~2001!.

7D. J. Den Hartog and R. P. Golingo, Rev. Sci. Instrum.72, 2224~2000!.8A. Brablec, D. Trunec, and F. S˘ tastny, J. Phys. D32, 1870~1999!.9I. Condrea, E. Haddad, B. C. Gergory, D. Lafrance, J. L. LachambrePacher, F. Meo, and H. H. Mai, Rev. Sci. Instrum.70, 387 ~1999!.

10R. O’Connell~personal communication!.11A. B. Filuk and J. E. Bailey, Rev. Sci. Instrum.63, 4783~1992!.12P. R. Bevington,Data Reduction and Error Analysis for the Physica

Sciences~McGraw–Hill, New York, 1992!, p. 203.


PHYSICS OF PLASMAS VOLUME 10, NUMBER 5 MAY 2003

Sheared flow stabilization experiments in the ZaP flow Z pinch a…

U. Shumlak,b) B. A. Nelson, R. P. Golingo, S. L. Jackson, and E. A. CrawfordUniversity of Washington, Aerospace and Energetics Research Program, Seattle, Washington 98195–2250

D. J. Den HartogDepartment of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706

~Received 7 November 2002; accepted 9 January 2003!

The stabilizing effect of a sheared axial flow on them51 kink instability in Z pinches has beenstudied numerically with a linearized ideal magnetohydrodynamic model to reveal that a shearedaxial flow stabilizes the kink mode when the shear exceeds a threshold. The sheared flow stabilizingeffect is investigated with the ZaP~Z-Pinch! Flow Z-pinch experiment at the University ofWashington. An axially flowing Z pinch is generated with a 1 mcoaxial accelerator coupled to apinch assembly chamber. The plasma assembles into a pinch 50 cm long with a radius ofapproximately 1 cm. An azimuthal array of surface mounted magnetic probes located at themidplane of the pinch measures the fluctuation levels of the azimuthal modesm51, 2, and 3. Afterthe pinch assembles a quiescent period is found where the mode activity is significantly reduced.Optical images from a fast framing camera and a ruby holographic interferometer indicate a stable,discrete pinch plasma during this time. Multichord Doppler shift measurements of impurity linesshow a large, sheared flow during the quiescent period and low, uniform flow profiles during periodsof high mode activity. Z-pinch plasmas have been produced that are globally stable for over 700times the theoretically predicted growth time for the kink mode of a static Z pinch. The plasma hasa sheared axial flow that exceeds the theoretical threshold for stability during the quiescent periodand is lower than the threshold during periods of high mode activity. ©2003 American Instituteof Physics. @DOI: 10.1063/1.1558294#

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I. INTRODUCTION

Some of the first attempts to achieve controlled thermnuclear fusion were based on the Z pinch. A large axial crent was driven through a column of ionized gases to copress and heat the plasma to high density and temperatur1–3

The Z pinch has appealing properties as a magnetic conment configuration for a fusion reactor: the geometrysimple and linear, the maximum magnetic field is at tplasma surface and low external to the plasma, and therent producing the magnetic field dissipates energy inplasma.4,5 The equilibrium is described by a simple radiforce balance between the azimuthal magnetic field geated by the axial plasma current and the plasma pressur

~ j3B!r5~¹p!r . ~1!

For the case of no applied magnetic fields, the equilibriumgiven by

Bu

mor

d~rBu!

dr1

dp

dr50. ~2!

The pinch plasma was observed to be violently unstable wgrowth times corresponding to Alfve´n transit times. The in-stabilities were understood theoretically and experimentas gross magnetohydrodynamic~MHD! modes with azi-muthal mode numbersm50 and m51, sausage and kinkmodes, respectively.6

a!Paper UI2 6, Bull. Am. Phys. Soc.47, 325 ~2002!.b!Invited speaker.

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The MHD instabilities of a Z pinch can be stabilized. Aclose-fitting, conducting wall can be placed around the pinplasma.7 Image currents in the conducting wall developlimit the growth of any plasma perturbations. However, tconducting wall must be placed too close to allow plastemperatures of fusion interest.

By applying linear MHD stability analysis Kadomtsederived an equilibrium that would be stable to them50mode.8 The mode can be stabilized if the pressure doesfall off too rapidly. Namely,

4G

21Gb>2

d ln p

d ln r, ~3!

whereG is the ratio of specific heats andb52mop/B2 is alocal measure of the ratio of plasma pressure to magnpressure. This condition must be satisfied everywhere inplasma for stability against them50 mode. However, tailor-ing the pressure profile cannot stabilize the kink instabilit

Both the sausage and kink instabilities can be stabiliby imbedding an axial magnetic field into the plasma. Tcondition for stability is found by applying an energy principle and is given by the Kruskal–Shafranov condition,9,10

Bu

Bz,

2pa

L. ~4!

The equilibrium given in Eq.~2! is now modified. The radialforce of the azimuthal magnetic field balances the plaspressure and the magnetic pressure of the axial field.Kruskal–Shafranov condition forces the design of shor


license or copyright, see http://pop.aip.org/pop/copyright.jsp

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1684 Phys. Plasmas, Vol. 10, No. 5, May 2003 Shumlak et al.

pinches and limits the plasma current and the plasma psure that can be stably achieved in a Z pinch. Furthermorethe addition of an axial magnetic field opens all of the manetic field lines and connects all portions of the plasma toelectrodes. Parallel heat conduction is much faster thanpendicular heat conduction which is the case for closed filines without the axial field. The combined constraintsshort pinches and parallel heat losses led many earlysearchers to abandon the Z pinch as a magnetic confineconfiguration.

Experiments have generated Z-pinch plasmas with inhent axial plasma flows exhibiting stable confinementtimes much longer than the predicted growth times.11,12 Thepossibility of using sheared flows to stabilize the Z pininstead of axial magnetic fields has prompted recent theoical and experimental efforts. A stable, high-density Z-pinconfiguration would have profound implications for manetic confinement thermonuclear fusion.5,13,14

II. SHEARED FLOW STABILIZATION THEORY

The effect of plasma flow on the MHD instabilities inZ pinch has been investigated theoretically by applyingear stability analysis to the Z-pinch equilibrium.15 The mainconclusion is an axial plasma flow with a linear shearvz /a.0.1kVA is required for stability of the marginallystable equilibrium given by Eq.~3! when the conducting walis far away.

Nonlinear simulations have been performed to studyeffect of a sheared flow on the stability of them50 mode ina Z pinch. The simulations were performed using the Maccode,16 a time-dependent, resistive MHD code. An equilirium is initialized with a uniform current density through thplasma and no current beyond the pinch radiusa and with anaxially periodic density perturbation of 1%. The equilibriuis also initialized with a plasma flow of constant shear insthe pinchr ,a and no shear beyond the pinch radius. Tflow is maintained through the simulation only by inertiThe value of the flow shear is adjusted between simulatito investigate its effect on stability. Results showing the prsure contours are presented in Fig. 1 for a simulationcontains no flow~plots on the left! and a simulation thacontains a flow such thatvz(r 50)50 and vz(r 5a)50.2kaVA ~plots on the right!. The figure shows the evolution of the pressure contours~a! at an intermediate time an~b! immediately before the static Z pinch disrupts. The initstates are not shown. The simulation of a static Z pinshows a well developedm50 instability. The Z-pinchplasma with a sheared axial flow shows a substantiallydevelopedm50 instability. The turbulence at the edge of thplasma is conjectured to result from a decrease in the flshear at the edge due to numerical viscosity.

