Controlled Thermonuclear Fusionin a Staged Z-Pinch

Principal Investigators:

Frank J. Wessel and Norman RostokerUniversity of California

Department of Physics and AstronomyIrvine, CA 92697-4575

Submitted by:

The Regents of the University of California

March 30, 2000

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DISCLAIMER

This report was prepared as an account of work sponsoredbyanagency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.

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DISCLAIMER

Portions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.

TABLE OF CONTENTS

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..ii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..iii

Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..iv

l. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

l.l Description of the Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l

1.21mpacts of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Summary of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4

2. THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...6

2.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8

2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11

2.preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3. Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...26

3.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3,2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...37

3.preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .."4O

4. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5. APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...43

A. Neutron diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...43

B, Zero-D slugmodel code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..""47

ii

C. Publications and presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

D. Personnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...61

. . .111

ABSTRACT

In a “Staged Z-Pinch” electric energy is converted to kinetic energy of a plasma liner and thenefficiently transferred to a coaxial-target plasma. Magnetic fields interior to the plasma linerstabilize the implosion and provide a means to amplify current in the target while heatingit to ICF conditions. Thermonuclear break-even is predicted in a compact-laboratory devicewith the following approximate parameters: 50 kJ stored bank energy, 2 MA current, 1.8-psdischarge risetime. The expected outputs are: Y = 4 x 1015 neutrons/pulse, m- % 1015cm-3-s, T = 2 ns, n = 7 x 1023cm-3, and T! = 10 keV.

iv

FORWARD

First and foremost it is important to recognize the many individuals who participatedand contributed to this work, aside fi-om the project principal investigators: Frank J. Wessel,Norman Rostoker, and Haiiz Ur Rahman. In particular recognition is due the graduate stu-dents Allan Van Drie (experimental) and Paul Ney (theoretical). Without their effort andcontinued commitment to this study there is little prospect that this study would have beensuccessful. There are many others as well (recognized here in alphabetical order) who par-ticipated as collaborative researchers: Vitaly 13ystritskii, Amnon Fisher, William Heidbrink,Gennady Sarkisov, Sasha Shishlov, Yuan Xu Song. A big thanks is also due to all of theundergraduates and visiting scientists: Chris Boswell, Christian Davidson Nathen DeBolt,Eric Melby, Forest Patton, Dina Peterson, Tom Tierney IV, Lorreta Wylene Weathers. Asincere apology for others who might have been overlooked in this context.

This study was one of three funded as a competitive procurement from the DOE Officeof Fusion Energy beginning in August 1993 in response to DOE’s request for proposals for“Innovations in Tokamak Improvements and New Confinement Systems.” According to theDOE announcement, “These programs will contribute to the technical breadth of the fusionenergy program and could lead to reactor concepts offering advantages in size and simplicityover tokamak reactors.” A total of $1.2 million in each of fiscal years 1993, 1994, and 1995will be made available to these three programs. According to DOE, “This initiative wastaken in part as a result of recommendations made to the Department of Energy by theFusion Energy Advisory Committee which recommended that a non-tokand fusion conceptprogram, at some level, should be supported as a matter of policy.”

The winning proposals were: (1) “Ion Rings for Magnetic Fusion,” Prof. Ravi Sudan,Cornell University which are aimed at demonstrating the production of a fully field-reversedlarge orbit ion ring, the magnetic compression of the ring, and studies of the lifetime of thering, (2) “Penning Trap Systems for Producing Fusion Plasma,” Dr. Dan Barnes, Los AlamosNational Laboratory, which studied the injection of low energy, low canonical momentumparticles into a spherical Penning trap. The goal of the program is to demonstrate theexpected degree of spherical convergence, combined with theoretical analysis to determinethe efficacy of this approach for fusion plasma, (3) ‘“Thermonuclear Fusion in a Staged Z-Pinch)” Dr. Frank Wessel, University of California at Irvine.

The Staged Z Pinch studies described here builds on the prior successes of multi-shellimplosions demonstrated at UCI, the Ecole Polytechnique in France, and the Kurchatov In-stitute in Russia that implosions onto a gas target or small fiber retain their axially-uniformcharacter until peak current transfer, thereby avoiding the most dangerous instabilities char-acteristic of earlier Z-pinches and demonstrating enhanced energy transfer. By driving large(megampere) currents through the fiber on fast (100 ns) time scales, high density and tem-perature plasmas result. The Irvine work seeks to study such methods to heat, compress andsustain the process by storing and delivering additional energy to the fiber from a surround-ing gas or plasma. The only project of these three that succeeded in successfully generatingneutrons from hydrogenic reactions is the latter, which was terminated prematurely, approx-imately four years after project initiation, for lack of technical progress.

v

1. INTRODUCTIONResearch on controlled fusion energy over the past few decades has led to the construc-

tion of big machines capable of supplying multi-mega joules of energy. To achieve fusionbreak-even and beyond, many of these concepts may require even larger energies than areprovided by existing machines. The complexity and cost of these machines may impedethe construction of iiture machines, leading to a halt in testing ideas related to controlledthermonuclear fusion. On the other hand the Z-pinch is the simplest and the cheapest of alltypes of fusion machines.

MegaJoule class Z-pinch machines are not attractive for fusion energy production becausethe entire load region needs to be replaced after each shot. However they may be useful fortesting various fusion concepts. The 50 KJ to 100 kJ machines can be operated at a highrepetition rate without breaking the vacuum.

The Staged Z-Pinch is a specific z-pinch configuration that couples energy plasma-dynamically, in stages, and that is projected to achieve break-even thermonuclear gain in asmaI1-laboratory device .1 It combines elements of magnetic and inertial fusion, hence maybe referred to as: magneto-inertial fusion (MIF). An attractive aspect of this concept is itsscalability. It can be fielded on small to large machines.

1.1. Description of the ConceptThe basic configuration for the Staged Z-Pinch is illustrated in Fig. 1. A z-pinch liner

implodes onto a co-axial D-T (target) plasma, that is magnetized by a combination of axisl-and azimuthal-magnetic fields. The liner could be initiated from a gas shell, metal foil,or wire array, and the target from a cryogenic fiber or gun- injected plasma, or both. Asthe liner accelerates toward the axis its kinetic energy increases, until stagnation when thetrapped magnetic-field pressure is compressed beyond equilibrium. The field compressiontimescales are substantially shorter than the electric-energy and liner-acceleration timescales,and current is amplified in the target in a few nanoseconds. The trapped magnetic fields riseto ultrahigh values, differentially, providing a dynamically-changing shear. The enormous-magnetic pressure confines fusion-reaction products, reducing heat loss. For a D-T target,predictions are for thermonuclear yields of 1015neutrons/shot in a laboratory facility, similarto the one at the University of California, Irvine. At these levels thermonuclear break-even is a realistic, near-term prospect.

A single, cryogenic-fiber z-pinch is also projected to achieve fusion conditions.2-4 In thisconfiguration the load impedance presented by the 100 – pm diameter fiber is initially largeand the current must follow a precise time- profile in order to stably attain the Pease-Braginskii current ;5 for deuterium these requirements are of the order of 1.6 MA in 120 ns.Cryogenic-fiber experiments have not yet achieved the densities and temperatures requiredfor efficient-thermonuclear burn. Alternately, in plasma-focus systems the yields are report-edly as high as 1012neutrons/shot, due primarily to beam- target reactions.6 The 10 MA, 50ns, 1 MJ Saturn Facility, at Sandia National Laboratories, has reported thermonuclear yieldsof 3 x 1012in a deuterium-gas-puff pinch imploded onto a deuterated polyethylene fiber;7 aconfiguration similar to the Staged Z-Pinch, but without an interior-magnetic field. RecentRussian experiments, performed in collaboration with LANL scientists, have reported yieldsas high as 3 x 1013in a magnetized-target fusion (MTF) experiment using explosiw+drivengenerators.8 However, the origin of this yield is not yet certain.

1

MAGNETO-INERTIAL FUSION

DYNAMICS:STAGED Z-PINCH

o LINER ACCELERATES TO THE AXISo MAGNETIC FLUX IS COMPRESSEDo EDDY CURRENTS HEAT PLASMA& TARGETo STAGNATION TIME<< IMPLOSION TIME

Bo

BENEFITS:OINERTIAL ENERGY-TRANSFER TIMESCALESOMAGNETIC SHEAR ELIMINATES INSTABILITIESOBREAKEVEN FUSION WITH <50 kJ BANK ENERGYOPOSSIBLE TO BURN ADVANCED FUELS

Figure 1: Schematic illustration of the Staged Z- Pinch

Thus, staging presents a new insight into the problem of pulsed-energy deposition ina high-density plasma. Indeed, the significance of this innovation was recognized when webegan our study of the Staged Z-Pinch concept, funded by the DoE. At that time our primaryobjectives were to:

- identify energy transfer, coupling, and heating mechanisms in the target fiber,- understand the stability of the combined-pinch configuration, and- characterize the pinch at meaningful experimental parameters.

1.2. Impacts of the ResearchThe largest energy consumers in the world market are developed countries that comprise

13In the near future, as developing countriesonly a small fraction of the world’s population.demand their equal share of the world-energy resources, it will become clear that alternate-energy technologies are critical in maintaining world order. Any concept that advances theprinciples needed to attain fusion will have a profound effect.

The Staged Z-Pinch is one concept that undertakes this challenge. It is based on sound-physical principles and realistic technologies. Although this concept has not advanced to alevel that is sufficient to design a commercial-reactor system, the potential exists for it toprovide, in the neat-term, a thermonuclear- burning plasma. Reactor scenarios are inevitable,once a high-gain yield is demonstrated. Moreover, this concept supports the nuclear test-bantreaty, since the plasma is predicted to attain ICF conditions.

The physics of the Staged Z-Pinch involves fundamental problems of long- standing con-cern, including plasma stability in a dynamically-changing and high-magnetic shear, mag-netic diffusion in a high-density plasma, plasma-dynamic energy tramsfer, transport of fusionproducts in a high-magnetic field, material equation-of-state at extreme-energy density, andradiation transport in a burning plasma. A host of advanced technology issues are alsoimpacted, as z-pinches are currently under investigation for fusion application elsewhere.

2

Finally, the plasma-dynamic energy- transfer in the Staged Z-Pinch is significant as a meansto achieve high-specific-energy and -power density, with unusually short- timescales.

1.3. Summary of the ResearchDuring this performance of this project we have largely succeeded in satisfying the ob-

jectives stated above at the end of Section 1.1. Specifically, we have: assembled a MA, psclass pulsed-power driver, 9 developed and installed relevant diagnostics,l” extruded 100-pmdiameter, D2 cryogenic- fibers,ll performed preliminary investigations of z-pinch implosionsat 1.2 MA with 1 ps implosion times;12 and D2 gas targets. Our theoretical and computa-tional accomplishments include: developing an improved formulation of current amplificationin the Staged Z Pinch target,l benchmarked 1-D code calculations, confirmed by LASNEXand compared against UCI waveform data, and finally developed 2-D modeling capability,including the key physics content for the Staged Z-Pinch, based on the code Mach2.

1.4 REFERENCES

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

H.U. Rahman, F.J. Wessel, N. Rostoker, “StagedZPinch’’, Phys. Rev. Lett 74, p.714(1995); H. U. R*man, P. Ney, F. J. Wessel, A. Fisher and N. Rostoker, Proc. 2ndInt. Conf. on High Density Pinches, Laguna Beach, April 26-29 (1989), AIP Conf.Proc., p. 195.

J.D. Sethian, A.E. Robson, K.A. Gerber and A.W. DeSilva, Phys. Rev. Lett. 59,892(1987).

J.E. Hammel and D.W. Scudder, Proc. 14th European Conf. on Controlled Fusionand Plasma Physics, 1987, Pt.2, p.450.

M. G. Haines, “ The Dense Z-Pinch Program at Imperial College”, AIP ConferenceProceedings 299, Dense Z- Pinches, London, UK 1993, p. 472.

S. I. Braginskii in Plasma Physics and the Problem of Controlled Thermonuclear Fu-sion, Pergamon Press (1961), p. 135; R. S. Pease, Proc. Phys. Sot. London B 70, 11(1957).

V. V. Yan’kov, “Z-Pinches”, Sov J. Plasma Phys. 17, p. 305(1991).

R. Spielman, et al., “Deuterium Gas Puff and CD2 Fiber Array Z-Pinch Experimentson Saturn”, XX IEEE Int. Conf. on Plasma Science, Williamsburg, VA, Session 6A3,(1991).

I. R. Lindemuth, R. E. Reinovsky, et.al., “Target Plasma Formation for MagneticCompression/Magnetized Target Fusion”, Phys. Rev. Lett 75, p. 1953(1995).

F. J. Wessel, V. M. Bystritskii, B. Moosman, N. Rostoker, Y. Song, T. Tierney, A. VanDrie, P. Ney, and H. U. Rahman, “Staged Z-Pinch,” 10th IEEE Intl. Pulsed PowerConferencej Albuquerque, NM 1995, p. 112(1995).

B. Moosman, V. M. Bystritskii, C. Boswell, F. J. Wessel, “Moire deflectometry di-agnostic for transient plasma, using a multipulse N2 laser,” Rev. Sci. Inst. 67, p.1(1995).

H. U. Rahman, E. L. Ruden, K. D. Strohmaier, F. J. Wessel and G. Yur, “Closed CycleCryogenic Fiber Extrusion System: Rev. of Sci. Inst. 67, p. 3533(1996).

http: //mainpinch.ps .uci.edu

U. S. Energy Information Agency, “International Energy Outlook”, U. S. Departmentof Energy EIA 0484(1995).

H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostoker, ‘(Inertial Confinement Fusion

15. F. J. Wessel, P. L. Coleman, N. Loter, H. U. Rahman, J. Rauch, J. Thompson,“Energetic Plasma Radiation Source: Tandem Puff, Pinch-on-Wire,” Jour. Appl.Phys., March 1997.

16. D.J. Albaresj M.A. Krall and C.L. Oxley, Phys. Fluids, 4, 1031, (1961).

17. F. J. Wessel, F. S. Felber, N. C. Wild, and H. U. Rahman, “Generation of HighMagnetic Fields using a Gas-Puff Z Pinch,” Appl. Phys. Lett. 48, 1119 (1986); F. S.Felber, M. M. Malley, F. J. Wessel, M. K. Matzen, M. A. Palmer, R. B. Spielman, M.A. Liberman, and A. L. Velikovich, “Compression of Ultrahigh Magnetic Fields in aGas-Puff Z-Pinch,” Phys. Fluids 31,2053 (1988).

