S. L. Jackson et al- Effects of Initial Gas Injection on the Behavior of a Sheared-Flow Z-Pinch

8/3/2019 S. L. Jackson et al- Effects of Initial Gas Injection on the Behavior of a Sheared-Flow Z-Pinch

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41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 1013, 2005, Tucson, Arizona

Effects of Initial Gas Injection on the Behavior of a Sheared-Flow Z-Pinch

S. L. Jackson , U. Shumlak , B. A. Nelson , R. P. Golingo , R. C. Lilly , and T. L. Shreve

Aerospace and Energetics Research Program

University of Washington

Seattle, Washington 98195-2250

A fusion thruster based on a ow-stabilized Z-pinch holds promise as a high-power,high-specic-impulse space thruster. Several challenges must be met in the developmentof a Z-pinch space thruster, one of which is preventing the destruction of the Z-pinch byclassical magnetohydrodynamic instabilities. Linear stability analysis has shown that owshear could limit the destructive effects of these instabilities. This result is supportedby experimental measurements made on the ZaP Flow Z-Pinch Experiment, which hasformed sheared-ow Z-pinch plasmas that exhibit characteristics of stability for over onethousand theoretical instability growth times. A second challenge is designing the thrusterto withstand the power load from the fusion reaction. A deuterium-tritium-fueled Z-pinchoperating at a temperature of 15 keV is estimated to have a peak fusion power density of 2 10 16 W/m 3 , which would be difficult to handle in steady-state. Pulsed operation of thethruster would reduce the energy-handling requirements.

Nomenclature

m Mode numberr Radial coordinatey Vertical coordinatez Axial coordinate

I. Introduction

A fusion thruster based on a ow-stabilized Z-pinch holds promise as a high-power, high-specic-impulsespace thruster. Previous analyses suggest that the thruster would have a thrust of 10 5 N with a specicimpulse of 106 s.10 The principal challenge that must be met in the development of a Z-pinch space thruster ispreventing the destruction of the Z-pinch by classical magnetohydrodynamic (MHD) instabilities. This paperpresents results that indicate that sheared ow can be used to prevent the destruction of the Z-pinch as longas the necessary ow is maintained. These results were obtained during an experimental and computational

Graduate Student, Department of Aeronautics & Astronautics, AERB Room 120, Box 352250, AIAA Member (SS). Associate Professor, Department of Aeronautics & Astronautics, AERB Room 120, Box 352250, AIAA Member (MH). Research Associate Professor, Department of Electrical Engineering, AERB Room 120, Box 352250. Research Associate, Department of Aeronautics & Astronautics, AERB Room 120, Box 352250, AIAA Member (MB). Undergraduate Student, Department of Aeronautics & Astronautics, AERB Room 120, Box 352250, AIAA Member (SS).

Copyright c 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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American Institute of Aeronautics and Astronautics Paper 2005-3853


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investigation of the effects of changing the amount of gas injected into the experiment prior to the plasmapulse. The impact of these results on the operation of a Z-pinch fusion space thruster is discussed, in lightof other characteristics of the thruster.

A Z-pinch is a plasma column with an axial current owing through it. This axial current creates anazimuthal magnetic eld that connes and compresses the Z-pinch, resulting in a high-temperature, high-density column of plasma. If the plasma is hot enough, dense enough, and well-enough conned, fusionreactions will occur, resulting in the release of energy that can be used for space propulsion. 5

A fusion thruster based on a sheared-ow Z-pinch is an attractive concept for space propulsion for tworeasons. Like other magnetic connement fusion concepts, the Z-pinch results in a hot, dense plasma that isconned by a magnetic eld rather than a physical wall, meaning that the temperature of the plasma is notlimited by the melting point of the wall. Unlike other magnetic connement concepts, however, the sheared-ow Z-pinch requires no external coils to produce stabilizing magnetic elds. The eld that compresses andconnes the Z-pinch is produced by the current through the Z-pinch itself. This makes a Z-pinch thrustermore mass and energy-efficientenergy is not lost to resistive heating in heavy external magnetic eld coils.