III. THE ZAP FLOW Z-PINCH EXPERIMENT

The ZaP ~Z-Pinch! experiment at the University oWashington is used to investigate the effect of plasma flon the stability of a Z pinch and to determine the possibiliof confining hot plasmas in a simple Z-pinch configuration17

The experiment is designed to generate a Z-pinch pla


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with a large axial flow. The experiment is composed ofcoaxial acceleration region connected to an assembly regThe experiment is initiated by the injection of neutral gausually hydrogen, with fast puff valves located in the middof the 100 cm coaxial acceleration region. A capacitor bapower supply is discharged across the coaxial electroionizing the neutral gas, and accelerating the plasma. Wthe plasma reaches the end of the coaxial acceleration regthe plasma along the inner electrode moves radially inwand assembles along the axis in the 50 cm long assemregion. The plasma along the outer electrode continuemove axially and radially inward during the assembly of tZ pinch. The plasma finally connects between the end ofinner electrode and the outer electrode end wall formincomplete Z pinch. Inertia maintains the plasma flow staand plasma is continually exiting from the coaxial acceletor and assembles into the pinch. The Z-pinch plasma fortion in the ZaP experiment is shown schematically in Fig.

Nonlinear simulations of the plasma formation in thZaP experiment have been performed using the Mach2 cWhile the code lacks a time-dependent ionization model,simulations show qualitative agreement of the plasma formtion described above. The code also shows quantitaagreement with the acceleration time and plasma densmeasured in the experiment.

The coaxial accelerator has an inner electrode withcm radius and an outer electrode with a 10 cm radius whextends into the assembly region. A machine drawing ofZaP experiment is shown in Fig. 3 identifying the relevafeatures. Recent modifications include a shaped end on

FIG. 1. Nonlinear simulation results showing the pressure contours inpinch that contains no flow~plots on the left! and a Z pinch that contains aflow such thatvz(r 50)50 and vz(r 5a)50.2kaVA ~plots on the right!.The figure shows the evolution of the pressure contours~a! at an interme-diate time and~b! immediately before the static Z pinch disrupts. The initistates are not shown.


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1685Phys. Plasmas, Vol. 10, No. 5, May 2003 Sheared flow stabilization experiments in the ZaP . . .

inner electrode and an exit hole on the outer electrodewall to reduce stagnation the plasma flow. For referencepinch midplane is defined asz50. The end of the innerelectrode is atz5225 cm, and the neutral gas is injectedz5275 cm. The capacitor bank power supply is configureither for 28 kJ of stored energy at 9 kV or 46 kJ of storenergy at 8 kV. The plasma current peaks at 230 kA witquarter cycle time of 28ms and at 275 kA and has a quartcycle time of 30ms, respectively.

FIG. 2. Schematic representation of the Z-pinch plasma formation inZaP experiment:~a! neutral gas is injected into the annulus of the coaxaccelerator,~b! breakdown of the gas and current flows to accelerateplasma axially,~c! plasma moves radially toward the axis at the end ofaccelerator,~d! plasma assembles along the axis,~e! plasma is attachedbetween the inner electrode and outer electrode end wall and inertia mtains the axial plasma flow.


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IV. EXPERIMENTAL RESULTS

The diagnostics on the ZaP experiment are designemeasure plasma evolution, equilibrium including flow, astability.

A. Formation of a Z pinch with sheared flow

An axial array of 23 surface-mounted magnetic probare installed in the outer electrode extending fromz52120 cm to 20 cm. The probes indicate the current disbution and the acceleration of plasma in the accelerationgion. Time traces of the azimuthal magnetic field in the aceleration region is shown in Fig. 4. The initial current shepropagates down the acceleration region and into the assbly region. A propagation speed of approximately3104 m/s can be measured. Later in time the field valualong the axial array converge indicating a decrease in racurrent density and plasma acceleration.

The evolution of the electron number density in tplasma is determined from a two chord, visible He–Ne herodyne quadrature interferometer. The chords can be plaat the pinch midplane in the assembly region or at locatiin the acceleration region both downstream and upstreamthe neutral gas injection plane. Figure 5 shows the averdensity along chords through the middle of the annulus

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FIG. 4. Azimuthal magnetic field at several axial locations as measuredthe surface mounted magnetic probes. The initial current sheet propadown the acceleration region. Later in time the field values converge icating a decrease in the plasma acceleration.

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FIG. 3. Side view drawing of the ZaPexperiment identifying the relevanfeatures. The top and bottom ports ithe assembly region are used for spetroscopic measurements of the Z-pincplasma, and the side ports are used fobtaining images from the fast framing camera and measuring density othe Z-pinch plasma. The smaller sidports in the acceleration region arused to measure density during plasmacceleration.


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tween the electrodes of the coaxial accelerator atz5265and 225 cm. The data show the initial plasma sheet amoves downstream pastz5265 and225 cm. After the ini-tial plasma density atz5225 and265 cm, the density re-mains at an elevated value before dropping toward zero

After the plasma reaches the end inner electrode,plasma begins to assemble along the axis into the Z-pplasma. Optical emission images obtained from a fast fraing camera through the pinch midplane port are presenteFig. 6. The images in the figure are taken every 1ms andview the plasma through a notch pass filter which paslight with wavelengths between 500 and 600 nm. The plasis viewed through a 4.7 cm diam hole through the ouelectrode which provides a scale for spatial extent ofimages. The images show the development of a stable sture centered in the experimental device.

When the He–Ne interferometer is located at the pinmidplane, the Z-pinch plasma density can be determinOne chord traverses the plasma along the geometric deter, and a second chord is parallel to and 2 cm abovefirst chord. The plasma density is assumed to have spatuniform values outside and inside the pinch. The radiusthe pinch is determined from optical emission and specscopic data. The line-integrated densities measured fromtwo chords of interferometer data are combined withpinch radius to compute the plasma density inside the pinThe plasma electron number density is determined to1016–1017 cm23 inside the pinch.

B. Evolution of the Z-pinch plasma

An azimuthal array of eight equally-spaced, surfacmounted magnetic probes are installed in the outer electat the pinch midplane. The probes measure the azimumagnetic field at surface of the outer electrode. The magnfield values from the probe array are Fourier analyzeddetermine the evolution of the low order azimuthal mod(m51,2,3) of the Z-pinch plasma. Typical data are plottedFig. 7 showing the time evolution of them51 and m52Fourier modes of the magnetic field. The average azimumagnetic fieldB0(t) is defined as the simple average ofeight surface magnetic probes at each time. The ave

FIG. 5. Chord-averaged density in the acceleration region atz5225 and265 cm. After the initial plasma density rise the density remains atelevated value before dropping to zero.


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azimuthal magnetic field is used to normalize the Fourmode data at the pinch midplane, accordingmin(1,Bm(t)/max(B0(t),e)), whereBm(t) is the value of them mode component of the azimuthal magnetic field ande50.01 T. The min and max functions are necessary to pvent divide by zero errors during periods of low signal leels. Them53 mode~not shown in the figure! is also ana-lyzed and is lower than them52 level at all times. Thefigure also shows the evolution of the plasma currentreference.

The plasma arrives at the pinch midplane at appromately 20ms. Magnetic mode fluctuation data before thtime are caused by signal noise and are not shown. Thetuation levels of the asymmetric modes are high whenZ-pinch plasma is assembling. After the pinch has formthe fluctuation levels for bothm51 andm52 change char-acter for approximately 15ms, from 31 to 46ms. Thechange in character is identified by lower levels and

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FIG. 6. Optical emission images of the plasma through the side port apinch midplane obtained with a fast framing camera equipped with a nopass filter which passes light with wavelengths between 500 and 600The images show a stable structure centered in the experimental deviceplasma is viewed through a 4.7 cm diam hole through the outer electwhich provides a scale for spatial extent of the images.