18. N.S. Edison, B. Etlicher, A.S. Chuvatin, S. Attelan, and R. Aliaga, Phys. Rev. E, 48,3893, (1993).

19. F.J. Wessel, B. Etlicher, and P. Choi, “Z-Pinch Implosion of an Aluminum Plasma Jetonto a Coaxial Wire: Enhanced Stability and Energy Transfer,” Phy. Rev. Lett. 69,No.21(1992).

20. S. M. Goldberg, A. L. Velikovich, “Snowplow Mechanism and Stability in lMulticascadeLiner Systems”, AIP Conf. Proc. 299, Dense Z-Pinches, p. 42(1994).

21. J. H. Degnan, et. al., “Compact Toroid Formation, Compression, Acceleration”, Phys.Fluids B5, p. 2938(1993); J. H. Degnan, “Electromagnetic Implosion of SphericalLiners”, Phys. Rev. Lett. 74, p. 98(1993).

22. B. Moosman, “Preionization of Target Fiber Plasmas”, Ph.D. thesis, University ofCalifornia Irvine, May 1997.

5

2. THEORYZ-pinches are inherently unstable mainly due to Rayleigh-Taylor (RT) instability which

appears during the run-in phase of the pinch. The reason for the growth of this instabilityis the development of a steep density gradient across an accelerating interface between theplasma and the magnetic field. There are several ways to control or at least mitigate someof the most dangerous modes associated with RT-type instabilities.2’6 ’7’8’g’10’11’12J3Some ofthese methods have been successfully implemented on several facilities. Even if by somemechanism the RT-instability is controlled, the plasma column becomes unstable in its finalphase of implosion during stagnation, because of the rapid growth of MHD instabilities.These instabilities are usually unavoidable in conventional Z-pinches and have been observedin almost every Z-pinch experiment. The most dangerous modes of MHD instabilities are thesausage (m= O)mode and the kink (m= 1) modes that can virtually destroy the uniformityof the cylindrical plasma column. The upper limit on the growth time of these instabilitiesis the Alfven time scale 7A s a/~,& where a is the radius of the plasma column and VAis theAlfven velocity. Unless the stagnation time of the pinch is faster than the A.lfven time scale,these instabilities will certainly appear and disrupt the pinch. Tkapping an axial magneticfield inside the plasma column will develop an outward magnetic pressure which will hinderthe growth of the sausage instability. On the other hand, an azimuthal magnetic field outsidethe pinch with a trapped tial magnetic field inside the pinch can lead to a sheared magneticfield profile that can easily stop the growth of the RT- instability provided it is maintainedduring the implosion. As a disadvantage, the trapping of a magnetic field inside the plasmacolumn leads to a softer pinch. However, the axial magnetic field alone does not stabilizethe kink or higher m modes, but these modes usually have a much higher growth time ascompared to the stagnation time of a staged Z-pinch. The chances of developing these modesin a fast pinch are very low.

The staged Z-pinch in general 5’15corresponds to a wide range of configurations, e.g.Z-Z pinch, Z-O pinch,14 composite pinch,lG nested wire array,2 puff on puff etc. All theseconfigurations usually involve similar types of physical mechanisms for coupling energy fromone load to another. Experiments have shown that these pinches are relatively stable andprovide much better coupling of energy to the final load. In this paper we focus on one ofthe simplest of the staged Z-pinch configurations which is basically the combination of a Z-Zpinch and a Z-d pinch. This scheme stabilizes most of the dangerous instabilities associatedwith the conventional Z-pinch. As a result higher compression leading to a much higherenergy density Z-pinch can be achieved. In this scheme the load plasma is made from twocoaxial cylindrical plasma columns. The outer plasma column is a cylindrical shell made ofKr plasma which is highly radiative, and thus remains cold during the implosion. Since theresistivity of the plasma goes as T–312, the magnetic field can easily diffuse through such aresistive plasma shell. The inner plasma column on the other hand is made of a deuteriumor a deuterium-tritium (DT) mixture which does not radiate heavily as it heats up. An axialmagnetic field is applied externally through out the entire region of the load plasma. Duringthe implosion, the combination of axial and azimuthal magnetic field components create asheared magnetic field profile that maintains the stability of the outer shell as the implosionprogresses. On the other hand the target plasma is less radiative and therefore continuouslyheats up during the implosion. The magnetic field cannot easily diffuse through this plasma.As a result it leads to an interesting configuration, in which most of the magnetic flux is

6

trapped in between theinner s.nd outer plasmas. Astheimplosion proceeds theintensityofthe trapped magnetic field rises due to the compression of magnetic flux. This will sustainthe required amount of shear in the magnetic field profile which is necessary for the stabilityof the pinching plasma shell. On the other hsnd the inner pinch will either remain flux freeor will retain a highly reduced level of magnetic flux. In the final phase of pinch the energydensity of the target plasma achieves a remarkably large value due to the stable implosionand remains almost perfectly uniform up until the peak implosion. After peak implosionwhen the plasma column bounces back due to an increased level of the internal pressure, theMHD instabilities start growing rapidly.

In this paper we present a numerical study based on a 2-dimensional MHD-modeling ofthis combination staged pinch and demonstrate the stable implosion that results in achievinga high energy density target plasma. Intense generation of soft X-rays and/or neutrons maybe achieved by properly choosing the load parameters and applying the appropriate strengthof 13Z.The main purpose of this study is to investigate the possibility of achieving break-evenin the controlled thermonuclear fusion energy using a low energy (= 50 kJ) electrical driver.The incentive for choosing a low energy driver is its high repetition rate. Multi-mega jouleclass machines are normally operated in a single shot mode and after each shot the entireload region has to be replaced. In this paper, section II describes the code and the simulationmodel. Section III describes the results of the simulation for a staged Z-pinch using the UCImachine parameters showing the optimum initial conditions and the effect of axial magneticfield on the stability of the pinch. Section IV provides the conclusion of this paper.

2.1. Simulation ModelThe staged Z-pinch is a complex configuration and it is hard to simulate all features

of this type of pinch. To begin with it consists of a circuit capable of producing a pulsedcurrent of extremely high magnitude which requires a sophisticated circuit equation to modelit accurately. The circuit equation can only provide a current profile with respect to time.The current has to flow through a coaxial load of two completely different types of plasmas.The outer shell of the load is made of a highly radiative plasma like Kr carrying almostthe entire mass of the load. The inner coaxial column is made of a hydrogenic plasma withan insignificant mass as compared to the Kr shell. Both these plasmas can be modeledby MHD type equations but the true simulation of the outer plasma requires a radiationmodel that can correctly evaluate physical properties like resistivity, diffusivity etc. Thecurrent produced by the generator flows through the combination of load plasmas in acomplex spatial profile following the path of lowest impedance which shifts rapidly duringthe implosion and stagnation. Initially the lowest inductive path is the outer surface of theKr plasma shell but the lowest resistive path is the inner core of the hydrogenic plasma thatbecomes hot during the implosion. Thus the preferential path of current flow is through theouter surface, but towards peak implosion the current switches to the inner load because ofits highly conductive nature and almost similar value of inductance. Since the combinationof an axial magnetic field 13Zwith an azimuthal magnetic field Be is very important for thestability and energy coupling of the staged Z-pinch, the model must be capable of treatingall three components of the magnetic field. Keeping all these factors in mind, the Mach2code developed by the Phillips laboratory seems to be the most appropriate for modeling ofthe staged Z-pinch.

7

Mach2 is a single fluid, 2~D , time dependent MHD code. It calculates resistive andthermal diffusion using various models for transport coefficients. It treats electron, ion andradiation temperatures separately. The equation of state can be calculated using analyticalor tabular (SESAME) models. The code has the capability of calculating flux limited, singlegroup, implicit radiation difision. The treatment of generalized Ohms law includes explicitHall effect and thermal source terms for magnetic fields. This code can handle complexexperimental shapes with a cylindrical or planar symmetry. It can handle multiple materialsand has the capability of including material strength. The computation can be carried outeither in Lagrangian, Eulerian or mixed mode.

Fusion Neutron Production Rate and Energy Gain are calculated using,

PDT= 5.6Z10-13TZDnT(CFV)DTPDD = 3.3Z10-13TZDnD(CYV)DDwhere (OW)DT and (O-V)~~ are determined from a table look up.

The model solves the following set of MHD Equations:

Continuity Equation:

a# t

= –v . (pq

Momentum Equation:

wP~ = 1 (Iw – ;l?zg~~)]–pdvjvi + Vj[–(p + Q)@i + C#i+ ~Electron Specific Energy Equation:

tkP# = –pil” V&e– Pe@iViuj + ~/LoJ2+ V - (tseVTie)– acpxT~+ PDTIDD +

CYei(Te– Tti)Ion Specific Energy Equation:

tk”P& = –pill’”V&i+ [–(pi + Q)# + @!i]vivj + V o(KiVTi) – acp – w(T. – Ti)Magnetic Induction:

82-w= –vx(tix B)-vx(qvxB)-v x&(:x @Elastic Stress:

@z 2~djid- vkvk~$Anadequate radiation model is also included in this code which calculates the radiation

output from different types of plasmas like KR and DT plasmas.

2.2. Simulation ResultsThe main purpose of carrying out the numerical simulation is to investigate the possibility

of achieving high yield thermonuclear fusion energy from a low energy Z-pinch machine. Wehave chosen the parameters of a low energy machine that was designed to test similar typesof ideas at the University of California, Irvine. The total inductance of the transmission lineof this machine is 25 nH, total capacitance of 50 ~f charged to 37.5 kV mtimum voltage todate. The current profile produced by the simulation matches well with the experimentallyobserved profile from a typical shot. Our first goal is to optimize different controllable

8

parameters in such a manner that the maximum energy of the generator can be transferedto the load at the peak implosion time. Since most of the mass is carried by the outershell of the Kr plasma, its mass is optimized such that the maximum possible electricalenergy transfers to the load in the form of kinetic energy. A 4 kG axial magnetic field isalso included because this is a minimum level of axial flux required for the control of RTinstability. Once these parameters are fixed, the parameters of the DT core plasma areoptimized in order to maximize the neutron yield. For this purpose we used the Mach2 codein 1-D mode without applying any perturbation. In all these calculations, the injected gasdistribution was simulated by a uniform density, right circular cylinder of DT plasma, 1 cmhigh and 1.9 cm in radius, surrounded by a Kr shell of thickness 0.1 cm. Figure 1 illustratesone of the initial configurations based on UCI Kr-DT gas puff parameters. The electrodeswhich confine the top and bottom of the load are considered to be perfectly conducting walls.Figure 2 shows the plot of optimized fusion energy output as function of initial density andtemperature of the DT plasma. In this figure the vertical z-axis represent the total fusionenergy gain (from a particles and neutrons), whereas the x and y-axes represents the initialtemperature and mass of the DT plasma, both these quantities are plotted on logarithmicscale. There is a sharp peak in the density corresponding to the DT mass density of 1.0x10–7g/cm3 which gives the maximum fusion energy. On the temperature axis the peak is not assharp as on the density axis. However, some initial heating of the target plasma is necessaryfor significant energy yield. The peak fusion energy output is around 83J which correspondsto a neutron yield of 7.0 x 1013,this is obtained with an initial temperature of 80eV for thetarget plasma. The target plasma can be preheated using a plasma gun or by applying anelectrical pre-pulse prior to the main implosion pulse.

To examine the issue of magnetic shear stabilization of R-T instability in the stagedZ-pinch, a number of 2-D MHD calculations are performed using this code. The optimumparameter of Kr plasma and DT plasma obtained from 1-D calculations are used. In thesecalculations, a configuration similar to Figure 1 is used together with an initial perturbationof density. Initially a random cell-to-cell density throughout the cylinder was introduced intothe calculation. The cell resolution along the pinch axis is 0.01 cm, allowing wavelengths assmall as 0.5 mm. To follow the evolution of the R-T instability, the calculations were runin an Eulerian mode and were carried out both with and without the axial magnetic field.Without any axial magnetic field the pinched plasma becomes highly unstable due to therapid growth of RT instability during the early stages of implosion. Finally the simulationgets terminated at about 0.8 ps. By applying a 2 kG axial magnetic field the growth of RTinstability is significantly reduced and the simulation can run up to 0.9435ps. The simulationresults of the early phase of implosion for the case of no axial magnetic field is shown in Figure3, which describes the density ISO-contours for three different time steps up until 0.8 ps. Itis clear from Figure 3 that in the case of no axial magnetic field the pinch becomes highlyunstable in the very early stages of the implosion. The instability predominantly appearsin the inner region of the DT plasma, whereas the growth of instability in the Kr shell isslower. Ultimately the entire shell becomes highly unstable and the calculation terminatesalmost 200 ns before the peak implosion. Observing the current and magnetic field profileswe can explain this behavior. The axial current easily diffuses through the outer plasmashell and transfers to the inner boundary of the DT plasma. The rapid diffusion throughthe Kr plasma is due to the higher resistivity caused by radiative cooling. Because of the

9

much lower resistivity of the inner DT plasma resulting from its poor radiative efficiency,diffusion of magnetic field and current through the inner plasma region is rather difficult.Since the DT plasma column is much lighter in mass than the outer Kr plasma shell, itimplodes at a much faster rate. This increased level of acceleration causes the instability togrow in the inner region faster than in the outer shell region. Figure 2 also shows that theinclusion of an axial magnetic field improves the stability significantly. Particularly the innerplasma column remains stable up until the peak implosion. However, the outer boundaryof the outer shell becomes unstable but with a significantly reduced growth rate. The casewith 2KG of axial magnetic field ran up to 0.9435ps and the results of the later stage ofimplosion are presented in Figures 4, 5 and 6. The density ISO-contours at three differenttimes of implosion are shown in Figure 4 and temperature ISO-contours are shown in Figure5. The plots on the left hand sides are shown for a typictil r-z plane, where as the oneson the right hand side are profiles of density and temperature at mid plane versus r. Ineach calculation the total mass of Kr is 3.5x10–4 g/cm3 and DT-mass is 1.0x10–7 g/cm3which is insignificant as compared to the Kr mass. The peak current delivered to the loadwas typically 1 MA, with implosion times (or quarter period rise time of the current) of 1ps which compares with the experimental profile. During the implosion, Kr plasma remainssignificantly cooler than the DT plasma due to the enhanced radiation loss of thermal energy.As a consequence, the density of the Kr plasma becomes much higher as the compressionprogresses. Interestingly no mixing is observed between the two plasmas during the entirephase of implosion, although it was allowed in the simulation model. The reason for this isobvious from Figure 6, which shows the current and magnetic field profiles at the mid planeof the Z-axis. There is a strong compression of magnetic field in between the two plasmaswhich isolates both plasmas from each other.