A Z-pinch without adequate ow shear is susceptible to two types of magnetohydrodynamic (MHD)instabilities. The m = 0 sausage mode occurs when the plasma column begins to become thinner at anypoint along its length. Magnetic pressure builds at this point, causing the column to become thinner still,

until nally it breaks and the plasma current is disrupted. The m = 1 kink instability occurs when theplasma column begins to kink or bend. Magnetic pressure builds inside the bend, pushing it farther outuntil the column is broken and the current is lost. Figure 1 shows the m = 0 sausage and m = 1 kinkinstabilities in a Z-pinch. These MHD instabilities usually destroy the Z-pinch within tens of nanoseconds,

(a) (b)

Figure 1. m = 0 sausage and m = 1 kink instabilities in a Z-pinch. (a) m = 0 sausage mode. (b) m = 1kink mode.

and in the past have limited its usefulness for space propulsion.The m = 0 sausage instability can be stabilized by the appropriate choice of pressure prole. 3 The

m = 1 kink instability can be stabilized through the addition of axial magnetic elds or by the effectsof a close-tting wall. 4, 7 These methods of stabilizing the kink instability are undesirable, however, for thereasons mentioned above. Instead, sheared-ow stabilization is used to stabilize the m = 1 mode. Simulationshave shown that ow shear also limits the growth of the m = 0 mode. 10

II. ZaP Flow Z-Pinch Experiment

Linear stability analysis has shown that ow shear could limit the destructive effects of classical MHDinstabilities. 8 This result is supported by experimental measurements made on the ZaP Flow Z-PinchExperiment, which has formed sheared-ow Z-pinch plasmas that exhibit characteristics of stability for overone thousand theoretical growth times. 9

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The ZaP Flow Z-Pinch experimental apparatus, shown in Fig. 2, consists of a coaxial acceleration regionand an attached assembly region. Neutral gas is injected into the acceleration region and ionized. The

Figure 2. The ZaP Flow Z-Pinch Experiment consists of a coaxial acceleration region and an attached assemblyregion. Neutral gas is injected into the acceleration region, ionized, and pushed by Lorentz forces into theassembly region where a roughly 100 cm-long sheared-ow Z-pinch is formed.

resulting plasma is then accelerated into the assembly region where the Z-pinch is formed. Axial andazimuthal magnetic probe arrays indicate that formation of the Z-pinch is followed by a 1040 s-longquiescent period, characterized by low magnetic mode activity. Following the quiescent period, magneticmode activity increases.

A two-chord He-Ne interferometer is used to record the time evolution of the chord-integrated densityat various axial locations and impact parameters. During the quiescent period, a highly pinched plasma isobserved at or near the axis of the experiment, and lower density is observed off-axis, as shown in Fig. 3.The ow shear required to prevent destruction of the Z-pinch is present during the quiescent period. Theshear drops at the end of the quiescent period and is lower than the threshold after the end of the quiescentperiod. 9

Fig. 3(a) shows the total plasma current and the normalized m = 1 magnetic mode. Roughly half thetotal plasma current ows through the Z-pinch, while the other half ows through plasma in the accelerator.

The normalized m = 1 magnetic mode is calculated from measurements made by an azimuthal array of eightmagnetic eld probes imbedded in the outer electrode at the axial location labeled z = 0 in Fig. 2. Alsoknown as Bdot probes, each probe measures the change in magnetic eld versus time at its azimuthallocation. A running integral is used to calculate the magnetic eld at each probe location versus time. Thevalues of the magnetic eld at the probe locations at a given time are Fourier decomposed to yield themagnitudes of the m = 0 and m = 1 modes of the magnetic eld. The value of the m = 1 Fourier componentuctuates as the Z-pinch moves off the axis of the experiment. When the m = 1 component is normalized bythe m = 0 Fourier component, or average magnetic eld, the normalized m = 1 mode is equal to twice thedisplacement of the Z-pinch from the axis of the experiment. 1 The quiescent period is empirically denedas the time period when the value of the normalized m = 1 magnetic mode is less than 0.2. The horizontaldashed line in Fig. 3(a) denotes the value 0.2 and the vertical lines indicate the beginning and end of thequiescent period.

The quiescent period is also indicated in Fig. 3(b), which shows the chord-integrated electron numberdensity measured by the He-Ne interferometer along two chords located at the same axial location, z = 0.One chord passes through the center of the cylindrical assembly region containing the Z-pinch, at impactparameter y = 0 cm. The second is located slightly off-axis, at impact parameter y = 2 . 5 cm. The arrival of the plasma at z = 0 is indicated by the high electron number density along both chords beginning at 23 s.The presence of a dense Z-pinch is indicated by the drop in the off-axis density measured at y = 2 . 5 cm andthe concurrent rise in the density measured by the on-axis chord at y = 0 cm that occurs at the beginningof the quiescent period. This density difference persists throughout the quiescent period, indicating the

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(a)

(b)