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FIG. 7. Time evolution of Fourier components of thmagnetic field fluctuation at the pinch midplane form51 and m52 showing the quiescent period from31 ms to 46ms. The values are normalized to the aerage magnetic field value at the pinch midplane. Tevolution of the plasma current~dashed curve! is in-cluded for reference.

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creased frequency for the fluctuations. After this quiescperiod the fluctuation levels then again change charactercrease in magnitude and frequency, and stay high untilend of the plasma pulse.

The optical emission images in Fig. 6 show a structthat becomes brighter and remains stable for the duratiothe data collection. The timing of the stable period corsponds to the stable time shown in the magnetic data.images indicate the pinch is stable during this time agaall m50 modes visible through the optical access hole. Tpinch radius is estimated to be 1 cm. The images provvisual confirmation of the gross stability of the Z-pincplasma. Furthermore, the images indicate the plasma istered in the vertical plane with respect to the experimengeometry.

As stated previously, the plasma electron number denat the pinch midplane is determined to be 1016–1017 cm23

inside the pinch assuming a 1 cmpinch radius and a uniformdensity within the pinch radius. If it is assumed thatplasma current flows outside of the pinch radius, thentotal plasma temperature can be determined from the mnetic field at the outer electrode and the density informatiThe magnetic field measured at the 10 cm outer electrodthe pinch midplane is 0.15–0.25 T. The magnetic field atpinch radius is then 1.5–2.5 T. The total plasma tempera(Te1Ti) is estimated from force balance to be 150–200

Density profiles at a single time are obtained withdouble-pass holographic interferometer that uses a puruby laser. The laser pulse length is less than 50 ns.


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integrated density profiles are deconvolved using an Amethod. Deconvolved density profiles are shown in Figobtained~a! early in the plasma quiescent period at 22msand ~b! late in the plasma quiescent period at 27ms. Theprofiles show a discrete plasma pinch with a radius of 0.5during assembly. The plasma density is peaked. Late theescent period the plasma pinch expands to 1 cm in radiusdevelops a hollow core structure. The values of the pinradius and density are consistent with the data fromHe–Ne interferometer. The hollow density structure suggea hot plasma core has developed. The total plasma tempture profile can be calculated using force balance withmagnetic force and assuming a cold plasma outside ofpinch radius and no plasma current flows outside ofpinch radius. The total plasma temperature peaks at 60early in the quiescent period and approximately 200 eV lin the quiescent period. However, the temperature valuessensitive to the assumed current distribution. More diagntic information is needed before an accurate temperaturefile can be determined.

Numerical simulations indicate the Z-pinch plasmaheated through compression from the larger radius ofcoaxial accelerator to the pinch radius and by resistive hing once in the pinch. The evolution of the plasma tempeture can be qualitatively determined by measuring the lradiation emission from different ionization states of imprity ions. A photomultiplier tube~PMT! is connected to theoutput of a 0.5 m spectrometer which views the plasthrough fused-silica optics. The combination of the sp

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FIG. 8. Deconvolved density profilesfrom the holographic interferometeobtained~a! early in the plasma quies-cent period at 22ms and~b! late in theplasma quiescent period at 27ms. Ahollow structure is seen to develop indicating a hot plasma core.


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FIG. 9. Time-dependent emission of the C-III line a229.7 nm and theC–V line at 227.1 nm atz510 cm.The appearance ofC–V emission late in the quiescenperiod is evident.

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trometer grating and the output slit width limits the spectview recorded by the PMT to full width at half maximum~FWHM! of 0.18 nm. The time-dependent emission of tC-III line at 229.7 nm and one of theC–V triplet lines at227.1 nm are recorded at two axial locations alongZ-pinch plasma. Data from the PMT measurement az510 cm are shown in Fig. 9. The appearance of theC–Vemission late in the quiescent period indicates a progresheating of the plasma.~For these pulses, the neutral hydrgen gas was doped with methane to increase the carbonpurity emission intensity.!

Impurity line radiation is also measured with a 0.5imaging spectrometer with an intensified charge-coupledvice ~ICCD! detector. The ICCD detector is set to a gatitime of 100 ns and the trigger time is varied between plaspulses. The spectrometer images 20 spatial chords throthe plasma onto the ICCD camera using telecentric viewtelescopes.18 The telescopes are connected to the spectreter with a fiber bundle composed of 20 fused silica fibeThe chords image 20 points spaced 1.24 mm apart alondiameter through the pinch. Optical access to the midplanprovided through the radial viewports and oblique viewpopositioned at a 35° angle to the plasma column, as showFig. 3. The presence of theC–V emission is confirmed withthis diagnostic. The chord with the largest amplitude is intpreted as the location of the plasma center. The measC–V triplet at 227.1, 227.7, and 227.8 nm is fit with a temperature broadened Gaussian with the predicted cewavelengths and relative intensities. An ion temperature170 eV provides the best fit.

Velocity profiles are determined by measuring the Dopler shift of impurity line radiation. The velocity of the impurity ions are assumed to be representative of the veloof the main plasma ions.19,20The assumption is supported bthe relatively high plasma density which has an ion collistime of approximately 200 ns. Doppler shifts are calculaby viewing the plasma through the oblique viewport with tICCD spectrometer. The oblique view has a directional coponent along the axis and, therefore, is sensitive to Dopshifts from axial flows. The ICCD detector is set to a gatitime of 1 ms and the trigger time is varied between plaspulses. Figure 10 shows the output from the ICCD spectro


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eter tuned to the C-III line at 229.7 nm. The trigger time fthe ICCD is 30ms which is during the quiescent period. Thdata show a shift of the C-III line being emitted from thcentral plasma, chords 5–18, and a lesser shift of thebeing emitted from the edge plasma, chords 1 and 20. Sthe bottom oblique viewport is being used, the plasma hacomponent of the axial velocity that is moving towards tviewport and produces the expected blueshift.

After the quiescent time the plasma flow velocity is sinificantly reduced. Figure 11 shows the output from tICCD spectrometer tuned to the C-III line at 229.7 nm aviewing the plasma through the oblique viewport. The trger time for the ICCD is 38ms which is after the quiescenperiod and when the magnetic mode activity is high. Tspectra for all of the spatial locations are centered on229.7 nm reference line in the figure. The peaks are broaindicating random plasma motion and plasma heating duflow stagnation on the electrode end wall, identified in Fig.

When the edges of the emissivity profile are seen,data can be deconvolved to provide profiles with an iproved spatial dependence.21 An accurate deconvolution isnot possible without simultaneous data to identify the ed

FIG. 10. Chord-integrated C-III line~229.7 nm! emission at 30ms with a1 ms gate obtained with the ICCD spectrometer showing the Doppler sof the impurity line in the core of the pinch and a smaller shift towardsedge of the plasma. The solid line is positioned at 229.7 nm for referen


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and center of the plasma. However, an approximate veloprofile can be determined by fitting the chord integrated dwith shifted and broadened Gaussian functions. Typicadeconvolutions are not possible for data obtained outsidthe quiescent period. To allow for a meaningful comparisapproximate axial velocity profiles are shown in Fig. 12. Tdata were obtained during the pinch assembly, duringquiescent period, and during the high fluctuation periodcompilation of the magnetic field fluctuation at the pinmidplane for them51 mode is shown in Fig. 13 for threpulses corresponding to the pulses used for the velocityfiles. A quiescent period from 22ms to 38ms is evident. Theshaded regions in the figure indicate the times during whDoppler shift spectra were recorded.