Figures 7 to 12 represents the implosion with the same parameters as of figures 4 to6 but the axial magnetic field is increased to 4 KG instead of 2 KG. The left hand sideof figures 7 and 10 represent two sets of density ISO-contours at six different times, twobefore the implosion and four after the implosion. The peak implosion time is at 0.95psdescribing a minimum radius of the pinched column. Up until the peak implosion timeno significant distortion is observed. A small level of surface perturbation is apparent atthe inner and outer surface of the Kr plasma shell that may be due to an extremely slowgrowth rate of RT-instability. Figure 10 presents three snap shots of density ISO-contoursafter the peak implosion time and up until l.Ops. This figure clearly shows the growthof an instability that is similar to the sausage mode (m=O) but with an asymetric growthalong the Z-axis. This is due to a strong axial flow of@as~a which eme~ges after the peakimplosion time. Axial plasma flow develops due to J x B force when J acquires a radialcomponent due to an uneven growth of the sausage instability. Both Kr and DT plasmasremain isolated even during the growth of this instability. The left hand sides of figures 8and 11 are corresponding temperature ISO-contours which shows the perfect stability anduniformity of DT-plasma column up until the peak implosion time. The right hand side ofall these figures are profiles of density and temperature at mid plane versus r. The highestvalue of the temperature of DT plasma is about 7 keV whereas for 2 kG it is less than 6keV.Without any axial magnetic field the temperature never achieved more than few 100 eV.This clearly demonstrates enhanced level of energy coupling to the DT load by controllingthe growth of the RT-instability. Figure 9 and 12 show the current density and magnetic

10

field profiles versus r at mid plane. From figure 9 it is apparent that at the outer boundaryof Kr plasma shell the values of both 13Zand Be is approximately 1.OMG, this produces astrong magnetic shear which stabilizes the RT-type instabilities. Compare it with figure 6where the value of 130was also 1.OMG but the value of Bz is between 100 to 300KG. Thisrepresents a weak shear in total magnetic field limiting the growth of RT- instability butnot completely eliminating it. During the implosion some tial current diffuses through theKr plasma shell and starts flowing on the surface of the DT plasma column. This difhsedcurrent gets amplified at the peak implosion to a value comparable to the outer current. InFigure 9 it is also apparent that oppositely directed azimuthal currents are flowing on theinner surface of the Kr plasma shell and the outer surface of the DT plasma column. Thisdevelops due to the large value of DB/6%. The azimuthal current seems to exceed the axialcurrent at the time of peak implosion. This may be due to the compression of the pinchedplasma beyond equilibrium as a result of inertia. This type of current amplification hornflux compression has been predicted in the past by Rahman et. al.[5, 15].

2.3. DiscussionThe research on controlled fusion energy over the past few decades has led to the construc-

tion of big machines capable of holding multi-mega joules of energy. To achieve break-evenand beyond, the popular concepts may require even larger energies than the existing ma-chines. The complexity and cost of these machines may impede the construction of futuremachines, leading to a halt in testing ideas related to controlled thermonuclear fusion. Onthe other hand the Z-pinch is the simplest and the cheapest of all types of fusion machines.The MJ class of Z-pinch machines are not attractive for any kind of energy production be-cause the entire load region needs to be replaced after each shot. However they maybe usefulfor testing concepts and other defense related applications. The 50 KJ to 100 kJ machinescan be operated on a high repetition rate without breaking the vacuum.

We have discussed the possibility of achieving break-even from a 50 kJ machine using theconcept of staging the implosion and thus controlling the instabilities. We considered thesimplest configuration that can be easily implemented on the several types of existing 50-100kJ class machines. We have shown that the most dangerous instabilities can be controlled.The control of these instabilities leads to an efficient energy coupling. Besides controlling theinstabilities, the rapid transfer of energy to the target plasma is also crucial in order to avoidradiative losses in the target plasma. Staging permits the use of long pulse machines sinceat each stage the duration of energy transfer becomes shorter by many orders of magnitude.

Optimization of system parameters is very important in achieving break-even. To datewe have only optimized the parameters related to the target plasma keeping the machineparameters fixed. In reality all parameters need to be optimized including machine parame-ters, type and shape of the liner etc., and in this way one may find a regime that could leadto the net production of fusion energy from a small size machine.

11

Figure Captions

Figure 1. Initial density profile of a 4 cm diameter krypton gas puff shell filled with DT.

Figure 2. Fusion energy output as a function of initial mass density and temperature of theDT plasma.

Figure 3. Density ISO-contours at three different times for Bz = O are shown on the lefthand side whereas the right hand side shows the corresponding density profiles at mid theplane versus r.

Figure 4. Density ISO-contours at three different times for l?z = 2KG are shown on the lefthand side whereas the right hand side shows the corresponding density profiles at mid theplane versus r.

Figure 5. Temperature ISO-contours at three different times for 13z = 21YG are shown onthe left hand side whereas the right hand side shows the corresponding temperature profilesat mid the plane versus r.

Figure 6. For BZ = 2KG the profiles of axial and azimuthal current density profiles at themid plane versus r are shown on the left hand side whereas the magnetic field profiles areon the right hand side.

Figure 7. Density ISO-contours at three different times for l?z = 41YGbefore the peak com-pression are shown on the left hand side whereas the right hand side shows the correspondingdensity profiles at mid the plane versus r.

Figure 8. Temperature ISO-contours at three different times for 13z = 4iYG before thepeak compression are shown on the left hand side whereas the right hand side shows thecorresponding temperature profiles at mid the plane versus r.

Figure 9. Before the peak compression and for BZ = 4KG the profiles of axial and azimuthalcurrent density profiles at the mid plane versus r are shown on the left hand side whereasthe magnetic field profiles are on the right hand side.

Figure 10. Density ISO-contours at three different times for 13z = 41KG after the peak com-pression are shown on the left hand side whereas the right hand side shows the correspondingdensity profiles at mid the plane versus r.

Figure 11. Temperature ISO-contours at three different times for 13z = 4KG after thepeak compression are shown on the left hand side whereas the right hand side shows thecorresponding temperature profiles at mid the plane versus r.

Figure 12. After the peak compression and for BZ = 4KG the profiles of axial and azimuthalcurrent density profiles at the mid plane versus r are shown on the left hand side whereasthe magnetic field profiles are on the right hand side.

12

1.0 1111111 1111111 11111, 1,1, 1,1, i,l, l,lll Ill,. . . {

. .

0.8– ,:.-.........:..,

~ 0.6–Eu. .,.-,

N- “’:”‘

o.4– ‘

,,.,.,,

0.2+”:’

....,,..:,.,:,..... . .. -.,.:.... ,, . .... . .

pT “

.:. , ,,

,.. ““’\., j....,’

..: ,.:“;l~1

........:.. ““l

,.. ‘:’ ~,.:..,,. I

.’”’~

““ ~t<

0.0”+0.0

r (cm)

Figure 1Initial density profile of a 4 cm diameterKrypton gas puff shell filled with DT

13

14

t = 0.5000 p,s

‘“”w:wiiiiik’’’”””

t = 0.7000 fJ.s

#

q-i+lq-’(I I

2:0

0;0 0:5 1;0 1:5 2:0

t= 0.8000 us1.0

0.8

0.6

0.4

0.2

0.00.0 0.5 1.0 1.5 2.0

r (cm)

—

—

—

—

—

—

1-

Plasma deyjty,

t = 0.5000~s;Iltl:l 11, llllllltltl, l,

1.0:

10+$8 :

0.8—

0.6 L

—

o.4~

—

0.2::4 D-T >

o.o~, ,,, ,,, llllll!illl 11,1,0.0 0.5 1.0 1.5 2.0

t = 0.7000J.Lsltttltl l 11111111111:18111111111 11111111:111

1.5: —

1(3+18~——

l.o~ ——

—

0.5 { —

jd D-T ~ Kr

O.o<111111111111lllllll:lllllll~lll,lf[ ~i-0.0 0.5 1.0 1.5 2.0

t = 0.8000J.LS

4Iltltll lllllllllllllll 11111111111111111111

5. -J —

10+18 ~-1

4. .-J —

3.1

—

‘“ -1 =–

-4\1,,111 ,,, ,,, ,,tltf:ll

0:0 0.5 1.0

r (cm)

Bz = OkG

t = 0.9000 us t = 0.9000us

0.8

‘j0.44’’’-?.

1“,,.’

0.00:0 0:2 0:4 0:6 0:8 1:0

t = 0.9205 US

1N 0.4 ,:/,,

o.o$+T”-l-0:0 0:2 0:4 0:6 0:8 1:0

/’-T

Y t = 0.9435 us

1.0

0.8

0.6

0.4

0.2

0.0 \0:0 0:2 0:4 0:6 0;8 1:0

r (cm)

t I I I I 1 I I

l.2– 1

10+=’

l.o–

0.8 –

0.6 –

o.4– Kr

D-T0.2 – F

* ~

%0.0 1

\I 1 1 1 I 1

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9205wI I 1 1 1 I 1

2.0 ;

10+19

1.5–.

0:0

1.5

I (3+20

1.0

0.5

I

A

0.00.0

Plasma denssty, B== 2kG

0:2 0:4 0:8 0:8 1:0

t = 0.9435~I I t 1 I I

/D-T

I I I I I I i I0.2 0.4 0.6 0.6 1.0

r (cm)

t = 0.9000 us1.0

0.8

0.6

E

D-T

0.4

0.2

0.0 i-l0:0 0:2 0:4

!

0:6 0:8 1:0

Kr

t = 0.9205 us1.0r,!

0.8 ‘--

/.

n 0.6

gu

mL0:0 0:2

!

0:4 0:6 0:8 1:0

D-T Kr

1 ./ t = 0.9435 w1.0

0.8

0.6

0.4

0.2

0.0 \0!0 ‘ 0!2 0:4 Ok 0:8 1:0

r (cm)

t = 0.9000 ys

600 –

500 –

400 –

D-T300-~ m -

200 –

Krloo–

0 1 1 1 I I —I I

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9205 LL8

1000- I

I6ool=--l

1---Kr

0 i,, , tI 1 1 I I I I I

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9435 ~I 1 I 1 I 1 ! I 1 I

6000Y

5000N4000

3000

2000

r

D-T

1000N /Kr

Ilx

oF

I I I I I 1 I [ I0.0 0.2 0.4 0.6 0.8 1.0

r (cm)

Plasma temperature, B== 2 kG17

t = 0.9000 wt = 0.9000p3J 1 I I I 1 1 I I I

L

2.5–

1~+lo !

2.0–

- l.5–

‘a

I

v /

Jz

? 1.0:h II

1bl

Je: 1 1

Ill \ ii- R +w,’ u

1 \I f I I I 1 I 1

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9205ps1 I 0 I

1

1 I I I 1

6.T

10+10

- 4.:

%

~ Jzh 2.:

:I A1[

7 (Jo

II ---0. -;.-4 II~JeUd

1 I 1 I 1 I I I 10.0 0.2 0.4 0.6 0.8 1.0

t = 0.9435p

lo+:~

y. -“-hi t

t“l’1’l’l’i’l’l’l’l’r0.0 0.2 0.4 0.6 0.8 1.0

r (cm)

I I 1 I t I I I I

3.—

10+5

/

:klksGJ0.0 0.2 0.4 0.6 0.6 1.0

t = 0.9205 &

lo:r_TTT’l4.

~ 3.

m

2.

I

‘“3--- 1’-’

W-w

0. I J .— _ __1 i I 1 1 1 1 I

0:0 0:2 0:4 0:6 0:8 1!0

t = 0.9435 us

I

‘/1 Bz1I1I

1 I I./

I

2.5– ‘

10+6

2.0 –

- l.5—Q

mi.o–

\\

o.5– \\\

/,x

0.0-----

I i I 1 I 1 I i0.0 0.2 0.4 0.6 0.6 1.0

Current and Magnetic Field Components: Bz = 2kG.18

r (cm)

t = 0.9000 &s t = 0.9000~

0.8

< >;..,‘. :...

. . ... .\.>.

.[

:,;’.<:i. ,,

. ..,

. . .

.

0.6

0.4

0.2

,... .,,..

.<

‘!‘ $,/‘.>

‘...>. . .~\\.

. . t

0.00:0 0:2 0:4 0:6 0:8 1:0

t = 0.9500 us

1.0

0.8

N 0.4

0.2

0.0

D-T

/ F t = 0.9548 US

I I 1 I I1

1 I t

l.2–10+19

l.o–

0.8 –

0.6 –

o.4–

o.2– D-T IQ4

\0.0 1 LI 1 I I I 1 1 I

0.0 0.2 0.4 0.6 0.8 1.0

1.0

0.8

0.6

0.4

0.2

0.00:0 0:2 0:4 0:6 0:8 1:0 0:0 0:2

r (cm)

Plasma density before peak compression,19

0:4 0:6 0:8 1:0

r (cm)

BZ=4kG

t = 0.9500J.ls1 I t I I I t I t

3.0 – f

10+20

2.5–

2.0 –

l.5–

l.o–

0.5 – , 0

0.0 tI 1 I 1 I I I I

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9548wt I t I I 1 I I !

3.0 – I1(3+20

2.5 –

2.0 –

l.5– I

l.o–

/D-T0.5– / “

n0.0 \, 1 I 1 I i I 1

1.0

0.8

0.6

I

0.4 ‘

0.2

0.0

1.0

0.8

~ 0.6

0

N0.4

0.2

“k”!