Figure 3. (a) Normalized m = 1 mode at z = 0 and total plasma current for a 6 kV ZaP plasma pulse. Magneticmode activity is low during the quiescent period, which extends from 35 s to 68 s. (b) Chord-integratedelectron number density measured at z = 0 and two impact parameters. One chord passes through the center

of the cylindrical assembly region containing the Z-pinch. The other is located 2.5 cm above the center of theassembly region. Both chords are perpendicular to the axis of the assembly region. The difference betweenthe measurements at the two locations indicates the presence of a highly pinched plasma at or near the axisof the experiment during the quiescent period.

presence of a dense Z-pinch at or near the axis of the experiment during the quiescent period.Fig. 4 shows a series of unltered Z-pinch photos taken through a hole in the outer electrode with a

fast-framing camera. The images show a Z-pinch with a radius of 1 cm along the axis of the experiment.The empirical value of 0.2 used to dene the quiescent period corresponds to a displacement of 1 cm, or theradius of the Z-pinch.

Interferometer measurements also show the acceleration of plasma along the electrodes in the accelerationregion towards the assembly region during formation of the Z-pinch. Fig. 5(a) shows the normalized m = 1mode and plasma current for the plasma pulse whose chord-integrated electron number density is shownin Fig. 5(b). As shown in Fig. 6, one interferometer chord measures the density near the exit from theacceleration region, while the other is located just downstream of the gas injection plane.

Just prior to a plasma pulse, hydrogen gas is injected by nine gas valves located at the gas injectionplane. When the voltage is applied to the electrodes, this gas is ionized, forming a plasma that is acceleratedalong the electrodes by the Lorentz force, towards the assembly region. 2 The sharp rise in density measuredby both chords occurs as the current sheet passes rst the chord closer to the gas injection plane and thenthe chord at the exit of the accelerator. Both interferometer chords show the continued presence of plasma

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(a) (b) (c) (d)

(e) (f) (g) (h)

Figure 4. Unltered Z-pinch photos taken 0.2 s apart through a hole in the outer electrode with a fast-framing

camera at (a) 47.7 s. (b) 47.9 s, (c) 48.1 s. (d) 48.3 s. (e) 48.6 s. (f) 48.8 s. (g) 49.0 s. and (h) 49.2 s. A Z-pinch with a diameter of approximately 2 cm is observed through the 2 inch diameter window.

in the accelerator throughout the quiescent period, indicating that gas is being ionized and accelerated fromthe acceleration region into the assembly region, maintaining the ow in the Z-pinch. Depletion of plasmain the acceleration region corresponds to the onset of large mode uctuations and the end of the quiescentperiod.

The correlation between the drop in density in the accelerator and the end of the quiescent period ledto the analysis that is the primary focus of this paper. It is hypothesized that when the plasma in theaccelerator is exhausted, there is then no plasma to maintain the ow in the Z-pinch and the Z-pinch isquickly destroyed by an instability. If this is true, then injecting more gas before the voltage is appliedshould lengthen the quiescent period.

III. Computer Simulation of Accelerator Exhaustion

A computational study of the accelerator exhaustion was conducted using MACH2, a 2 12 -dimensionalresistive MHD solver. 6 All three components of vector quantities are modeled, but may only vary in the rand z directions. The simulation geometry is shown in Fig. 7. The simulation was initialized with an initialgas density of 1 . 879 10 3 kg/m 3 in the block at z = 0. 75 m, the region that contains the location thatcorresponds to the gas injection plane in the experiment. This density was assumed to be uniform over theblock and corresponds to the total mass injected at the maximum gas line pressure used in the experimentalinvestigation described in (see Sec. IV).

Contour plots of mass density at several times are shown in Figs. 8(a)8(d) for the simulation. Fig. 8(a),shows the plasma being pushed along the electrodes in the acceleration region towards the assembly regionby the Lorentz forces. Because the magnetic eld in the accelerator decreases with increasing radius, muchof the plasma is pushed outward, against the outer electrode. A pocket of dense plasma begins to formagainst the outer electrode, extending from z = 1. 25 m to z = 0. 75 cm in Fig. 8(b). The Z-pinch beginsto form on axis as plasma moves from the acceleration region into the assembly region. Fig. 8(c) shows theroughly 100 cm-long Z-pinch in the assembly region, during what would be the quiescent period. A pocketof plasma remains in the acceleration region, fueling the Z-pinch as it is accelerated into the assembly region.Eventually the dense pocket of plasma in the acceleration region is exhausted and the mass density theredrops, as shown in Fig. 8(d). When this exhaustion occurs, the density at various locations along the Z-pinch