During the pinch assembly the magnetic fluctuation leis high and the plasma axial velocity profile is uniform wia value of approximately 43104 m/s. During the quiescen

FIG. 11. Chord-integrated C-III line~229.7 nm! emission at 38ms with a1 ms gate obtained with the ICCD spectrometer showing a negligible Dpler shift of the impurity line. The solid line is positioned at 229.7 nm freference.

FIG. 12. Plasma axial velocity profiles based on the C-III line at 229.7as a function of geometric radius obtained during the pinch assembly, duthe quiescent period, and during the high fluctuation period.~The times areindicated in Fig. 13.! The plasma flow is peaked with a large shear atedge during the quiescent period. The plasma flow is low and unifduring pinch assembly and after the quiescent period. The data havefit with shifted Gaussians but not deconvolved to allow for a unifocomparison.


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period the magnetic fluctuation level is low and the plasaxial velocity profile is peaked with a large shear at the edThe velocity profile shows a large axial velocity in the inncore of the pinch to be 105 m/s. The velocity remains relatively uniform in the inner core and then drops off to a lowvalue of 43104 m/s towards the edge of the pinch. After thquiescent period the magnetic fluctuation level is high athe plasma axial velocity profile is low with a maximumvelocity of approximately 104 m/s.

V. DISCUSSION AND COMPARISON TO THEORY

During the quiescent period the plasma flow is organizinto a profile that has a large radial shear of the axial velity. The shear is maximum close to the plasma edge. Athe quiescent period the plasma becomes turbulent andflow velocity is mostly uniform with a maximum consideably less than during the quiescent period.

The measured axial flow shear can be compared torequired threshold predicted by linear theory. Experimenplasma values at the peak plasma current are used forcomparison. The magnetic field at the outer electrode is msured to be 0.18 T for a magnetic field value at the charteristic pinch radiusBa51.8 T assuming zero plasma curredensity forr .a. The electron number density in the pinchmeasured to ben5931016 cm23. The Alfven velocity isVA5Ba /AmoMin51.33105 m/s whereMi is the mass of ahydrogen ion. The growth rates of them50 and m51modes are approximatelykVA assuming a static plasma. Fothe case ofka5p the growth time would be 24 ns forstatic Z-pinch plasma with the magnetic field strength adensity measured on the ZaP experiment. The required avelocity shear for stability according to the shear flow stalization theory presented in Ref. 15 is 4.23106 s21.

The experimental results show a stable period of 17mswhich is over 700 growth times. The experimentally mesured axial velocity shear is 1.93107 s21 during the stableperiod and approximately zero afterwards when the magnmode fluctuations are high. The correlation of the expe

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FIG. 13. Compilation of three pulses of the magnetic field fluctuation atpinch midplane for them51 mode showing the quiescent period fro22 ms to 38ms. The shaded regions indicate the times during which Dpler shift spectra were recorded.


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mental stability data with the plasma flow measurementconsistent with the shear flow stabilization theory presenin Ref. 15.

A coincidental relation has been experimentally mesured. Magnetic fluctuations are low when a sheared aflow is present, and the magnetic fluctuations are high wthe shear is reduced. However, at this point a causal relacannot be determined. It has not been determined thatdecrease in the plasma velocity shear leads to the increathe magnetic fluctuations.

The plasma density in the accelerator region, shownFig. 5, remains at an elevated level until 42–45ms. Themagnetic field distribution in the accelerator region, shoin Fig. 4, indicates a Lorentz force that remains appromately constant once established from 25 to 45ms. At thattime the magnetic field values converge indicating the acerating force has decreased significantly. Shortly aftertime, the quiescent period ends. It is conjectured the plasource has been exhausted and the plasma flow inZ-pinch stagnates.

VI. CONCLUSIONS

The ZaP experiment has generated Z-pinch plasmasan axial plasma flow that is sheared in the radial directiMagnetic fluctuations are low when a sheared plasma flopresent. The magnetic fluctuations are large when the plaflow shear is lower, during the initial pinch assembly aafter the quiescent period. The experimental measuremindicate a Z-pinch plasma that becomes progressively hoduring the quiescent period. The experimental evidencconsistent with the theory that gross MHD modes of thepinch can be stabilized with a sufficiently sheared axplasma flow. The sheared flow stabilization of the Z pinhas important implications for the flow Z pinch. A flowpinch designed with a sheared flow could make a simsteady-state fusion device, such as described in Ref. 14.ditionally the flow stabilization effect may be applied


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ACKNOWLEDGMENTS

The authors wish to acknowledge T. R. Jarboe for vaable discussions.

This work is supported through a grant from the Depament of Energy.

1W. H. Bennett, Phys. Rev.45, 890 ~1934!.2A. S. Bishop,Project Sherwood~Addison–Wesley, Reading, 1958!.3W. A. Newcomb, Ann. Phys.~N.Y.! 10, 232 ~1960!.4R. J. Bickerton, Nucl. Fusion20, 1072~1980!.5C. W. Hartman, G. Carlson, M. Hoffman, R. Werner, and D. Y. ChenNucl. Fusion17, 909 ~1977!.

6A. A. Ware, Nucl. Fusion Suppl.3, 869 ~1962!.7R. R. John, S. Bennett, and J. F. Connors, AIAA J.1, 2517~1963!.8B. B. Kadomtsev,Reviews of Plasma Physics~Consultants Bureau, NewYork, 1966!, Vol. 2, p. 153.

9M. D. Kruskal and M. Schwarzschild, Proc. R. Soc. London, Ser. A223,348 ~1954!.

10V. D. Shafranov, At. Energ.5, 38 ~1956!.11A. A. Newton, J. Marshall, and R. L. Morse, inProceedings of the Third

European Conference on Controlled Fusion and Plasma Physics, Utrecht,1969 ~Wolters-Noordhoff, Groningen, 1969!, p. 119.

12V. G. Belan, S. P. Zolotarev, V. F. Levahov, V. S. Mainashev, A. I. Morzov, V. L. Podkovyrov, and Yu. V. Skvortsov, Sov. J. Plasma Phys.16, 96~1990!.

13C. W. Hartman, J. L. Eddleman, R. Moir, and U. Shumlak, Fusion Tenol. 26, 1203~1994!.

14C. W. Hartman, J. L. Eddleman, A. A. Newton, L. J. Perkins, andShumlak, Comments Plasma Phys. Controlled Fusion17, 267 ~1996!.

15U. Shumlak and C. W. Hartman, Phys. Rev. Lett.75, 3285~1995!.16R. E. Peterkin, Jr., M. H. Frese, and C. R. Sovinec, J. Comput. Phys.140,

148 ~1998!.17U. Shumlak, R. P. Golingo, B. A. Nelson, and D. J. Den Hartog, Ph

Rev. Lett.87, 205005~2001!.18D. J. Den Hartog and R. P. Golingo, Rev. Sci. Instrum.72, 2224~2001!.19R. D. Benjamin, J. L. Terry, and H. W. Moos, Phys. Rev. A41, 1034

~1990!.20W. L. Rowan, A. G. Meigs, R. L. Hickok, P. M. Schoch, X. Z. Yang, an

B. Z. Zhang, Phys. Fluids B4, 917 ~1992!.21R. P. Golingo and U. Shumlak, ‘‘A spatial deconvolution technique

obtain velocity profiles from chord integrated spectra,’’ Rev. Sci. Instru~in press!.