D-’%’—

,,...

t = 0.9000 j-ts

0:0 0:2 0:4 0:6 0:8 1:0

t = 0.9500 us

0.00:0 l\0:2 0;4 0:6 0:8 1:0

D-T Kr

/ / t = 0.9548 us1.0

0.8

0.6

0.4

0.2

0.00:0 0:2 0:4 0:6 0:8 1:0

r (cm)

t = 0.9000 usI I ! I I 1 I I

600 –

500 –

400 –

D-T300–“- *

200–

loo–Kr

0 1 I 1 I I 1 I I I0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9500 @1 I ! 1

7000 – *

6000—

5000 –

4000 – -T

2000 –

1000

: ,_~, ,,, ,,, :0

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9548 ps7000 –

I I 1 I t I I I I

6000 —

5000 –

4000 – D-T

3000–

2000–

1ooo–

0 I I 1 I 1 I 1 I 10.0 0.2 0.4 0.6 0.8 1.0

r (cm)

Plasma temperature before peak compression, BZ= 4 kG20

t = 0.9000ps1 I 1 t\ I t I I

2.5 –1(J+1O

/

Jz2.0 –

Je :l.5– ;’

‘s ,.;

II

~

11

h 0.5 – 1

- 10.0 , --

L --0.5 –

f I I 1 I I I I 10.0 0.2 0.4 0.6 0.8 1.0

t = 0.9500psJ 1 I 1 I I I ! I 1 L

8.–

10+11

6.–

h 2.–

o.–~I

-2. – I I I I I I 1 I 10.0 0.2 0.4 0.6 0.8 1.0

t = 0.9548w1* I I I 1 I 1 I 1

II6. – II

10+11

4.–

+

.*-}-w< z

-2.

r (cm)

t = 0.9000~

3.:

10+5

ml.=

o.

0.0 0.2 0.4 0.6 0.6 1.0

t = 0.9500 ust I 1 I t I I I 1

-4

I4. ~ ,

, 0+6 1

/

B=I

3.–. 1

g+ ;

m 2.: 1I

1.+1\ -.

\_--%

o.

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9548 usJ’1’’’’’’’’’’’’’’”” ,

h-Al I

3.: /

IB=

10+6 1I1

r (cm)

Current and Magnetic Field Components Before Peak Compression: Bz = 4kG.21

t = 0.9700 ~s1.0

0.8

0.6

0.4

0.2

0.0

t = 0.9871 us

1.0

0.8

0.6

gw~ 0.4

0.2

0.00:0 0:2 0:4 0:6 0:8 1:0

t = 1.0000 us1.0

0.8

0.6

0.4

0.2

0.00:0 0:2 0:4 0:6 0:8 1:0

r (cm)

t = 0.9700~I I I

11 I I 1

6.T

10+19

4.:

IQ

/

2“ : D-T

o. 1 .I I I 1 I I I I0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9871PI I I 1 I 1 I I

3.0– i

10+19

2.5 –

2.0 –

l.5–

‘“” : D-T /

0.5–

0.0 \,I 1 I I I I I I i0.0 0.2 0.4 0.6 0.8 1.0

t = 1.0000LLsI I I I

rI I 1 [ I

2.0:

10+19

1.5~

1.0:

D-TI p

0.5:

0.0 1 i 1 i 1 I i I 10.0 0.2 0.4 0.6 0.8 1.0

r (cm)

Plasma density after peak compression,22

B= =4kG

Kr

t = 1.0000 ~

r (cm)

Plasma temperature after peak23

t = 0.9700 flsI I 1 I I I I I t

2500

2000 —

1500 –

1ooo– D-T

500 —

,,, [,,, ,,, ,,, :0

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9871 w1 I t I t I 1

2000 ~

1500 ~

E1000:

500: D-T

,~, ,,, a :0 I0.0 0.2 0.4 0.6 0.8 1.0

t = i .0000 psI I 1 I 1 I I 1

1500:

1000:

500: D-T

; ,<,,,,,,,, :0 10.0 0.2 0.4 0.6 0.6 1.0

r (cm)

BZ =4kG

,,-,:.. ... i,. —.

t = 0.9700J.ls t= 0.9700 J.181 1 I I I I I I I 1

: I2.5– j

10+11 : I

2#lJ– 1I /

Jz-

‘q 1.5= ;

3: ;- l.o–b : 1

: I

o.o–I I i I 1 I i I 1

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9871psJII’I’F’ 111’ 111’ !IIL

t = 1.0000p8-k’’’’’’ ”’”~

-0.5

;1

0:0 0:2

Current and

t I 1 I I I I I I

l.o–I 0+s

- I0.8— \-

\\

fi0.6—g

\

m o.~~

o.2–

0.0 – -\_1 1 1 I I I 1 I i

0.0 0.2 0.4 0.6 0.8 1.0

t = 0.9871 us

t = 1.0000 w

r (cm)

Magnetic Field Components24

6.

10+5

m

\o.

I 1 1 I I t I I I 10.0 0.2 0.4 0.6 0.8 1.0

r (cm)

After Peak Compression: Bz = 4kG.

2.4. REFERENCES

1. C. Deeney, M. R. Douglas, R. B. Spielman, T. J. Nash, D. L. Peterson, P. L’Eplattenier,G. A, Chandler, J. F. Seamen, and K. W. Struve, Phys. Rev. Lett. 81,4883 (1998).

2. M. R. Douglas, C. Deeney, N. F. Roderick, Phys. Rev. Lett. 78,4577 (1997).

3. S. A. Soroken, A. V. Khachaturyan, S. A. Chaikovskii, Sov. J. Plasma Phys. 17, 841(1991)

4. S. Chandrasekax, Hydrodynamic and Hydromagnetic Instability (Dover, New York,1981)

5, H. U. Rahman, F. J. Wessel and N. Rostoker, Phys. Rev. Lett. 74,714 (1995).

6. A. L. Velikovich and S. M. Golberg, Phys. Fluids B 5, 1164(1993).

7. F. L. Cochran, J. Davis, and A. L. Velikovich, Phys. Plasmas 2, 1(1995).

8. R. B. Baksht et al., Fiz. Plazmy 21, 959(1995) [Plasma Phys. Rep. 21,907(1995).

9. T-F. Chang, A. Fisher, and A. Van Drie, J. Appl. Phys. 69, 3447(1991).

10. V. Smirnov, Plasma Phys. Controlled Fusion 33, 1697(1991).

11. S. Chandrasekar, Hydrodynamic and Hydromagnetic Instability (Dover, New York,1981).

12. S. A. Sorokin, A. V. Khachaturyan and S. A. Chaikovskii, Sov. J. Plasma Phys. 17,841(1991).

13. A. B. Bud’ko, M. A. Liberman, L. Velikovich, and F. S. Felber, Phys. Fluids B 2,1159(1990).

14. H. U. Rahman, P. Ney, F. J. Wessel, A. Fisher, and N. Rostoker, High Density Pinches,(2nd International Conference, Laguna Beach, USA, 1989), AIP Conf. Proc. p. 195.

15. H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostokerj J. Plasma Phys. 58, 367(1997).

16. A. Chuvatin, P. Choi, B. Etlicher, Phys. Rev. Lett. 76, 2282(1996)

3. EXPERIMENTS

3.1. ApparatusIn this section we will describe the characteristics of the ZOT generator and its various

diagnostics used in studying the pinch dynamics.

3.1.1. ZOT Generator

3.1.1.1. OverviewZOT is a low impedance direct drive generator, comprised of two 25 pF capacitor banks

in parallel, a flat plate transmission line, and a coaxial load feed; total of 25 pH inductance.The maximum charge voltage is 50 kV, but ZOT was always run at the reduced voltage37.5 kV, giving a total stored energy of 35 kJ and peak current of 1.5 MA in a 1.8 ps quarterrisetime. Fig. 3 shows a schematic overview of ZOT, while Fig. 2 shows a picture of ZOThorn the same perspective. Fig. 4 shows a cross-section of the load region.

Figure 2: Picture of the top of the generator.

26

. . -----

Go-%

i“ Em

27

I

“’”i...\:<:~

‘-KG”PLC”:G”..”Helmholtz Coils.

1’ /Y1

Mylar Insulator/r \ I 1 \ \

Vacuum TransmissionInterface Platelines

Jc

I / [

Cable Guns

‘Diagnostic Ports

To Vacuum SystemFigure 4: Cross-section of the load region. At point A are four I-dot probes eacheach pair being 180° apart, and one I-dot at point C. The closest current probe toIt is 8cm from the center of the Z-pinch.

90°the

apart. Two more pairs are at point B,Z-pinch is a Rogowskii coil at radius D.

3.1.1.2. Gas Valve and NozzleThe geometry for the types of loads we are interested in studying are formed from puffing

the gases from a fast gas valve through a nozzle into the A-K region. Initially, we had asingle low pressure (<100 psi plenum) gas valve and 4 cm dia. nozzle to do regular Z-pincheswith Neon and Krypton to test the generator. Later we developed a high pressure (up to1000 psi plenum) gas valve with a 3/4” dia. hole in the center to allow either a cryogenicDz fiber or another gas puff to be fed into the center of the outer liner. Fig. 5 shows thisdouble gas puff valve configuration. It allows us to independently adjust the two types of

Push Piston

Hammer

Popit

Coil

)Down Chamber

up

ml

Ch

n

ta

Figure 5: Schematic of double gas puff valve.

gas species used, the timing of opening the valve and the plenum pressure. The outer nozzleis still 4 cm dia. and the inner nozzle is 1.7 cm dia. or the inner nozzle can be removed toprovide a solid 1.7 cm dia. jet, as shown in frefcathodel. So with this system we can studythe implosion dynamics of a Krypton shell onto a D2 shell or jet. The outer nozzle has a 7°

29

inward tilt to compensate for the divergence of the gas as it exits the nozzle. The nozzle ismade from a Tungsten Copper alloy (3070 W, 7070 Cu) which served for over 300 shots at a1.5MA

Figuregas jet

No

current level with very minimal erosion.

6:in

gas breakdown pin was needed as the jitter of any single valve between

lake

the

solid

:iggerpulse t; the driving circuit and gas flowing out of the valve- was small. This jitter wasmeasured using a simple gas breakdown pin at 1.5 kV and 10 cm from the exit of the nozzle.The standard deviation of this jitter was measured to be 9psecs. This is not enough tochange mass in the load significantly. We could see this in our shot to shot reproducibilityof implosion times.

3.1.1.3. A-K ConfigurationFig. 7 shows the spiral anode that adds a Q component fi-om the t9current produced

from the spiral. The ratio 13Z/.Be=l/5. This was done to add some shesr stabilization to theouter liner as it implodes. However, ideally both the cathode and anode should be spiraledfor a uniform 13Zfield. This could be part of the reason why we didn’t see any sizableimprovement in the pinch stabilization with the spiral anode. Another mode just like thisone but with straight vanes was used for the D2 filled Kr shots. The tubing in the cathodeis made of the same Tungsten Copper alloy as the cathode nozzle.

3.1.1.4. Systems TimingTiming starts with the pulsed axial magnetic field, B.. This is generated from a set of

Helmholtz coils, which can produce uniform axial fields in the load region up to 2.6 kguass.Delay units set the timing when the gas valves/nozzles, pre-ionizer, Helmholtz coils (B.),

30

Figure 7: Picture of the spiral anode. The Rogowskii loop is embedded in the outer ring.L/.R=2l psecs > risetime of the main current, so Vm90~~kiicc -l~ain. Not sho~ are the twolayers of braided shielding that covers the resistor and RG/58 cable.

streak camera and laser fires, as shown in Fig. 8. Typically, the timing of the pre-ionizer

r-+~+-=.-lD4 Pre

Iom”zer

B ~:++

-f

D5 D3 D8-1

A Ou(er Gm Valve/Nozzle J!k.rerFires

t-

D7

“-t-

Inner Gas Vive lNozzle

~He’mhO’’zcOi’(B’)~Z(7I’Fires

Figure 8: Timing diagram of the various systems. D3 through D7 are fixed and Dl, D2, D8and D9 are adjusted for each shot. Point A is triggered from a probe when the current tothe helmholtz coils start. This delay is fixed at 7.5 ms so that Bz is maximum when ZOTfires. If no Bz is required then the system is triggered by a hand trigger at point B.

and helmholtz coils is fixed while the others are varied shot to shot depending on the loadmass wanted and the the point in the implosion you want the streak camera and laser tolook.

3.1.1.5. UV Pre-Ionizer

31

Sixteen cable plasma guns provides UV radiation for pro-ionizing the gas that forms theouter liner. They are 11 cm from the outer liner. Their position is shown in Fig. 4. Theguns are driven by a 6.25 pF capacitor charged to 30kV, 2.8kJ stored energy. Its risetimeis 1.5~secs. The timing of the firing of the guns is shown in Fig. 8. The guns are firedaround 0.7psecs before the generator, which is long enough to provide UV radiation, butshort enough to keep the unwanted high density plasma from reaching the AK-gap untilafter the pinch has imploded. At 11 cm it takes 2.4psecs for the high density plasma to theAK-gap, which leaves 2.40.7psecs=l.4psecs for the pinch without unwanted plasma in theAK-gap. In addition, a 56% transparency screen is placed in between the guns and AK-gapto attenuate the plasma.

3.1.2. Diagnostics

3.1.2.1. ElectricalGood electrical signals are necessary, although not sufficient, conditions to ensure proper

powerflow to the load and quality pinches. To keep track of the powerflow (Current) B-dotloops are placed at different locations on ZOT. B-dots are placed from the railgap switchesto as close as 8 cm to the load. The B-dots are calibrated using a 4 cm dia. short circuit loaddone at a reduced voltage and current level of around 3 kA and 140 kA. Voltage is monitoredby a capacitive voltage probe located between the the flat plate transmission line.

3.1.2.2. X-rayX-ray diagnostics were used primarily for pinches involving Neon. Enough energy per ion

was available to excite Neon K-shell, but not enough to be very useful for Krypton whichstays much colder. Most of the neutron producing loads used Krypton as the outer liner, soexcept for the XRDS the other X-ray diagnostics where not not fielded for those shots.

3.1.2.2.1. =DsTwo vacuum XRDS were used to measure the absolute power radiated. One to measure

the Ne IX and Ne X K-shell radiation (0.9 to 1.4 keV) and the other to measure the extremeultraviolet (XUV) radiation (150 to 280 eV) An aluminum foil photocathode was used witha 10 ~m beryllium filter which gives a relatively flat response for the Ne IX and Ne Xlines, while a 2 pm aluminized kimfol (C@ld~s) filter was used for the lines in the XUV.For the higher quality Krypton pinches, you can The absolute sensitivity of these filteredXRDS is plotted against photon energy in Fig. 9; which also includes the effect of the copperanode screen transparency (T=81 .270). The sensitivity for the beryllium filter varies from3.0 to 3.6 A/MW over that K-shell range. An intermediate value of 3.4 A/MW was chosen tobest represent the response over this range. Unfortunately, for the kimfol filter the sensitivityvarys much more, from 3.0 to 30 A/MW. In this case an intermediate value of 10.0 A/MWwas chosen. Sensitivities are based on Sandia’sl XRD Design software.