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(a)

(b)

Figure 5. (a) Normalized m = 1 mode and total plasma current for a 6 kV ZaP plasma pulse. (b) Chord-integrated electron number density measured at two axial locations. The interferometer chord located atz = 25 cm measures the density near the exit from the acceleration region. The chord located at z = 65cm measures the density just downstream of the gas injection plane. The difference in arrival times of theplasma at the two axial locations indicates acceleration of plasma along the electrodes in the acceleration regiontowards the assembly region. The end of the quiescent period is correlated with the exhaustion of plasma inthe accelerator.

begins to uctuate. Although the processes observed in the simulation are qualitatively similar to those thatoccur in the experiment, the times in the simulation do not exactly match the times in the experiment.

IV. Experimental Investigation of Effects of Initial Gas Fill Proles

An experimental investigation of the relationship between the length of the quiescent period and theamount of gas injected initially was conducted on the ZaP Flow Z-Pinch Experiment. The amount of gasinjected was controlled by changing the gas line pressure. As shown in Fig. 9, the total number of particles

injected increases with the gas line pressure. These values were obtained experimentally by using each of ve gas puff circuits individually to puff gas into the experiment after closing a gate valve to shut off theexperiment from the vacuum pumps. The four outer gas puff circuits control two valves each that puff gasradially inward through the outer electrode into the acceleration region. The inner gas puff circuit controlsone valve that puffs gas radially outward through the inner electrode into the acceleration region. The idealgas law and the volume of the experiment were then used to calculate the total number of particles injected.Ten measurements were made for each gas puff circuit, and the ve averages were added together to yield

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Figure 6. Drawing of the ZaP Flow Z-Pinch Experiment showing the axial locations of the interferometerchords used to make the measurements shown in Fig. 5(b). The interferometer chord located at z = 25 cmmeasures the density near the exit from the acceleration region. The chord located at z = 65 cm measuresthe density just downstream of the gas injection plane.

z

r

-1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.750

0.025

0.05

0.075

0.1

Figure 7. Geometry used for the MACH2 simulation, with the radial coordinate axis scaled to show detailsof the simulation grid. A high-density gas is initialized in the block at z = 0. 75 m, and the nosecone and endwall hole are included. The simulation geometry can be compared to the experimental geometry shown inFig. 2.

the values plotted versus line pressure in the gure. The standard deviations for the ve valves were addedtogether to obtain the error bar values shown.

Fig. 10 shows the average quiescent period lengths, based on the normalized m = 1 magnetic mode,for ten plasma pulses taken at each gas line pressure. The error bars show the standard deviation of thequiescent period lengths for each set of ten pulses. The length of the quiescent period increases with gas linepressure, or total number of particles injected. The length of time during which a dense Z-pinch is observedin the experiment using the two-chord He-Ne interferometer is also plotted in the gure, and shows the sametrend. The behavior of both the quiescent period length and the dense Z-pinch period length with increasinggas line pressure is similar to the behavior of the mass injected plot of Fig. 9, where a steep slope from gasline pressures ranging from 2250 T to 3250 T gives way to a more gentle slope at higher pressures.

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z

r

-1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.750

0.025

0.05

0.075

0.1

(a)

z

r

-1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.750

0.025

0.05

0.075

0.1

(b)

z

r

-1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.750

0.025

0.05

0.075

0.1

(c)

z

r

-1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.750

0.025

0.05

0.075

0.1

(d)

Figure 8. Contour plots of mass density for the simulation with initial mass density 1. 879 10 3 kg/m 3 . (a) Att=25 s, plasma is pushed along the electrodes in the acceleration region towards the assembly region by theLorentz forces. (b) At t=39 s, a pocket of dense plasma has developed in the back of the accelerator, and theZ-pinch begins to form on the axis as plasma moves from the acceleration region into the assembly region. (c)At t=45 s, a roughly 100 cm-long Z-pinch is present in the assembly region and is fueled by plasma from theaccelerator. (d) At t=57 s, the plasma in the accelerator is exhausted and the density at various locationsalong the Z-pinch begins to uctuate.