PHYSICS OF PLASMAS12, 062505s2005d

Formation of a sheared flow Z pinchR. P. Golingo,a! U. Shumlak, and B. A. NelsonAerospace and Energetics Research Program, University of Washington, Seattle, Washington 98195-2250

sReceived 4 January 2005; accepted 15 April 2005; published online 27 May 2005d

The ZaP Flow Z-Pinch project is experimentally studying the effect of sheared flows on Z-pinchstability. It has been shown theoretically that whendVz/dr exceeds 0.1kVA the kink sm=1d mode isstabilized.fU. Shumlak and C. W. Hartman, Phys. Rev. Lett.75, 3285s1995d.g Z pinches with anembedded axial flow are formed in ZaP with a coaxial accelerator coupled with a 1 m assemblyregion. Long-lived, quiescent Z pinches are generated throughout the first half cycle of the current.During the initial plasma acceleration phase, the axial motion of the current sheet is consistent withsnowplow models. Magnetic probes in the assembly region measure the azimuthal modes of themagnetic field. The amplitude of them=1 mode is proportional to the radial displacement of theZ-pinch plasma current. The magnetic mode levels show a quiescent period which is over 2000times the growth time of a static Z pinch. The axial velocity is measured along 20 chords throughthe plasma and deconvolved to provide a radial profile. Using data from multiple pulses, the timeevolution of the velocity profile is measured during formation, throughout the quiescent period, andinto the transition to instability. The evolution shows that a sheared plasma flow develops as the Zpinch forms. Throughout the quiescent period, the flow shear is greater than the theoreticallyrequired threshold for stability. As the flow shear decreases, the magnetic mode fluctuationsincrease. The coaxial accelerator provides plasma throughout the quiescent period and may explainthe evolution of the velocity profile and the sustainment of the flow Z pinch. ©2005 AmericanInstitute of Physics. fDOI: 10.1063/1.1928249g

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I. INTRODUCTION

One of the earliest studied magnetic plasma confinegeometries was the Z pinch.1,2 Static Z pinches are unstabto the m=0 ssausaged and m=1 skinkd modes. Numericaanalysis has shown that Z pinches can be stabilized wradially sheared, axial flow.3–7 The ZaP Flow Z-Pinch experment at the University of Washington is presently studythe effect of sheared flow on the stability of the Z pinch.8,9 Zpinches with an embedded flow are generated by couplcoaxial acceleration region with a pinch assembly regiostationary Z pinch persists in the assembly region for minstability growth times during a quiescent period inmagnetic mode fluctuations. During this period an axial flshear is measured in the Z pinch. At the end of the quieperiod, the flow shear is below the threshold given by Re

A Z pinch is one of the simplest magnetic confinemconfigurations. It consists of column of plasma with an acurrent, where the self-azimuthal magnetic field provconfinement. The Z-pinch equilibrium can be describedthe magnetohydrodynamic force balance equation

=P + rsV · = dV = j 3 B, s1d

where P is the pressure,r is the mass density,V is thevelocity, j is the current density, andB is the magnetic fieldWhen the gradients are only in ther direction, no axial magnetic fields are applied, and the flow is only in thez direc-tion, Eq. s1d reduces to

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Electronic mail: [email protected]
1070-664X/2005/12~6!/062505/9/$22.50 12, 06250


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the equilibrium of a static Z pinch. This equilibrium has bwell studied.

Typically Z pinches are unstable tom=0 ssausaged andm=1 skinkd modes. Traditional methods have been usestabilize Z pinches. Both modes can be stabilized by aping an axial magnetic field.10,11This method places a limit othe maximum plasma pressure. The kink mode can belized with close-fitting walls.12 The maximum temperaturethe plasma is limited by the heat load to the wall. Kadomshowed the sausage mode can be stabilized by adjustinpressure profile, but the Z pinch is still unstable to themode.13 Linear stability calculations have shown thasheared axial flow can stabilize the kink mode in a Z pinchwhere the pressure profile is marginally stable to the saumode. The required amount of flow shear is given by

dVz

drù 0.1kVA, s3d

wherek is the axial wave number andVA;B/Îm0r is theAlfvén velocity. The ZaP experiment is presently studythis result.

A description of the Z-pinch formation process, expmental device, and diagnostics is given in Sec. II. A seoperational parameters is identified where a quiescent pis measured in the magnetic mode amplitudes. The exmental results from this set of operational parameters
presented in Sec. III. Section IV compares the results to co-
© 2005 American Institute of Physics5-1


http://dx.doi.org/10.1063/1.1928249

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062505-2 Golingo, Shumlak, and Nelson Phys. Plasmas 12, 062505 ~2005!

axial accelerator models and to the flow shear stabilizathreshold. Conclusions and future work are discussed inV.

II. EXPERIMENTAL APPARATUS AND METHODS

The ZaP experiment uses a unique technique to fopinches with an embedded flow. Previous experiments ucoaxial accelerators have seen pinchlike structures at thof the inner electrode that persist throughout the cupulse.14,15 By introducing an assembly region at the endcoaxial accelerator, ZaP forms Z pinches with an embeflow.

A. Method of operation for ZaP

Z pinches are formed by collapsing an axially moviannular current sheet onto thez axis. A machine drawing othe experiment is shown in Fig. 1 for reference. The insteps in the formation process are similar to those ofpuffed coaxial accelerators. Hydrogen neutral gas, stimes mixed with methane, is puffed between two coaelectrodes at the gas injection plane. While the gas densstill concentrated at the gas inlet, a voltage is appliedtween the electrodes. The neutral gas breaks down at thinlet location, forming an annular current sheet. Thej 3Bforce accelerates the current sheet along the electrodeinitial steps of the formation have been studied in odevices.14,16–18

The addition of a Z-pinch assembly region differentiaZaP from these other machines. When the current sreaches the end of the acceleration region, the Z pinch bto form. As the current sheet travels past the end of theelectrode, the inner region of the current sheet collapsesthe axis. The outer region of the current sheet continutravel along the outer electrode, stretching the current sas it continues to assemble along the axis. This procecompressing and stretching continues until the outer reof the current sheet reaches the electrode end wall. Thmaining current sheet then collapses onto the axis coming the Z-pinch formation process. The formation proc

FIG. 1. Diagram of the ZaP experiment showing the 1 m assembly reThe gas puff valve inlets are at the neutral gas injection plane. The csheet forms at the gas injection plane and is accelerated for 0.5 m bebegins to collapse on axis. The Z pinch forms in the assembly region.of the measurements shown are made at thez=0 plane of the experimenStagnation of the flow at the electrode end wall is alleviated by providinexhaust through the electrode end wall.

generates a Z pinch with an embedded axial flow.


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B. Experimental device

The geometry of the acceleration region is similaaccelerators used at the Los Alamos Scientific Labs in1960s.19 The electrodes for the experiment are containedvacuum vessel, see Fig. 1. The inner electrode is a 1 m10 cm outer diameter copper tube. A shaped coppercone is attached at the exit of the acceleration region.assembly region is formed by extending the outer elec1 m beyond the end of the inner electrode. The outertrode is a 20 cm inner diameter copper tube. Gas is pinto the midpoint of the acceleration regionsz=−75 cmdwith nine fast puff valves. One valve is located on the inelectrode and injects neutral gas into the annulus threight symmetrically placed ports. Eight valves are locatethe outer electrode. Each of these valves injects neutrathrough a port opposite an inner electrode port. The timineach valve can be varied to control the initial neutral gaprofile. Most of the measurements shown in this papemade atz=0 cm s20 cm from the tip of the inner electronose coned. An electrode end wall is attached to the endthe outer electrode. A hole is placed in the center of thewall to allow plasma to exit. All plasma facing surfaces hbeen sprayed with 0.25 mm of tungsten.