3.1.2.2.2. PIN’sA PIN diode with the same 10pm beryllium filter is used to also measure the Ne IX and

Ne X radiated power. The absolute sensitivity of this filtered PIN is plotted against photonenergy in Fig. 10.

3.1.2.2.3. Pinhole CameraThe pinhole camera measures the quality of the final compression of the pinch. You can

observe the final radius of compression, instabilities and hot spots in the pinch.

32

10

1

2pm ICimfol

P

-------.,2~m Kimfol+50nm Al

;II Ill,, lltllllll [1111111111111111111 11111111111111111111 111111

,’:

,,’

100200 300 400 500 600 700 800 90010001100120313001400150016001700

Energ~ eVFigure 9: Plot of absolute sensitivity for the K-shell XRD (solid line) and the XUV XRD(dashed line) vs. photon energy.

FigureEnerg~ eV

10: Plot of absolute sensitivity for the K-shell PIN vs. photon energy.

The camerais made from asingle2’’ dia. KFnipplethatis gate valved tothe generator,so it is easy to take on and off to process the film between shots. The SB-5 x-ray film isplaced at oneendof thenipple andthefiltered pinhole =semblyis at the other end. Thepinhole assembly is light tight, but allows vacuum through. A 100 pm dia. pinhole is usedfor Neon Z-pinches and a 500-1000 pm dia. pinhole for Krypton Z-pinches, even then it ishard to get much of an image for Krypton. 10 pm of Beryllium is used as the filter, which

33

gives amaximum response with the SB-5 film between l-2 KeV. With thecamera on thegenerator the pinhole is 404 mm from the Z-pinch and the film is 33o mm from the pinhole.This gives a magnification, m = –330/404 = –0.82.

3.1.2.3. NeutronTwo types of detectors were used to measure total neutron yield per shot, a Ag activation

detector and bubble detectors. The values obtained from both types agreed with each otherto within their uncertainties.

3.1.2.3.1 Ag Activation CounterTotal neutron yield is measured through the @-decay of Silver (Ag) activated by the burst

of neutrons produced during the shot. The more neutrons produced, the more &decay of theactivated Ag measured. The system consists of a photomultiplier tube (PMT) attached toone end of a rectangular piece of plastic scintillator. The remaining sides of the scintillatorare wrapped with 10 mill thick Silver foil. This foil is then covered in another layer of plasticscintillator. All this is taped to be light tight and the whole assembly is embedded in apolyethylene moderator. The PMT detects the light produced by the /3-particle travelingthrough the plastic scintillator. The output signal from the PMT is then sent through aamplifier to condition the signal to be properly read into a PC based multichannel scaler,where the @-decay is recorded, see Fig. 11.

~ r-”-”

hAmplifier

MCS

on PC

PMT /

PlasticScintillator —

PolyethyleneBeads ~

(Moderator)

Figure 11: Illustration of the Ag activation system.

Silver is composed of 52% 107Ag md 48% 109Ag The moderated neutrons activate Silverprimarily through the 10gAg(n,~) llOAg resonant reaction with a cross section of 93 barns, and

34

with a lesser extent through ‘07Ag(n, ~) 108Agwith a cross section of 35 barns. These are thecross sections at thermal energies. The polyethylene moderator slows the fast neutrons downto the thermal energies required to activate the silver. The decay halflife of llOAg is 24.4 seesand 2.41 reins for 108Ag. The detector has an efficiency of 7.04x103 neutrons/decay countfor llOAg decay and an efficiency of 35.3x103 neutrons/decay count for 108Ag decay. Thedetector can accurately measure yields down to about 107 at the distance of 75 cm from thesource (i.e. the D2 load).

3.1.2.3.2 Bubble DetectorBTI neutron bubble detectors2 are reusable, time integrating, passive dosimeters that

allow instant, visible detection of neutron yield. They are insensitive to gamma radiationand thermal neutrons. they have a flat neutron response from 200 KeV to 15 MeV. Adetector consists of an elastic polymer throughout which droplets of superheated liquid havebeen dispersed. When these droplets are struck by neutrons they form small gas bubbles thatremain ilxed in the polymer to provide a visual record of the neutron yield. Its uncertaintyis =/-20% and is due to its temperature sensitivity and to the accuracy that you can countupto 200 hundred bubbles. When more than 50 bubbles are produced two to three differentpeople count the bubbles a few times each and the average of that is taken. Any count morethan 10% off the average was considered a miss count and not included.

3.1.2.3.3 Time-of-FlightFour different PMT/scintillator detectors are placed at various distances from the gener-

ator and angles WRT the z-axis of the Z-pinch. Measuring the Time-of-Flight (TOF) of theneutrons produced during a shot gives the energy spectrum of those neutrons. Thermallyproduced neutrons will have no preferred direction so there will be no angular dependence onits energy spectrum. However, instability produced neutrons can have a defined direction.

In order to measure a TOF your have to assume a time at which the neutrons are pro-duced. For thermally produced neutrons this occurs near the time of peak z-pinch compres-sion. This time can be taken from the voltage and current signals, and from the gamma-rayproduced during fusion that is also picked up by the TOF PMTs.

While for instability produced neutrons this can occur upto a few hundred nanosecondsafter the peak compression when the Z-pinch becomes completely unstable and even beforethe peak compression for an unstably imploding Z-pinch. The first detector is placed as closeas possible to the generator.

3.1.2.4. Optical

3.1.2.4.1 StreakWe used a Hamamatsu Streak Camera with a M17645 Slow Streak Unit to look at the

radial dimension of the implosion swept over time. Since are implosion times are around1 psec we use it in its slowest mode of 500 ns per full sweep . A thin slice in the center ofthe pinch is chosen to represent the entire height of the pinch. From this information wecan qualitatively see the stability of the implosion and quantitatively measure pinch radius,velocity, acceleration and mass. Unfortunately, this camera is old and doesn’t always workreliably, so only about 25~0 of the shots have usable streak camera information.

A fiber optic runs horn the N2 laser to the streak camera to synchronize the Schlireenimage to the streak image. A streak timing monitor signal recorded on the scope synchronizes

35

the streak image to all the electrical signals. Fig. 12 shows a typical streak image.

+ 500 ns ~Figure 12: Negative streak image of regular Neon liner implosion. Peak voltage and Idotoccurred at point A, the dot at point B is from the iV2laser. The halo at C is mass stillimploding, most likely because of instabilities that left mass behind. An ideal pinch wouldhave all the mass imploding to a small radius at a single point in time.

3.2. ResultsThere are two shot series that produced significant number of neutrons, which are the

one that we will be looking at in detail here. The main distinguishing feature of these shotsis a high Z outer liner imploding onto a deuterium filled core. This is in contrast to othertypes of loads involving deuterium that produced much lower neutron yields. These whereregular pinch loads composed of a mix of deuterium with Neon. This mix from varied from10% to 90% of deuterium by number (i.e. pressure).

3.2.1. Kr onto D2 Implosions

3.2.1.1 Shots 659 to 793In these series of shots we wanted to study the neutron yield produced from imploding

a high Z outer liner onto a smaller solid core of Deuterium. We also include an external 13Zfor stabilization.

The high Z outer liner is a 4 cm dia. Krypton Shell while the D2 core is 1.7 cm dia.Thesolid D2 core is formed by removing the center nozzle so the gas can flow out as a jet insteadof shell. The mass of the Krypton liner is adjusted to give a implosion time of around 900to 1000 nsecs. This corresponds to a liner mass of around 800pg/cm. The external B. wasvaried from O to 400 gauss, while the mass of the Krypton and Deuterium was varied onlyslightly from their optimal pinching conditions.

The main diagnostic for this series of shots were the bubble detectors for neutron yieldand the TOF detectors for the energy distribution. Unfortunately, the streak camera wasnot working so the liner’s mass is estimated from similar series of shots done later with thestreak camera working. The Ag activation detector was not yet built at this time nor theN2 laser Schlieren. The XRD and PIN diodes are fielded as a standard practice. Since theKrypton remain cold the PIN doides are primarily useful in looking when the hard x-raysproduced after the maximum liner compression subside due to the unavoidable breakup ofthe pinch. This information is useful since these x-rays can produce signals on our TOFdetectors that could be confused with DD neutron signals.

Fig. 13 shows the results of these series of shots. The minimum sensitivity of the bubbledetectors when placed as close to the load as possible is 9.5x106, so graph is grayed outbelow this level. As can be seen, the neutron yield decreases with increasing 13Z. Thistype of behavior was found in previous work when others had tried Deuterium pinches withexternal 13Zfields3. This work was done on early Z-pinches back in the 1950’s. As a note,there are a few differences from these early Z-pinches and today’s Z-pinches. Back then theyformed Z-pinches by discharging current through a long capillary tube filled with the D2 gasat low pressure (usual around a few milliTorr). As the implosion progresses Deuterium isswept up in a slowplow fashion onto the axis. Whereas today, Z-pinches are formed throughfast gas-puff valves or wire arrays for the larger generators. These liners start out as shellsso mass does not snowplow during the implosion. Despite the difference, similar dependenceon BZ was found.

The Time-of-Flight (TOF) detectors gave a neutron energy spectrum at 2.5 MeV asexpected, so long as the neutron yields were above the mid 108 levels. Otherwise the PMTsscintillator would not see enough neutrons to register a signal. It was a trade off betweengetting enough neutrons to measure and placing the PMT’s back far enough from the loadto improve time/energy resolution. Fig. 14 is an example of the TOF data. The top graph

37

1010

109

z5\~ 108.-?

107

00 100 200 300 400

B= (Gauss)Figure 13: Distribution of neutron yields for various values of BZ. Each X is the yieldfrom any one shot and the circles are the average yields for that value of 13Z. The averageneutron yield for .BZ= Othrough 400 gauss is 6.8 x 108, 2.4 x 108 , 1.3 x 108 and 3.8 x 107respectively. There are a total of 90 shots in this distribution. At 400 gauss four shotsregistered no bubbles so they are marked in the unsensitive region.

shows the signals from four different TOF detectors. All the detectors see the hard x-raysat ~000 nsecs, time of peak pinch compression. Then for 100 to 200 nsecs some more hardx-rays from the pinch breakup are seen on some of the detectors.neutron signal is seen. The closest detector is 2.3 m from the pinchat the point label A. The other detectors are 4.6 m, 6.8 m and 9.1 mthe DD neutrons at points B, C and D respectively.

3.2.1.1 Shots 941 to 963

Later in time the DDand see the signal firstfrom the pinch and see

In these series of shots we wanted to do the same study as in shots 659 to 793 (Kr lineronto D2 core), but with additional diagnostics and with higher Q fields. The additionaldiagnostics includes: Ag activation detector for measuring neutron yield; streak camera formeasuring radius, velocity, acceleration and mass of the pinch; IV2laser Schlieren for lookingat pinch stability.

However, some changes to the gas nozzle, cathode, and anode had been made sinceseries of shots 659 to 793. These changes were made to protect some of the gas valve/nozzlecomponents from the main current erosion and ablation damage. Both the cathode gas valvenozzle and anode tube were replaced with special Copper-Ttmgsten alloys that are erosionand ablation resistant. The biggest change was the insertion of plug into the hole where theD2 gas exits. The plug has holes drilled in it to allow the D2 to flow out but shorts outthe plasma that was working its way up to the D2 gas valve causing some damage. Thedriver for the external 13Zwas changed from a DC current source to a long pulsed driver

38

6

43z+2

o900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Time (nsec)

6

4

2

04 3 2 1 0

Energy (MeV)Figure 14: Sample TOF data. The top graph is the raw data from the TOF PMTs and thebottom graph shows the same data converted from a time to energy axis. Points A, B, CandDcorresponds to the DD neutrons at 2.5 MeV.

(long compared to pinch time scales). This allowed us to increase the maximum 13Zfieldfrom 400 gauss, to 2600 guass.

At zero 13Zfield the average neutron yield from the bubble detectors was 7.0 x 107 and6.1 x 107 from the Ag activation detector. This is one order of magnitude lower than theresults from the series of shots 659 to 793. This lower yield was a result of the changes madeto the system, mainly due the plug insert. It restricted the Dz gas flow too much.

39

1.4 REFERENCES

1.

2.

3.

Rick Spielman, X-ray detector: An x-ray radiation detector design code. TechnicalReport SAND85-0699, Sandia National Laboratories, Apr 1990. Target ExperimentsDivision.

Bubble Technology Industries Inc. Bti home page. www.magma.ca/ bubble, 2000.Highway 17, P.O. Box 100, Chalk River, Ontario Canada, KOJ lJO.

S. Glasstone and R.H. Lovberg. Controlled Thermonuclear Reactions, section 7.141,page 274. D. Van Nostrand Co., 1960.

4. CONCLUSIONSZ-Pinches have been of interest as fusion systems since the earliest days of fusion re-

search. With the invention of the Staged Z-Pinch concept there was hope that such systemscould produce net fusion energy in a compact device. The present program involved studyof the physics of the Staged Z-Pinch. There were two main efforts in this program: devel-opment of the z-pinch facility with an adequate diagnostic capability and development oftheoretical/modeling capability that could guide the experimental effort.

Numerous papers and conference presentations were made during this program. Thesepapers are compiled in Appendix C. Project personnel included: researchers, undergraduate,and graduate students. The names of these individuals are listed in APPENDIX D. Dr.Bryan Moosman finished his Ph.D. and is presently a researcher at the NRL. Alan VanDrie,who worked since the inception of this project to develop the facility, will finish his PhD insummer 2000. Paul Neyj the theory student at the University of California, Riverside, whodeveloped our simulation codes will be unable to finish his PhD research due to a lack ofprogram funding.

Roughly 4 years after program initiation we diagnosed a simple pinch driven by a mega-Ampere pulser, as well as a more complex load geometry that provides improved stability(but not quite a staged pinch). In addition, extruded cryogenic-target fibers were produced,the dynamics of which were separately investigated an exploded-fiber target. These resultsdemonstrate that the design goals of the project and schedule were on track. Even underthe best of circumstances a small z-pinch machine would invariably take several years aftercompletion, to fully diagnose the pinch. The staged z pinch configuration developed in thisprogram was even more complex. The accomplishments made in this program are even moreimpressive when one considers that there were no subcontracts to commercial vendors forhardware fabrication or design and most of the components were acquired as surplus, orcustom fabricated by students and research staff.