V. Discussion and Conclusions

The experimental study conrmed that injecting more gas into the accelerator initially leads to a longerquiescent period, and the computer simulation gives insight into the plasma dynamics involved. Theseresults support the hypothesis suggested by the observed coincidence between the exhaustion of gas in theaccelerator and the end of the quiescent period of the Z-pinch: that ow is maintained in the Z-pinch bythe ionization and acceleration of gas from the acceleration region into the assembly region. The resultssuggest that a stable Z-pinch could be maintained indenitely and run as a space thruster in steady-state,provided an MHD generator or some other device was used to extract energy from the exhaust to power the

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0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

2000 2500 3000 3500 4000 4500 5000 5500 6000

gas line pressure (T)

m a s s

i n j e c

t e d ( k g )

Figure 9. Mass injected into the experiment for the gas line pressures used in the experimental investigation.The mass injected increases with increasing gas line pressure.

Figure 10. Quiescent period length and dense Z-pinch period length for the gas line pressures used in theexperimental investigation. The quiescent period length is based on the normalized m = 1 magnetic mode at z =0. The dense Z-pinch period length is based on measurements made with the two-chord He-Ne interferometerat z = 0 cm. The quiescent period and dense Z-pinch period become longer with increasing gas line pressure.

accelerating electrodes.Other considerations, however, also play a role in the mode of operation of the thruster. The amount

of power produced by the Z-pinch may make steady-state operation undesirable. A deuterium-tritium-

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fueled Z-pinch operating at a temperature of 15 keV is estimated to have a peak fusion power density of 2 1016 W/m 3 , which would be difficult to handle in steady-state. The radiated energy and neutron energyabsorbed would also be large during steady-state operation. Pulsed operation of the thruster would reducethe energy-handling requirements, and therefore may be desirable.

Characterization of the effects of the radial and axial initial gas distribution would give further insight intothe operation of a Z-pinch thruster. Staggering the timing of the gas puff valves so that a signicant amountof gas is delivered during the quiescent period, instead of just before it, would be useful in determining if itis possible to replenish the gas in the accelerator as it is exhausted.

VI. Summary

A sheared-ow Z-pinch fusion thruster holds promise as a high-thrust, high specic-impulse fusionthruster. The ZaP Flow Z-Pinch Experiment has produced sheared-ow Z-pinches that exhibit charac-teristics of stability for over one thousand theoretical instability growth times. Interferometer measurementssuggest that the depletion of gas in the coaxial accelerator causes the end of the quiescent period observed inthe Z-pinch. Experimental measurements show that injecting more gas initially into the accelerator length-ens the quiescent period, and computer simulation results give insight into the processes that deplete the

plasm in the accelerator to fuel the Z-pinch. This suggests that the Z-pinch could be maintained as long asthe gas in the accelerator is replenished as quickly as it is exhausted. In light of these results, it may bepossible to operate a Z-pinch fusion thruster in steady-state, but other considerations, such as the amountof power radiated, may make pulsed operation more desirable.

Acknowledgments

The authors acknowledge the Department of Energy for its sponsorship of the ZaP Flow Z-Pinch Exper-iment.

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2005.3 B. B. Kadomtsev. Reviews of Plasma Physics , volume 2, chapter Hydromagnetic Stability of a Plasma, pages 153199.

Consultants Bureau, New York, 1966.4 M. Kruskal and M. Schwarzschild. Some instabilities of a completely ionized plasma. Proceedings of the Royal Society of

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1957.6 J. E. Sturtevant R. E. Peterkin Jr., A. J. Giancola. Mach2: A reference manualfth edition. Technical Report

MRC/ABQ-R-1490, Mission Research Corporation, July 1992.7 V. D. Shafranov. The stability of a cylindrical gaseous conductor in a magnetic eld. Soviet Journal of Atomic Energy ,

1(5):709, 1956. Translated from Atomnaya Energiya, 1(5):38.8 U. Shumlak and C. W. Hartman. Sheared ow stabilization of the m =1 kink mode in Z pinches. Physical Review Letters ,

75(18):32853288, 1995.9 U. Shumlak, B. A. Nelson, R. P. Golingo, S. L. Jackson, E. A. Crawford, and D. J. Den Hartog. Sheared ow stabilization

experiments in the ZaP ow Z pinch. Physics of Plasmas , 10(5):16831690, 2003.10 U. Shumlak, B. A. Nelson, R. P. Golingo, S. L. Jackson, P. C. Norgaard, T. L. Shreve, and K. T. Yirak. A ow-stabilizedZ-pinch fusion space thruster. AIAA 2003-4826. 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,Huntsville, Alabama , July 21-23, 2003.

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S. L. Jackson et al- Effects of Initial Gas Injection on the Behavior of a Sheared-Flow Z-Pinch