A capacitor bank, configured as a pulse formingwork, provides the energy for plasma breakdown and aeration. Two banks, each with four 170mF capacitors, arswitched into the plasma load withD-size ignitrons. Inductors are used between the capacitors to create a flattopcurrent wave form. Both capacitor banks are triggered asame time for the data shown here.

C. Diagnostics

The array of diagnostics on the ZaP experiment msures the general characteristics of the driving circuit,magnetic field, and plasma properties. The design of thstruments and the analysis of the data can be found ireferences of this section. The total plasma current anvoltage between the electrodes is measured in each pu20

Arrays of surface-mounted magnetic field coils are usemeasure the magnetic field. A linear array of magnprobes measures the axial variation of the azimuthalnetic field. These probes are spaced every 5 cm alonouter electrode. The location of the current sheet and rcurrent densities can be found with this array.21 If the currendensity is axisymmetric, the average radial current densj rbetween two probesi and i +1 at the outer electrode is givby

j r =Bi − Bi+1

m0szi+1 − zid, s4d

whereBi is the azimuthal magnetic field at axial locationzi.Four azimuthal arrays measure the azimuthal variation omagnetic field atz=−25, 0, 35, and 70 cm. These arrconsist of 8, equally spaced probes except atz=−25 cmwhere the top two probes have been removed for opaccess. The azimuthal Fourier componentsBm of the mag

.titt

netic field at each axial location are found with these arrays.


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062505-3 Formation of a sheared flow Z pinch Phys. Plasmas 12, 062505 ~2005!

The radial displacement of the current,Dr, is proportional tothe normalizedm=1 component,Bm/ kBl, by

Dr =rwall

2

B1

kBl, s5d

when all of the current is in the Z pinch.20 The magnetifield, current, and voltage probes are calibratedin situ. Thiskeeps the error in the calibration factors to less thanMost of the uncertainty in the measurements is due totizer bit noise.

The shape of the optical emission from the plasmmeasured with an Imacon fast-framing camera. Fscopes,22 a spectrometer with a photomultiplier tube acharged-coupled device camera,23 and a solid-statbolometer24 monitor the radiation from different regionsthe spectrum. The line-integrated plasma density, thrvarious chords of the device, is measured with a two chheterodyne, quadrature, HeNe interferometer.25–27 Thechords can be configured to measure the snowplow saxial variations of the density in the accelerator, and theerage pinch density. A holographic interferometer is usemeasure the radial density profile of the Z pinch.28

Passive spectroscopy is used to measure the velocthe plasma. Impurities entrained in the plasma emit linediation at discrete wavelengths. The motion of the impurrelative to the viewing optics causes radiation to be Dopshifted. By measuring the centroid and width of the linediation, the velocity and temperature of the impurities cafound. The impurities and plasma should have the sproperties due to the short equipartition times in the Z piThis has been verified by forming Helium plasmas and msuring the properties of the bulk Helium plasma and thepurity ions.

Light from 20 parallel chords, spaced 1.78 mm apthrough the plasma is collected with telecentric telescop29

Doppler shifted and unshifted spectra are collected by ving the plasma 35° and 90° to thez axis. The spectral intensities are resolved with a 0.5 m spectrometer, and recoduring a 100 ns interval on an image intensified chacoupled devicesICCDd. A shell model is then used to decovolve the line-integrated data to give the ion veloprofile.30 A complete discussion of the error determinatiofound in Ref. 30. Multiple pulses are used to determinetemporal evolution of the velocity profile. An ion DoppspectrometersIDSd sRefs. 31 and 32d has been used to verithe temporal evolution of the velocity. Ion temperaturemagnetic field measurements can also be made withICCD spectrometer.

III. EXPERIMENTAL RESULTS

A set of operating parameters has been identified wlead to long-lived, quiescent Z pinches. The inner gasvalve is triggered at −1.7 ms. Four outer gas puff valspaced 90° apart, are triggered at −1.5 ms. The otherouter valves are triggered at −0.5 ms. The capacitor bprovide a current pulse with a flattop, shown in Fig. 2, toZ pinch for 35ms. This configuration has generated lo
quiescent periods on the ZaP experiment.

.

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The figure of merit for the performance of the Z pincthe length of the quiescent period in the normalized magmode activity of the azimuthal array located atz=0 cm.Large fluctuations in the mode activity are seen duringformation of the Z pinch. The activity then decreases fperiod of time, during which a quiescent Z pinch is seenthe axis of the machine. The time when the normalized mamplitude is below an empirical value of 0.2 is defined asquiescent period. During the quiescent period, the maxidisplacement of the current given by Eq.s5d is about 1 cmthe approximate radius of the pinch. Later the characteamplitude of the mode fluctuations then change. Duringtime, instabilities are seen in the Z pinch. This sectionscribes the initial acceleration of the plasma, the measplasma properties atz=0 cm, and the evolution of the veloity throughout the lifetime of the Z pinch.

A. Current sheet acceleration

The initial current sheet and plasma acceleration aresistent with models developed for coaxial accelerators33–35

The location of the current sheet is measured with the

FIG. 3. Spatial variation ofBu measured by the linear array at 5ms inter-vals. The error in the magnetic field measurement is smaller than the ssize. The location and speed of the leading edge current sheet is foun

FIG. 2. The normalized magnetic mode amplitudes are shown for a tpulse. When the current sheet arrives atz=0 cm large fluctuations are sein the mode amplitudes. The normalized mode amplitude then decbelow an empirical value of 0.2. A quiescent Z pinch is seen on the athe assembly region during this period. At the end of the quiescent pthe amplitude and character of the mode changes. Kinks are seen inpinch after the quiescent period. The currentsdashed lined with the 35msflattop is shown for reference.

the initial rise of the field.


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array of magnetic field probes. The azimuthal magneticalong the outer electrode at 5ms intervals is shown in Fig.The location and velocity of the current sheet are found fthe initial rise of the magnetic field. The current sheemoving <40 km/s as it exits the acceleration region. Ascurrent sheet travels down the acceleration region, negas ahead of the current is ionized and entrained in therent sheet. The line-integrated plasma density increasthe current sheet travels from the neutral gas injection pto the exit of the accelerator, shown in Fig. 4. These reare compared to the theoretical predictions in the followsection.

B. Properties of the Z pinch

The properties of the Z pinch are measured at thez=0plane, see Fig. 1. The two-chord interferometer measureaverage density in the Z pinch. One chord of the interfereter is located through a diameter of the outer electrthrough the axis of the assembly region. The other cholocated 1.5 cm above the first chord. The difference inline-integrated density between the chords is proportionthe average pinch density, shown in Fig. 5. As the cursheet sweeps past this plane large magnetic mode activmeasured. During this period, approximately equal lintegrated densities are measured along both chords.

FIG. 4. The line averaged density measured at two axial locations iaccelerator. The density in the current sheet is increasing as it travelsthe acceleration region, consistent with snowplow models.

FIG. 5. sad Line-integrated density through two impact parametersb at thez=0 cm plane.sbd Normalized mode amplitudes atz=0 cm. During thequiescent period in the mode activity, a larger line-integrated densmeasured on the axis of the assembly region. The difference in the
integrated density is proportional to the average Z-pinch density.

lr-s

e

e

,

tis

r

the Z-pinch forms, a quiescent period is seen in the mdata. The line-integrated density through the center of tpinch is larger than the line-integrated density 1.5 cm athe axis. These data show a quiescent Z pinch with anage density of 231022 m−3. When the magnetic mode actity increases after the quiescent period ends, a uniformsity is again measured along both chords.