Experimental studies showed that the neutron production was much higher for a Kryptonliner imploding onto a deuterium core than in either a straight deuterium pinch or a linermixed with Krypton and Deuterium. Also time-of-flight data showed that thermal 2.45 MeVDD neutrons where produced. This suggests that some staging occurs. Studying and un-derstanding the inner deuterium core is very difficult experimentally. At the mega-Amperecurrent levels it was not possible to probe into the outer Krypton liner with standard cur-rent probes or laser diagnostics. This leaves only neutron diagnostics to study and infer thedynamics of the deuterium core. Should fiture studies of the Staged Z-Pinch occur, a smallgenerator of the level of 400 KA current, might be used to study just the staging process.This current would not be enough to produce high neutron yields, however, it would permitthe use of standard laser diagnostics to probe into outer liner to the Deuterium core.

Our neutron yields were consistent with theory, based on our initial estimates for thedeuterium density and temperature, and for our final compression radius of about 2 mm.However, these were not the optimal neutron yield conditions as predicted by the computersimulation. Higher initial deuterium temperatures and a smaller final compression radius ofabout 1 mm are required. However, the theory was different as to the effect of the externallyapplied 13Zfield. Computer simulations required 2 to 4 Kgauss fields to achieve the requiredmagnetic shear stabilization of the Deuterium core. Experimentally the use of this levelof magnetic field reduced the neutron yield since the final compression radius was still too

41

large.To design the highest-gain Staged Z-Pinch configurations it is essential to provide insights

into the pinch dynamics, plasma stability, and energy-coupling efficiency. The theory andcalculations were used to investigate testable regimes of high gain as well as enhance thecredibility and scientific basis of the concept.

Our codes contain the most detailed form for the Staged Z-Pinch physics. These codeswere benchmarked against the Livermore LASNEX computer code, confirming that thephysics of the staged pinch was essentially correct. Moreover, we also developed code ca-pability to treat 2 space dimensions with plasma radiation and a physical review paper isunder preparation to summarize these results. First order code requirements include: ma-terial EOS, radiation transport, mixing of different plasma components, magnetic diffusionand shear for a variety of possible pinch configurations. We have successfully modified theLLNL TRAC2 code which is a fast running code that uses explicit algorithms to solve thedynamic equations. MACH2 is a more comprehensive than TRAC2 and implicitly solvesthe time dependent MHD equations for arbitrary two-dimensional geometries with user-specified mixed-boundary conditions. The code allows Lagrangian, Eulerian, or adaptiw+grid control. The equations are split to solve similar physical processes, such as: magneticdiffusion, Lagrangian hydrodynamics, and advection, while carrying all three field compo-nents. It includes a detailed-radiation model with radiation transport, a tabular EOS fromthe LANL SESAME tables, and several EOS models for analytic treatment of special ma-terials. MACH2 also has a 3-D modeling option that was only used in limited studies toevaluate higher order mode stability, i.e., m ~ 1.

Theoretically we have maintained that unity gain thermonuclear fusion is possible in aStaged Z-Pinch on a small-scale device. Over the period of this investigation our physicsanalysis and calculations have consistently confirmed this; we have found, and the plasmaphysics community has not provided any credible scientific arguments why this concept willnot work as predicted. The experimental demonstration has yet to be completed.

42

APPENDIX

Al. Ag Activation Counter

A.1.l. Calibration Calculation

A: Neutron Yield Calibrations

The counter is calibrated using a Cf-252 neutron source (strength = 1.2x107n/s, averageenergy = 2.348 MeV). This makes it an excellent source to simulate the 2.5 MeV DD neu-trons. This was the strength when the source was last calibrated (Jan, 1998) which is 1 yearand 10 months (=1,833 years) later from when the source was used in these calibrations. Sothe strength is reduced down to,

7.43x106n/s = 1.2x107n/s (2-’-833’12-646’) (1)

where 2.646 years is the effective halflife of the Cf-252 source. Fig. 15 shows the raw cal-ibration data.

10000

1000

100

Points A and B are where the Cf-252 source was brought into and out of

M1

llOAg Beta Decay

BetaDecay

Background4

‘$

10

A B

I I I I I I I I I I I I

o 1000 2000 3000 4000

Time (see)

Figure 15: Graph of the raw calibration decay data, using a neutron Cf-252 source.

the lab in a portable wax container. Event bough it was 8 m away from the detector, it isstill close enough for the ~-rays from the source to increase the background rate. The sourceis then placed into the A-K gap load region of the generator for approximately 18 minutes,which is much longer than either decay halflife. This allows both decay rates to equalibriatewith the rate of activation. At equilibrium the decay rate equals the neutron rate from theCf-252 times an efficiency factor. At this point the source is quickly removed (2-3 sees) andplaced back into its wax container. This is our t=O sees to watch the two activated speciesdecay, Since the Cf-252 neutron rate is known, and both decays are measured and fittedby a least squares fit, the activation efficiencies for both Ag species are determined. Fig. 16show the data with the time shifted to t=O sees and the background properly subtracted.

43

10000

1000

100

10

.-

1

I I~ Contributionfiom y‘s

~ Saturation ratefrom just neutrons

-1oo 0 100 200 300 400 500

Time (see)Figure 16: Background has been subtracted and t=O shifted to the start of the decay. Noticethe large drop at t=O just due to ~-rays from the source.

This fitting gives a detector efficiency of 7.04x103 neutrons/decay count for the llOAg decayand an efficiency of 35.3x103 neutrons/decay count for the 108Agdecay.

The PMT in the detector is an old 11 stage Dumount 6364 and is run at around 1350 V.The gain of the tube drifts slightly from day to day so this voltage is adjusted slightly(+/-2OV) to give a background rate of 109 c/s. This was the background rate during thecalibrations and is done to ensure the same conditions during calibration.

A.1.2. Algorithm for Measuring Neutron YieldVarious techniques are possible such as fitting a least square fit decay curve to the data,

but a simple averaging technique works quite well.The number of activated llOAg and 108Ag left after t. seconds when the decays start at

t. seconds is,I?(t.) = ~~~0~02–(t”–tSli~110+ ~108~o@~-~s)/~108 (2)

where 6110and ~lf)sare the detector effiencies in Decay Counts/Neutron, ~llo = 24.4 sees andT1(J8= 2.41 reins are the decay halflives, and NOis the neutron yield from the shot. However,the PC multichannel scaler measures the total number of decays in 1 second intervals. Thetotal number of decays over an arbitrary 1 second interval between tn and tn+l seconds isjust N(tn) – N(t~+l),

N(tn) – N(tn+l) = NO[e1102tsl~110(2-tn/’T~~o _ p?a+l/Tllo)

+ qo8zts/Tlo8 (z–tn/r108 _ z–%+1/Tlo8)]

= No ~ qzt’frd (2-~/Td _ Z-%+drcl)

d=l10,108

44

(3)

which is equal to the measured number of decays,

~(t.) – ~(t.+l) = A.+1 + ~A t.+l (4)

Where A.+l is the total number of measured counts in time bin $.+l, 1? is the backgroundrate and A tn+l equals 1 second. Sum both sides (~~) and solve for the Neutron Yield IVO,

No =A–BAt

(5)

d=llo,lo8 n

Where A = ~ An+l is the total number of counts over time A t = ~ A t.+l. Typically, A t istaken till the decay starts to get close to the background. Depending on the typical amountof activation this will be 1 to 1.5 halflives of the 108Agdecay, which is 2 to 4 minutes. Themore activation the longer this time can be taken.

The accuracy of this algorithm is shown by the changes in neutron yield when varyingA-t. This change is about lxIOG. This sets a lower limit of about 107 for accurately usingthe detector. This limit corresponds to having enough counts under the decay curve overtime interwd At to measure compared to the fluctuations of the background.

A.2. Bubble DetectorsBD-1OOR bubble detectors are calibrated to a Am-Be source (strength = 1.13x107n/s,

fluence weighted average energy = 4.15 MeV). As seen in Fig. 17 the response for the2,45 MeV DD neutrons will be the same as that at 4.15 MeV. Since the response startsto drop sharply below 0.3 MeV the detectors will not be sensitive to neutrons that it mayintercept that had to scatter more than 2-3 times to reach it. This is an important point toconsider since the concrete floor subtends a large solid angle from the D2 load. A conversionfactor of lmRem = 28.8x103n/cm2 for the Am-Be source is used (as calculated from doseequivalent defined in NCRP Report No. 38). The conversion factor can be used to convertsensitivities in bubbles/mrem to bubbles/n cm–2 if desired. Detectors are calibrated at adistance from the source and a time period that produces approximately 100-150 bubbles.The source and the detectors are held in an upright position in a styrofoam jig parallel toeach other. The BD-100Rs are calibrated 5 times using the neutron source: 1 calibrationat each of 20°C, 24°C, 28°C, 35°C and 37°C. The BD-1OOR passes the QA process if thestandard deviation of the 5 calibrations is less than 2070. Hence, the response quoted foreach detector is the average response over the temperature range 20° to 37oC.

Measuring the neutron yield is just a matter of counting the bubbles. The yield for anyshot into 47r is

Yield =(;;RS) (2:::3)A(%)

(6)

where A is the active area of the bubble detector and r is the distance between the D2 load andthe bubble detector. Usually one detector was placed on the vacuum chamber wall, R=24 cmand one at R=l.O m. This gives a conversion of 9.5x10%/bubble and 1.7x108n/bubble forthose two distances respectively.

45

1X10-2

1X10-3

1X104

1X10-5

1X10-6

F Sensitivi@= 22 bubbleslmRem= 2.2 bubblesl@I

0.01 0.1 1 10 100

Energ~ MeVFigure 17: The BD-1OORbubble detector response curve.

APPENDIX B: Zero-D slug model code

Presented here is the code used to calculate the liner’s mass using a zero dimensionalslug model and the code to convert the neutron Time of Flight (TOF) data from the timedomain to the energy domain. For the slug model the main current profile is need and forthe TOF conversion the signals from the TOF PMT’s are required. All of the data signals,including the above, are collected on the scopes then downloaded into an Excel workbook onthe computer for analysis. It is convenient to work with the data within the Excel workbook,so the analysis code is written in Visual Basic for Applications (VBA). VBA is the standardmacro programing that is available within Excel.

This algorithm models the liner as a slug of mass acted on by only the magnetic forcefrom the main current.

Option Explicit

Option Base O

Private Const VI As String = “Volt and Current”

Private Const RVC As String =” R and V Charts”

Sub CalcJ5ingle_She11.Masso

Dim Icol%

Dim response As Variant

Icol = 15

‘ [f there is no data in this column then exit subroutine

If Worksheets(Vl). Cells(3, lcol).Value = O Then Exit Sub

If lsNumeric(Worksheets(Vl) .Cells(3, lcol).Value) And (Worksheets(Vl) .Cells(3, lcol).Value <> ““ )

Then

‘its ok

Else

Exit Sub

End If

Dim a#, b#

Dim N%, m%, nStart%, nStop%, nCalc%

‘Liner mass densi~ is in microgm/cm

Dim Mass#

‘Times are in ns

Dim Tstart# ‘the time during the implosion at which to start calculation

Dim Tfinal# ‘the time during the implosion at which to end calculation

Dim deltaT# ‘time step

Dim Tcalc# ‘calculated final time to go to Rinner given the mass and current

Dim Tdiff# ‘=Tcalc-Tfinal ‘Current is in KA

Dim i(l To 2001) As Double

‘Velocity is in cm/microsec

47

Dim v(1 To 2001) As Double

Dim Vstart#

‘Radi are in cm

Dim R(I To 2001) As Double

Dim Rinner#, Router#

Dim tt!

‘ Ask for liner mass

response = lnputBox(” Intial guess for inner liner mass, micrograms/cm”, “Data Workbook”, 800)

If response = ““ Then Exit Sub

Mass = response

‘ Ask for start time

response = inputBox(” Enter Initial Time, ns”, “ Data Workbook”, O)

If response = ““ Then Exit Sub

Tstart = response

‘ Ask for final time

response = lnputBox(” Enter Final Time, ns”, “Data Workbook”, 1000)

If response = ““ Then Exit Sub

Tfinal = response

‘ Ask for Intitial Liner radius

response = lnputBox(” Enter Initial shell radius, mm”, “ Data Workbook”, 20)

If response = ““ Then Exit Sub

Router = response

‘ Ask for final Liner radius

response = lnputBox(” Enter Final shell radius, mm”, “ Data Workbook”, 2.3)

If response = ““ Then Exit Sub

Rinner = response

‘ Ask for inital Liner velocity

response = InputBox(’] Enter Initial shell velocity, cm/microsec”, “ Data Workbook”, 1.0)

If response = ““ Then Exit Sub

Vstart = response

nStart = 2

‘Read the current into an array to greatly increase calculating speed.

With Worksheets(Vl)

For N = 2 To 2001

if .Cells(N, lcol).Vaiue = “” Then Exit For

tt = .Cells(N, Icol - 1). Value

If tt >-10 Then

i(N) = .Cells(N, lcol).Value

48

If (tt >= Tstart) Then

[f (nStart = 2) Then nStart = N ‘That’s 20 KA

If (tt >= Tfinal) Then

nStop = N

Exit For

End If

End If

End If

Next

If nStart <>2 Then nStart = nStart -1

If nStop <>2 Then nStop = nStop -1

deItaT = .Cells(3, Icol - 1).Value - .Cells(2, Icol - 1).Value

End With

‘Update Statusbar

Dim oIdStatusBar As String

oIdStatusBar = Application. DispIayStatusBar

Application. DisplayStatusBar = True

Application. Cursor = xlWait

‘Clear previous values

Worksheets(RVC) .Cells(8, 12). Value = “”

Worksheets(RVC) .Celis(9, 12). Value = “”

Worksheets(RVC) .Cells(lO, 12).Value = “”

‘Calculation

Application .StatusBar = “Calculating Shell Mass ....”

v(nStart) = Vstart

R(nStart) = Router

Do

a = deltaT * 2 * (10 A (-4)) / Mass

b = deltaT / 100

For N = nStart To nStop

v(N + 1) = v(N) + a * (i(N) A 2) / R(N) ‘in cm/microsec

R(N + 1) = R(N) - v(N) * b ‘in mm

If R(N + 1) <= Rinner Then

nCalc = N

Exit For

End If

Next

Tcalc = Worksheets(Vl). Cells(nCalc, Icol - 1). Value

TdifF = Tcalc - Tfinal

If Abs(Tdiff) <= deltaT Then

Exit Do

49

Else

Mass = Mass * (1 - Tdiff / (Tfinal + Tcalc)) ‘adjust the mass

End If

Loop

‘Write the start time of the current and mass

Worksheets(RVC) .Cells(8, 12). Value = Worksheets(Vl). Cells(nStart, Icol - 1). Value

Worksheets(RVC) .Cells(9, 12).Value = Mass

Worksheets(RVC) .Cells(lO, 12). Value = (1 / 200) * Mass * (v(nStop)) ‘ 2

‘First clear any old data

Sheets(” R and V“ ). Columns(” A:D” ). ClearContents

‘Ask if you want to graph R and V

response = MsgBox(” Graph Radius and Velociiy?”, vbYesNo, “Shell Mass Calculation”)

If response = vbYes Then

‘Write the new data into the R and V worksheet

Application. StatusBar = “Writing radius and velocity data into workbook ....”