Other diagnostics in the assembly region also seesame behavior of the plasma. The images of the total viplasma emission show a stable Z pinch during the quieperiod, shown in Fig. 6. The location of the centroid ofvisible emission corresponds with the location of curfound with the magnetic probes. The characteristic radiuthe Z pinch found with these images is 1 cm, which is csistent with the radius found with the ICCD spectrometerholography. The average magnetic field at the outer elecis 0.1 T during the quiescent period. The edge magneticis 1.0 T assuming that all of the current is located insidthe Z pinch. The total temperature from pressure balan124 eV. Measurements of the ion temperature made witIDS and ICCD spectrometers are approximately half oftotal temperatures computed from pressure balance. Amagnetic mode activity increases, the character of thpinch changes. Images of the total visible plasma emisshow a kink during this time, shown in Fig. 7. The initial hwavelength of the kink shown at 75.9ms is <1 cm.

g

-

FIG. 6. Images of the visible plasma emission show a stable, long-livpinch during the quiescent period. This series of images was taken tha 4.7 cm diameter hole in the outer electrode atz=0 cm. No filters havbeen used to obtain these images. The acceleration region is to thesPositivez is to the left.d

FIG. 7. Images of the visible plasma emission show a kink beginninform during increased mode activity. This series of images wasthrough a 4.7 cm diameter hole in the outer electrode atz=0 cm. No filtershave been used to obtain these images. The kink is moving in the posz
direction.

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C. Velocity evolution

The velocity evolution throughout the lifetime of thepinch is measured. The ICCD spectrometer is used tosure the impurity emission of the C III line at 229.7during a 100 ns interval of a pulse. The velocity evolutiomeasured by adjusting the time at which the spectra arcorded between multiple pulses. The start and end timthe quiescent period can vary by several microsecondeach pulse. Normalizing the time accounts for this varia

t =t − tstart

tend− tstart, s6d

where tstart is the start time andtend is the end time of thquiescent period for each pulse.

C III line emission is present throughout the evolutionthe Z pinch for the data shown. Characteristic, lintegrated, emissivity profiles are peaked as shown in8–11. The peak line-integrated C III line emission iscounts during the formation of the Z pinch, shown in FigThe brightness then increases and remains high throuthe quiescent period, shown in Figs. 9 and 10. The brighof the C III emission decreases as the quiescent period

FIG. 8. The C III line emission is measured with the ICCD spectromt=−0.40 with a 100 ns gated exposure. A characteristic line-integratedsion profile during the formation of the Z pinch is shown. A peaked prwith a maximum intensity of 300 counts is measured at this time.

FIG. 9. The C III line emission is measured with the ICCD spectromt=0.23 with a 100 ns gated exposure. A characteristic line-integratedsion profile from the first half of the quiescent period is shown. A pe
profile with a maximum intensity of 4000 counts is measured at this time.

-

-fn

.

utss,

shown in Fig. 11. These profile shapes allow a shell modbe used to calculate the velocity profile.30 Deconvolved velocity profiles from the four pulses are shown in Figs. 12–As expected the error in the velocity measurement is lawhen the brightness of the C III emission is low. The veity profile evolution is then measured throughout a stanpulse.

The evolution of the velocity profile is shown in Fig. 1Data in Fig. 16sad are obtained by varying the ICCD timiover 70 pulses. The radial velocity profile for each pulsethen found. The normalized time of each profile is givenEq. s6d. Figure 16sbd shows the magnetic mode activity fotypical pulse from the survey. As the Z pinch formssnegativetd a uniform velocity of 100 km/s is seen. As the activitythe magnetic mode decreases, a sheared flow begins toin the Z pinch. The velocity in the center of the plasma slto <40 km/s, creating a large positive velocity shear onedge of the Z pinch. Att<0.6, the edge velocity quickslows to less than 0 km/s. Changes in the magnetic mactivity are not seen when velocity shear briefly goes throzero. During the last part of the quiescent period a lnegative velocity shear is present on the edge of the Z p

-

-

FIG. 10. The C III line emission is measured with the ICCD spectromt=0.92 with a 100 ns gated exposure. A characteristic line-integratedsion profile during the second half of the quiescent period is showpeaked profile with a maximum intensity of 6000 counts is measured atime.

FIG. 11. The C III line emission is measured with the ICCD spectromt=0.96 with a 100 ns gated exposure. A characteristic line-integratedsion profile towards the end of the quiescent period is shown. A pe
profile with a maximum intensity of 1000 counts is measured at this time.

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The sign of the shear does not matter since a simple conate transformation can change the sign. Towards the ethe quiescent period, the velocity in the center of the Z pbegins to decrease and the edge velocity increases. Avelocity becomes uniform, the magnetic mode activitycreases. The magnetic mode activity is low with either ntive or positive velocity shears.

IV. DISCUSSION OF RESULTS

The results from the experiment are consistent with tries that describe coaxial accelerators and sheared flowbilization. The initial current sheet can be described wsnowplow models. Throughout the quiescent periodplasma flow in the Z pinch may be driven by deflagraprocesses in the accelerator.36 As the velocity shear decreases, the magnetic mode activity increases. The veshear levels are consistent with the calculated threshoRef. 3.

A. Current sheet acceleration

Snowplow models have been developed to describplasma during the acceleration of a current sheet.33–35 Thecurrent sheet in the ZaP experiment is modeled with the

FIG. 12. The velocity profile is found with the measured line emisshown in Fig. 8. A characteristic velocity profile during the formation ofZ pinch is shown. A mostly uniform velocity of<100 km/s is measured

FIG. 13. The velocity profile is found with the measured line emisshown in Fig. 9. A characteristic velocity profile during the first half of
quiescent period is shown. The velocity profile has a positive shear.

i-f

e

-

-a-

yn

e

dependent description given by Ref. 35. The driving ciris assumed to be a simple LRC circuit. The models assthat the plasma is accelerated by a massless piston, drivthe j 3B force. Neutral gas ahead of the current sheionized and entrained in the sheet. The equation of mand Kirchoff’s equation are used to describe the motiothe current sheet. The equation of motion can be writtenfunction of the attachment location along the inner electrz1std, when the piston shape,zsr ,td, is given by

zsr,td = r1z1std

r, s7d

wherer is the radial location of the current sheet andr1 is theradius of the inner electrode. The system of equationsolved numerically.

The model uses the fill density, capacitor bank chateristics, and electrode radius to predict the rundown velof the current sheet. The ZaP experiment injects neutrainto the annulus between the electrodes with fast puff vawhich have been characterized with a fast ionization gaThe fill density is 231022 m−3 if all the injected neutral gauniformly fills the annulus between the inner and outer etrodes. The capacitor bank characteristics are measure

FIG. 14. The velocity profile is found with the measured line emisshown in Fig. 10. A characteristic velocity profile during the second hathe quiescent period is shown. The velocity profile has a negative sh

FIG. 15. The velocity profile is found with the measured line emisshown in Fig. 11. A characteristic velocity profile towards the end oquiescent period is shown. The velocity shear is decreasing as the qu
period ends.

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used in the snowplow model. The initial rundown ofcurrent sheet is described by this snowplow model. Thsults are shown in Fig. 17. The largest uncertainty is theprofile of the initial fill density. The results from threedensities are shown. The measured location of the cusheet, Fig. 17sad, agrees with predicted location. The chanin the current, Fig. 17sbd, are small due to the small magtude of the changing inductance compared to the inducof the capacitor bank.