With Worksheets” R and V“ )

For N = 2 To 2 + nStop - nStart

m = N -2 + nStart

.Cells(N, 1). Value = Worksheets(Vl). Cells(m, Icol - 1).Value

.Cells(N, 2).Value = R(m)

.Cells(N, 3). Value = Worksheets(Vl). Cells(m, Icol - 1).Value

.Cells(N, 4).Value = v(m)

Next

End With

End If

‘Update the R and V graphs

Application. StatusBar = “Updating Graph ....”

Worksheets” R and V Charts” ). DrawingObjects(’J Chart 1“ ). Select

Calculate

‘Clean-up

Application. StatusBar = False

Application .DisplayStatusBar = oldStatusBar

Application. Cursor = xlNormal

End Sub

APPENDIX C

Publications and Presentations

Publications

1,

2.

3.

4.

5.

6.

7.

8.

9.

10.

H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostoker, “Inertial Confinement Fusion in aZ-Pinch,” Comments on Plasma Physics and Controlled Fusion, Vol. 15, p. 339(1994).

H. U. Rahman, F. J. Wessel, N. Rostoker, “Staged Z Pinch”, Phys. Rev. Lett 74, p.714(1995).

G. Yur, H. U. Rahman, J. Birn, F. J. Wessel, and S. Minamij “Laboratory Facility forMagnetospheric Simulation,” Jour. Geophys. Research 100, p.23,727(1995).

G. Yur, H. U. Rahman, F. J. Wessel, J. Birn, and S. Minami, “Magneto-tail Structuresin a Simulated Earth Magnetosphere,” Jour. Geophys. Research, submitted December1996.

B. Moosman, V. M. Bystritskii, C. Boswell, F. J. Wessel, “Moire deflectometry di-agnostic for transient plasma, using a multipulse N2 laser,” Rev. Sci. Inst. 67, p.1(1995).

H. U. Rahman, E. L. Ruden, K. D. Strohmaier, F. J. Wessel and G. Yur, ”Closed CycleCryogenic Fiber Extrusion System,” Rev. of Sci. Inst. 67, p. 3533(1996).

L. M. Steinhauer, et. al., “FRC 2001: A White Paper on FRC Development in theNext Five Years”, Fusion Technology 30, 116 (1996).

F. J. Wessel, P. L. Coleman, N. Loter, P. Ney, H. U. Rahman, J. Rauch, J. Thomp-son, “Energetic Plasma Radiation Source: Tandem Puff, Pinch-on-Wire,” Jour. Appl.Phys. 81, p. 3410(1997).

P. Ney, H. U. Rahman, F. J. Wessel, N. Rostoker, “Staged Pinch for Controlled Ther-monuclear Fusion;’ J. Plasma Physics Vol. 58, p. 367(1997).

N. Rostoker, M. W. Binderbauer, F. J. Wessel, H. Monkhorst, “Colliding Beam FusionReactor”, invited paper Am. Phys.Soc.Division of Plasma Physics General Meeting,New Orleans, LA, Nov. 1998. To be published 1999.

Conference Proceedings and Books

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostoker, “Inertial Confinement Fusion ina Z-Pinch,” Megagauss Physics and Technology Applications, Plenum Press, NY, W.Cohen, et al, editors, to appear 1994.

M. G. Haines, A. E. Danger, P. Choi, M. Coppinsj I. H. Mitchell, J. M. Bayley, T. D.Arber, J. P. Chittenden, P. Jaitly, J. Scheffel, B. Etlicher, and F. J. Wessel, “DenseZ-Pinch Research Experiment and Theory,” 14th Intl. Conf. on Plas. Phys. and Cont.Nut. Fusion Research, IAEA, Vienna, Vol. 2, pg. 635(1993).

N. Rostoker, F. J. Wessel, H. U. Rahman, B. Maglich, B. Spivey, and A. Fisher, “Mag-netic Fusion with High Energy Self-Colliding Ion Beams,” Beams 92, D. Mosher andG. Cooperstein, editors, National Tech. Info. Service, Springfield, VA, p. 357(1992).

H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostoker, “Radiative Collapse of a DensePlasma,” Beams 92, D. Mosher and G. Cooperstein, editors, NationaJ Tech. Info.Service, Springfield, VA, p. 1996(1992).

B, Etlicher, A. S. Chuvatin, L. Veron, F. J. Wessel, C. Rouille, and S. Attelan, “Dif-ferent Stabilization Processes in Z-Pinch Plasma Experimental Approach”, Beams 92,D. Mosher and G. Cooperstein, editors, National Tech. Info. Service, Springfield, VA,p. 2008(1992).

H. U. Rahman, P. Ney, F. J. Wessel, and N. Rostoker, “Inertial Confinement Fusion

in a Z-Pinch,” Dense Z-Pinches, American Institute of Physics, New York, 1993, M.G. Haines, A. E. Danger, and M. Coppins, Editors, p. 696(1994).

G. G. Peterson, F. J. Wesselj N. Rostoker, and A. Fisher, “Effect of Initial Conditionson Gas-Puff Z-Pinch Dynamics,” Dense Z-Pinches, American Institute of Physics, NewYork, 1993, M. G. Haines, A. E. Danger, and M. Coppins, Editors, p. 396(1994).

H. U. Rahman, P. Ney, F. J. Wessel, N. Rostoker, and V. M. Bystritskii, “Staged Z-Pinch for Inertial Confinement Fusion and Ion Acceleration,” T. Tajima, editor, ThePhysics of High Energy Particles in Toroidal Systems, American Institute of Physics,Conference Proceedings 311, p. 231(1994).

F. J. Wessel, H. U. Rahman, P. Ney, and N. Rostoker, “Z-Pinch,” MegagauSSPhysics

and Technology, Nova Science Publishers, New York, 1994, M. Cowan and R. B. Spiel-man, Editors, p. 905(1995).

V. M. Bystritskii, N. Rostoker, F. J. Wessel, H. U. Rahman, G. Mesyats, “Super-radiant X-Ray Source for Inertial Confinement Fusion,)’ American Institute of Physics,Current ‘Ikends in Fusion Research, Proceedings of the First International Symposiumon Evaluation of Current Trends in Fusion Research: Current Trends in InternationalFusion Research, Washington, DC, USA, 1zL18 Nov. 1994, E. Panarella, Editor, NewYork, NY, USA: Plenum, 1997. p. 347-64.

52

11. H. U. Rahman, F. J. Wessel, N. Rostoker, P. Ney, “Staged Z-Pinch for Inertial Con-finement Fusion,” American Institute of Physics, Current ‘Ikends in Fusion Research,Proceedings of the First International Symposium on Evaluation of Current Trendsin Fusion Research: Current Trends in International Fusion Research, Washington,DC,USA, 1418 Nov. 1994 E. Panarella, Editor, New York, NY, USA: Plenum, 1997.p. 333-45.

12. H. U. Rahman, P. Ney, F. J. Wessel, N. Rostoker, and V. M. Bystritskii, “Accelerationof Intense Ion Beams by a Z-Pinch”, Beams 94, W. Rix and R. White, editors, NationalTech. Info. Service, Springfield, VA, NTIS PB95-144317, p. 387(1995).

13. F. J. Wessel, V. M. Bystritskii, B. Moosman, N. Rostokerj Y. Song, T. Tierney, A.Van Drie, P. Ney, and H. U. Rahman, “Staged Z-Pinch~ Tenth IEEE InternationalPulsed Power Conference (Cat. N0.95CH35833). Albuquerque, NM, USA, 3-6 July1995). Edited by: Baker, W. L.; Cooperstein, G. New York, NY, USA: IEEE, 1995. p.112-17 Vol.1.

14. Moosman, B.; Bystritskii, V.M.; Wessel, F.J. Moire deflectometry diagnostic for tran-sient plasma using a multi-pulse N2 laser. Digest of Technical Papers. Tenth IEEEInternational Pulsed Power Conference (Cat. N0.95CH35833). Albuquerque, NM,USA, 3-6 July 1995). Edited by: Baker, W. L.; Cooperstein, G. New York, NY, USA:IEEE, 1995. p. 903-10 VO1.2.

15. V. M. Bystritskii, A. Gonzales, T. Olson, V. Puchkarev, L. Rosocha, F. J. Wessel, Y.Yankelevich, “Short-Pulsed-Electric Degradation of Aqueous Organics”, Proc. llthIntl. Conference on High Power ParticleBeams, Prague, p. 886-889, June 1996, Insti-tute of Plasma Physics, Czech Academy of Sciences, ISBN 80-902250-2-0.

16. L. J. Perkins, et al and F. J. Wesselj “High Density, High Magnetic Field Concepts forCompact Fusion Reactors,” 1.AEA-CN-64/GP-18, 16 th IAEA Fusion Energy Confer-ence, Montreal, Canada, 7-11 October 1996.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

V. M. Bystritskii, A. Gonzales, T. Olsen, L. Rosocha, V. Puchkarev, F. J. Wessel, T.Wood, Y. Yankelevich, D. Yee, “Application of Streamer Discharge for Polluted WaterCleanup,” Advanced Radiation Technologies Remediation, San Jose, February, 1996.

V. M. Bystritskii, T. K. Wood, Y. Yankelevich, S. Chuahan, D. Yee, F. Wessel, “PulsedPower for Advanced Waste Water Remediation,” llth IEEE Intl. Pulsed Power Con-ference, p. 79 (1997).

P. Ney and H. U. Rahman and N. Rostoker and F. J. Wessel, “UCI Staged Z Pinch”,The Fourth International Conference on High-Density Z-Pinches, 28-30 May 1997,Vancouver, Canada, N. R. Pereria, Editor, American Institute of Physics Proceedings,Volume 409, p. 259, 1997.

F. J. Wessel, B. Moosman, N. Rostoker, Y. Song, and A. Van Drie and P. Ney and H.U. Rahman, “UCI Staged Z Pinch Facility”, The Fourth International Conference onHigh-Density Z-Pinches, 28-30 May 1997, Vancouver, Canada, American Institute ofPhysics Conference Proceedings, N. R. Pereria, Editor, Volume 409, p. 39, 1997.

H.U.Rahman, P. Ney, F. J. Wessel and N. Rostoker, “Staged Z Pinches for ControlledThermonuclear Fusion Theoretical Studies”, 2nd Symposium on Current Trends inInternational Fusion Research: Review and Assessment, Washington, D. C. 10-14 May1997, E. Panarella, Editor, New Yorkj NY, USA: Plenum Press, p. 279, 1999.

F. J. Wessel, B. Moosman, P. Ney, H. U. Rahman, N. Rostoker, Y. Song, and A. VanDrie, “The UCI Staged Z Pinch”, 2nd Symposium on Current ‘llends in InternationalFusion Research: Review and Assessment, Washington, D. C. 10-14 May 1997, E.Panarella, Editor, New York, NY, USA: Plenum, p. 281, 1999.

V. M. Bystritskii, Y. Yankelevich, F. Wessel, T. Wood, D. C. Yee, A. Gonzales, T.Olson, V. Puchkarev, “Application of Streamer Discharge for Remediation of PollutedWater”, Environmental Applications of Ionizing Radiation, John Wiley and Sons, W.Cooper, R. Curry, K. O’Shea, Editors, Ju1’98, p. 613(1998).

V. M. Bystritskii, Y. Yankelevich, T. Wood, F. Wessel, and others, “Aerosol Plasmafor Aqueous Waste ‘lleatment”, IEEE Conference on Plasma Science, Sam Diego, CA19-22 May 1997, New York, NY IEEE p. 311(1997).

P. Ney, H. U. Rahman, F. J. Wessel, and N. Rostoker, “Modeling of the Staged Z-Pinch for Controlled Fusion”, Proceedings of the Third International Symposium onCurrent Trends in International Fusion Research, Washington, DC,USA, Feb. 1998 E.Panarella, Editor,in press, Physics Essays, 1999.

F. J. Wessel, M. Binderbauer, N. Rostoker, H. U. Rahman, J. O’Toole, “Beam Fu-sion Reactor Concept”, Proceedings of the Third International Symposium on Cur-rent Trends in International Fusion Research, Washington, DC,USA, Feb. 1998 E.Panarella, Editor)in press, Physics Essays, 1999.

54

,.;..,,,.,~~-}...{~,~(~+-+.-.T~; .)~-~.i?~--- ,-t .....>,~~:.q*,:.->:.,.,.,.,:::..,,/.:,,;..+:fj.::,-..-<y~;....~-;,; ,. ,....,..,,.,.. ---.>>.:::.-..;$;’,>*z.,..-.,,,,, .{/”’.< - -row-’-c :, ‘“~

27. F. J. Wessel and N. Rostoker, “BeamFusionR eactorConcept,” Fusion Power Asso-ciates and UCLA Workshop on Cost-Effective Steps to Fusion Power, January 25-27,1999, Marina del Rey Hotel, Marina del Rey, CA, S. O. Dean, Editor, in press January2000.

55

Abstracts

35th Annual, American Physical Society, Meeting on Plasma Physics, St. Louis, MO,November 1-5, 1993.

F. J. Wessel andN.Rostoker, University of California, Irvine and H. U. Rahman, “Staged Z-Pinch for inertial confinement fision,” paper [8S.3], Bulletin of the American PhysicalSociety 38, p. 2088(1993).

G. Peterson, F. Wessel, N. Rostoker, and A. Fisher, “Effect of Initial Conditions on Gas-Puff Z-Pinch X-ray Yieldj” paper [8S17], Bulletin of the American Physical Society 38,p. 2090(1993).