B. Deflagration processes

Coaxial accelerators can accelerate plasmas usingflagration process.21,36,37In a deflagration process, the ioniztion of neutral gas propagates in the upstream directionposite to the plasma velocity. The plasma is accelerateda process similar to an expansion wave. Other experimhave seen a transition from snowplow to deflagraprocesses.21 Unlike the snowplow model, deflagration pcesses can continuously supply plasma to the Z pinch.

As the current sheet enters the assembly region, theization process in the accelerator transits to a deflagrmode. Plasma density in the accelerator shows large p

FIG. 16. sad Contours of the velocity profile evolution atz=0 cm measurewith the ICCD. sbd Magnetic mode activity for a typical pulse from tsurvey. The evolution of the velocity profile atz=0 cm is measured badjusting the ICCD trigger time over many pulsessdata from 70 pulses ashownd. A normalized time is used to account for pulse to pulse variatiothe quiescent period. As the Z pinch is forming a uniform velocity profimeasured across the Z pinch. The center velocity slows as the quiperiod begins. The center velocity remains constant throughout the quiperiod. The edge velocity at this axial location remains high. Att<0.6 theedge velocity quickly decreases to zero. Changes in the magneticactivity are not seen when velocity shear briefly goes through zero. Acenter velocity slows towards zero and edge velocity increases, the mafluctuations increase.

in the density before the quiescent period as the snowplow


-l

t

e

e-

-hs

-ns

passes the axial location, see Fig. 4. Throughout the qcent period, plasma is present in the accelerator, see18sad. As the plasma density in the accelerator vanishesmode activity increases.

Throughout the quiescent period, the plasma in thecelerator is forced towards the Z pinch. Figure 18sbd showsthe evolution of the radial current density along the oelectrode in the accelerator. The snowplow starts at thetion of gas injection,z=−0.75 cm, and travels towards tassembly region. Current begins to shed from the snowand move in the −z direction. All the forces are in the potive z direction in the accelerator, suggesting neutral gashind the snowplow is being ionized during this time. Thj3B force accelerates the plasma towards the Z pthroughout the quiescent period sustaining the flow. A lradial current is measured at the end of the inner electWhen the deflagration process ends in the acceleratovelocity in the Z pinch decreases.

C. Comparison to stability theory

The quiescent period of the Z pinch lasts for manystability growth times. Average plasma characteristicssummarized in Table I. The characteristic radius of thpinch, a, measured by the fast framing camera, holograinterferometer, and ICCD spectrometer is 1 cm. The aveZ-pinch density during the quiescent period, found withtwo-chord interferometer is 231022 m−3. Assuming that athe current is in the Z pinch, the magnetic field at the pradius Ba is 1 T. These plasma parameters give an Alfvelocity of 150 km/s. Assuming the shortest kink walength is equal to the Z-pinch diameter, the largest wnumber is 314 m−1. The kink growth rate for a static Z pinis gkink=kVA which corresponds to a growth time of 21The Z pinch is stable for over 2000 growth times in theexperiment.

Instabilities are normally seen at the end of the quiesperiod. Since no axial fields are applied and the wall raditen times the pinch radius, traditional stabilization methcannot explain the quiescent period. Convective stabiliz

ntnt

e

ic

FIG. 17. sad Experimentally measured position of the current sheet anlocation predicted by a snowplow model for three fill densities.sbd Mea-sured and predicted current. The experimental position and currensdia-mondsd agree with the theoretical prediction. Changing the fill denchanges the velocity without significantly affecting the current.

of a 1 m Z pinch of a mode growing at 21 ns is not possible


old

heaigsve-iod,

arengeby

ty inhear

with. Z

xperi-ly re-as athea ex-.ctiv-thefilethe Zr isde-

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at the plasma speeds measured. The theoretical threshthe velocity shear given by Eq.s3d is 4.73106 s−1. Through-out the quiescent period the magnitude of the velocity son the edge of the Z pinch is above this value, shown in F19–21. Initially the velocity shear is positive. The edgelocity slows during a short interval of the quiescent percreating a negative velocity shear. Magnetic fluctuationsnot seen when the plasma is flowing and the shear chasign atz=0 cm. The stability of the Z pinch is determined

FIG. 18. sad The average density near the gas injection planesdashed linedand at the exit of the acceleration regionssolid lined. sbd Contours of theradial current in the accelerator.scd Magnetic mode activity measuredz=0 cm. Vertical lines are placed at the start and end of the quiescent pPlasma is present in the accelerator throughout the quiescent periodplasma may be formed from neutral gas which is behind the currentMeasured radial currents accelerate the plasma towards the assemblyThe radial current travels in the negativez direction, opposite to the diretion of force generated by current crossed with the self-generated fielddeflagration process supplies plasma to the Z pinch during the quieperiod in the magnetic mode activity atz=0 cm. The large current densitythe exit of the accelerator may turn the plasma towards the axis at thecone. As the deflagration process ends the magnetic mode activitz=0 cm increases.

TABLE I. Multiple diagnostics are used to understand the behavior of tpinch. The average plasma characteristics during the quiescent perisummarized below.

a 0.01 m

ne 231022 m−3

Ba 1.0 T

VA 150 km/s


of

r.

s

the magnitude of the shear, not the sign. As the velocithe center slows and the magnitude of the velocity sapproaches the threshold, the quiescent period atz=0 cmends.

V. CONCLUSION

The results from the ZaP experiment are consistentthe theoretical predictions of sheared flow stabilizationpinches with a sheared flow are generated in the ZaP ement using a coaxial accelerator coupled to an assembgion. The current sheet in the accelerator initially actssnowplow. As the Z pinch forms, plasma formation inaccelerator transits to a deflagration process. The plasmits the accelerator and maintains the flow in the Z pinch

During the quiescent period in the magnetic mode aity at z=0 cm, a stable Z pinch is seen on the axis ofassembly region. The evolution of the axial velocity proshows a large velocity shear is measured at the edge ofpinch during the quiescent period. The velocity sheaabove the theoretical threshold. As the velocity shearcreases towards 0.1kVA, the predicted stability threshold, tquiescent period ends.

The present understanding of the ZaP experiment sthat it may be possible for the Z pinch to operate in a st

.ist.n.

et

e

re

FIG. 19. The measured velocity shear att=0.23 is shown. A positive velocity shear is measured at this time. The magnitude of the velocity shabove the theoretical threshold, horizontal lines.

FIG. 20. The measured velocity shear att=0.92 is shown. A negative vlocity shear on the edge of the Z pinch is measured at this time. Thenitude of the velocity shear is above the theoretical threshold, horiz
lines.

conor.

ntirethorrk,

.S.

, and

d J.

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.

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state if the deflagration process can be maintained bystantly supplying neutral gas or plasma to the accelerat

ACKNOWLEDGMENTS

The authors wish to thank S. L. Jackson and the eZaP team for their efforts obtaining these results. The auwould also like to thank D. J. Den Hartog for his wodesigning, and assembling the ICCD spectrometer.

This work was supported with a grant from the UDepartment of Energy.

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FIG. 21. The measured velocity shear att=0.96 is shown. A negative vlocity shear is measured at this time, however, the magnitude of the veshear has decreased. As the velocity shear approaches the threshozontal lines, the quiescent period ends.


-

s

8U. Shumlak, R. P. Golingo, B. A. Nelson, and D. J. Den Hartog, PRev. Lett. 87, 205005s2001d.

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