V. Bystritskii, F. J. Wessel, H. U. Rahman, N. Rostoker, and G. Mesyats, “Ion-beamexcited, inner-shell, X-ray transitions,” paper [8S.18], Bulletin of the American PhysicalSociety 38, p. 2090(1993).

36th Annual, American Physical Society, Meeting on Plasma Physics, Minneapolis, lMN,November 7-11, 1994.

B. Moosma.n, V. Bystritskii, F. J. Wessel, “Nanosecond, Four Frame TEA N2 Laser Diag-nostic: paper [2R.21], Bulletin of the American Physical Society 39, p. 1562(1994).

S. Drum, F. J. Wessel, and W. W. Heidbrink, “Laboratory Simulation of Field-AlignedCurrents in the Magnetosphere,” paper [3Q.16], Bulletin of the Americzm PhysicalSociety 39, p. 1589(1994).

F. J. Wessel, A. Van Drie, V. Bystritskii, wd H.U.Rahman, andG.Yur, “The UCI StagedZ-Pinch,” paper [3T.28], Bulletin of the American Physical Society 39, p. 1606(1994).

H. U. Rahman, F. J. Wessel, N. Rostoker, P. Ney, and F. Aitouamer, “Modeling of theUCI Staged Z-Pinch ,“ paper [3T.29], Bulletin of the American Physical Society 39, p.1606(1994).

37th Annual, American Physical Society, Meeting on Plasma Physics, Louisville, KY,November 6-10, 1995.

A. Van Drie, H.U. Rahman, N. Rostoker, F.J. Wessel, “UCI Staged Z-Pinch/’ paper [8R.26],Bulletin of the American Physical Society 40, p.1849(1995).

P. Ney, H. U. Rahman, F. J. Wessel, N. Rostoker, “Thermonuclear Ignition in a Staged Z-Pinch,” paper [8R.27], Bulletin of the Americzm Physical Society 40, p. 1850(1995).

B. Moosman, V. M. Bystritskii, and F. J. Wessel, “X-Ray Backlighter for the UCI StagedZ-Pinch,” paper [8R.28], Bulletin of the American PhysicaJ Society40, p. 1850(1995).

Y. S. Song, T. E. Tierney, F. J. Wessel, A. Fisher, “Electron Beam, Gas-Valve/NozzleImaging Diagnostic: paper [8R.29], Bulletin of the American Physical Society40, p.1850(1995).

56

H.U, Rahman, K. Strohmair, P. Ney, E. Ruden, F.J. Wessel, “AFiberE xtrusionSystemwith a Closed-Cycle Refrigeration,” paper [8R.30], Bulletin of the American PhysicalSociety40, p. 1850(1995).

B. Moosman, V. M. Bystritskii, and F.J. Wessel, “Multi-Pulse, Nitrogen Laser Diagnostic,”paper [8T.33], Bulletin of the American Physical Society40, p. 1858(1995).

1996 Joint Meeting of the APS and the AAPT, Indianapolis, IN, May 2-5, 1996.

N. Rostoker, M. Binderbauer, H. Monkhorst, and F. J. Wessel, paper [K3.01] “CollidingBeam Fusion,” Bulletin of the American Physical Society40j p. (1996).

38th Annual, American Physical Society, Meeting on Plasma Physics, Denver, CO, Novem-ber 11-15, 1996.

A.Van Drie, H.U.Rahman, G. Sarkisov, A. Shishlov, Y. Song, and F. J. Wessel, UCI “StagedZ-Pinch,” paper [4S.11], Bulletin of the Americaa Physical Society,38th Annual Meet-ing on Plasma Physics, Denver, CO, November 11-15, 1996.

A. Shishlov, H.U.Rahman, E. Ruden, G. Sarkisov, Y. Song, and F. J. Wessel, “Experimentswith a cryogenic fiber~’ paper [4S.24], Bulletin of the American Physical Society,38thAnnual Meeting on Plasma Physics, Denver, CO, November 11-15, 1996.

B. Moosmaq Y. Song, L. Weathers, F. J. Wessel, “X-ray imaging of fibers,” paper [4S.22],Bulletin of the American Physical Society,38th Annual Meeting on Plasma Physics,Denver, CO, November 11-15, 1996.

P.K. Shukla, H.U. Rahman, P. Ney (IGPP, UCR, Riverside, CA.), F. Wessel, N. Rostoker,“Raleigh-Taylor Modes in the presence of sheared magnetic fields and plasma flow;’ pa-per [2Q.23], Bulletin of the Americm Physical Society,38th Annual Meeting on PlasmaPhysics, Denver, CO, November 11-15, 1996.

V.M. Bystritskii, A. Gonzales, T. Olson, V. Puchkarev, L. Rosocha, F. Wessel, Y. Yankele-vich, “Pulsed Discharge in Aerosol for Waste Water Clean-up,” paper [9T.05], Bulletinof the American Physical Society,38th Annual Meeting on Plasma Physics, Denver,CO, November 11-15, 1996.

IEEE Intl. Conference on Plasma Science, San Diego, CA, USA, 19-22 May, 1995.

Coleman, P,L.; Loter, N.; Rauch, J.; Thompson, J.; and others. “Tandem puff-on-wire”experiments on ACE 4. IEEE Conference Record - Abstracts. 1995 IEEE InternationzdConference on Plasma Science (Cat. N0.95CH35796). (IEEE Conference Record -Abstracts. Madison, WI, USA, 5-8 June 1995). New York, NY, USA: IEEE, 1995. p.210.

Van Drie, A.; Bystritskii, V.; Moosman, B.; Rahmanj H.U.; and others. UCI staged Z-Pinch. IEEE Conference Record - Abstracts. 1995 IEEE Internatiomd Conference onPlasma Science (Cat. N0.95CH35796). Madison, WI, USA, 5-8 June 1995). New York,NY, USA: IEEE, 1995. p. 252.

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IEEE Intl. Conference on Plasma Science, San Diego, CA, USA, 19-22 May, 1997.

Bystritskii, V.M.; Yankelevich, Y.; Wood, T.; Wessel, F.; s.nd others, Aerosol plasma foraqueous waste treatment. IEEE Conference Record - Abstracts. 1997 IEEE Interna-tional Conference on Plasma Science (Cat. N0.97CH36085). (IEEE Conference Record- Abstracts, New York, NY, USA: IEEE, 1997, p. 311.

Wood, B.P.; Tuszewski, M.G.; Pesensen, D.; Wessel, F. Cathodic arc plasma density andprofile measurements. IEEE Conference Record - Abstracts. 1997 IEEE InternationalConference on Plasma Science (Cat. N0.97CH36085). (IEEE Conference Record -Abstracts. New York, NY, USA: IEEE, 1997. p. 214.

Sarkisov, G.S.; VanDrie, A.; Moosman, B.; Song, Y.; and others. Measurement of theradial evolution of a gas-puff Z-Pinch by inverse bremstrahlung absorption of H~Nelaser light. IEEE Conference Record - Abstracts. 1997 IEEE International Conferenceon Plasma Science (Cat. N0.97CH36085). (IEEE Conference Record - Abstracts. NewYork, NY, USA: IEEE, 1997. p. 185.

Department of Energy, Innovative Confinement Concepts Workshop, March 3-6, 1997Marina del Rey CA

F. J. Wessel, B. Moosman, P. Ney, H. U. Rahman, N. Rostoker, Y. Song, and A. Van Drie,The UCI Staged Z Pinch. Conference Record. 1997

Current Trends in International Fusion Research-Review and Assessment. Washington, D.C, March 10-14, 1997.

H,U.Rahman, P. Ney, F. J. Wessel and N. Rostoker, “Staged Z Pinches for ControlledThermonuclear Fusion Theoretical Studies”, invited oral paper.

F. J. Wessel, B. Moosman, P. Ney, H. U. Rahman, N. Rostoker, Y. Song, and A. Van Drie,“The UCI Staged Z Pinch”, invited oral paper.

The Fourth International Conference on High-Density Z-Pinches, 28-30 May 1997, Vancou-ver,Canada.

P. Ney and H. U. Rahman and N. Rostoker and F. J. Wessel, “UCI Staged Z Pinch”, posterpaper.

l?. J. Wessel, B. Moosman, N. Rostoker, Y. Song, and A. Van Drie and P. Ney and H. U.Rahman, “UCI Staged Z Pinch Facility”, invited oral paper.

IAEA Technical Committee Meeting on Innovative Approaches to Fusion Energy, October20-23, 1997 Pleasanton, California, USA

F. J, Wessel, B. Moosma.n, P. Ney, H. U. Rahman, N. Rostoker, Y. Song, and A. Van Drie,The UCI Staged Z Pinch. Conference Record 971079.1997

U.S. Department of Energy, Innovative Confinement Concepts Workshop, March 3-6, 1997,Marina Del Rey, California.

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F. J. Wessel, B. Moosmanj P. Ney, H. U. Rahman, N. Rostoker, Y. Song, and A. Van Drie,“The Uc.1 Staged Z Pinch,” Invited Oral Paper.

CALIFORNIA UTILITY RESEARCH COUNCIL, TECHNOLOGY EXCHANGE CON-FERENCE, La Jolla, San Diego, California, November 3-5, 1997

F. J. Wessel, N. Rostoker, M. Binderbauer, H. Monkhorst, “Advanced Fusion Energy SelfCollider Reactor”.

39th Annual, American Physical Society, Meeting on Plasma Physics, Pittsburgh, Pennsyl-vania, November 17-21, 1997.

H. U. Rahman, P. Ney, F. J. Wessel, N. Rostoker, Stability of the Staged Z Pinch.”

F. J. Wessel, N. Rostoker, Y. Song, A. Van Drie, H. U. Rahman, “Staged Z Pinch.”

P. Ney, H. U. Rahman, F. J. Wessel, N. Rostoker, “Modeling of Staged Z Pinch Configu-rations.”

Innovative Confinement Concepts Workshop, April 6-9, 1998, Princeton Plasma PhysicsLaboratory, Princeton, NJ.

F. J. Wessel, N. Rostoker, Y. Song, A. Van Drie, P. Ney, H. U. Rahman, “The UCI StagedZ Pinch,” Invited Oral Paper.

M. Binderbauer, N. Rostoker, F. J. Wessel, H. Monkhorst, “Magnetic Confinement of Col-liding Beams in a Field Reversed Configuration,” Poster Paper.

40th Annual, American Physical Society, Meeting on Plasma Physics, New Orleans, LA,November 16-20, 1998.

P. Ney, H. U. Rahman, F. J. Wessel, N. Rostoker, “2-D Modeling of a Staged Z Pinch;’paper B1F8.

B. M. Johnson, A. Hershcovitch, F. J. Wessel, A. Van Drie, F. Patton, N. Rostoker, “Devel-opment of LIZ-MEV, a Low Impedance Z-Discharge Metal Vapor Ion Source,” PaperC2S61.

A. Hershcovitch, B. M. Johnson, N. Rostoker, A. Van Drie, F. J. Wessel, “Electron Beamsand Z-Pinches as Plasma Strippers and Lenses for Low Energy Heavy Ions,” PaperK6E5.

A. Van Drie, F. J. Wessel, N. Rostoker, H. U. Rahman, ”Enhanced Staged Z-Pinch Stability,Paper R8S39.

P. Ney, H. U. Rahman, F. J. Wessel, N. Rostoker, “Modeling of Several Staged Z PinchConfigurations,” Paper U9P36.

Third International Symposium on Current Trends in International Fusion Research, Wash-ington, DC, 8-12 March 1999.

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P. Ney, H. U. Rahman, F. J. Wessel, and N. Rostoker, “Modeling of the Staged Z-Pinchfor Controlled Fusion”, invited oral paper.

F. J. We%el, M. Binderbauer, N. Rostoker, H. U. Rahman, J. O’Toole, “Beam FusionReactor Concept” , invited oral paper.

APPENDIX D: Personnel Involved in the Staged Z Pinch Program

Scientists and Postdocs: period ofinvolvement, title

Dr. Norman Rostoker, 1994-12/1998, Prof. Emeretus, University of California, Depart-ment of Physics and Astronomy, Irvine, CA, 92717

Dr. Vitaly M. Bystritskii, 1994-10/1997, Research Physicist, University of California,Department of Physics and Astronomy, Irvinej CA, 92717

Dr. Yuan-Xu Song, 1995-1/1998, Research Physicist, University of California, Depart-ment of Physics and Astronomy, Irvine, CA, 92717

Dr. Hafiz Ur Rahman, 199412/98, Research Physicist, University of California, Instituteof Geophysics and Planetary Physics, Riverside, CA, 92521

Mr. Alexander Shishlov, 1-12/1996, visiting scientist, High Current Electronics Institute,Tomsk, Russia.

Dr. Gennady Sarkisov, 10/1996-4/1997, Lebedev Institute, Moscow, Russia.

Dr. Frank J. Wessel, 1994/1999, Research Physicist, University of California, Depart-ment of Physics and Astronomy.

Graduate students: period of involvement

Dr. Gus Peterson (Ph.D. 1994), 1989 to 1994.

Mr. Alan Van Drie (Ph.D. in progress), 1993 to present, physics graduate student, UCI.

Dr. Brian Mooseman (Ph.D. 1997), 1993 to 1997.

Mr. Thomas E. Tierney, IV, 1996-present, UCI physics graduate student, at Los AlamosNational Laboratory.

Undergraduate students: period of involvement

Jack Manson, 1989-1994,

Greg Squires, 1993-1995.

Christian Davison, summer 1994 REU student.

Jessie Campbell Tabor, summer 1994 REU student.

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Tom Tierney, 1994 to1996, UCIgraduate physics student.

George Parker, 1994, undergraduate physics student, UCI.

Chris Lena, 1993-1994.

Christopher Boswell, summer 1995 REU student.

Anthony W. Thomas, summer 1995 REU student.

Eric Melby, 1995 National Undergraduate Fellow.

Joshua Clapper, summer 1996 REU student.

Loretta Weathers, summer 1996 Princeton Plasma Physics Fellow.

Ilina Pesenson, 1996-1997, undergraduate physics student, UCI.

Yong Xian Guan, 1995-1996, undergraduate electrical engineering student, UCI.

Choi Wing Peon, 1995-1997, undergraduate electrical engineering student, UCI.

Forest Patton, 1996-6/1999, undergraduate physics student.

Jeremiah Williams, 6-8/1997, REU student.