Experimental investigation of thermal plasma formation from thick

PHYSICS OF PLASMAS 17, 102507 共2010兲

Experimental investigation of thermal plasma formation from thick aluminum surfaces by pulsed multimegagauss magnetic field T. J. Awe,1,a兲 B. S. Bauer,2 S. Fuelling,2 I. R. Lindemuth,2 and R. E. Siemon2 1

Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA University of Nevada, Reno, Reno, Nevada 89557, USA

2

共Received 28 June 2010; accepted 26 August 2010; published online 20 October 2010兲 The thermal ionization of a thick metal surface by pulsed multimegagauss magnetic field has been examined experimentally. Thick 6061-alloy Al rods with initial radii 共R0兲 from 1.00 to 0.25 mm, larger than the magnetic field skin depth, are pulsed to 1.0 MA peak current in 100 ns. Surface fields 共Bs兲 rise at 30− 80 MG/ ␮s and reach 1.5 and 4 MG, respectively. For this range of parameters, plasma forms at a threshold level of Bs = 2.2 MG. Novel load hardware ensures that plasma formation is thermal, by Ohmic or compression heating. Surface-plasma formation is conclusively indicated through radiometry, extreme ultraviolet spectroscopy, and gated imaging. When R0 = 0.50 mm rods reach peak current, Bs = 3 MG, the surface temperature is 20 eV, and Al3+ and Al4+ spectra and surface instabilities are observed. In contrast, R0 = 1.00 mm rod surfaces 关Bs共t兲 ⬍ 2.2 MG兴 reach only 0.7 eV and remain extremely smooth, indicating that no plasma forms. © 2010 American Institute of Physics. 关doi:10.1063/1.3491335兴 I. INTRODUCTION

How plasma forms from surfaces pulsed to megagauss level magnetic field is an important question for both basic science and for applications. If and when plasma is generated from the surface of a thick metal carrying an ultrahigh skin current is uncertain. Understanding plasma formation and developing predictive capability for the resultant evolving plasma is an ongoing fundamental challenge for plasma physics. Even for systems that can be described by radiationmagnetohydrodynamics 共R-MHD兲, the complex interplay of magnetic diffusion, hydrodynamics, and radiative energy transfer is a challenge to model, especially since material properties vary rapidly in space and time. For example, as megagauss level magnetic field diffuses into thick aluminum, phase transitions can cause the electrical conductivity of the surface to change by over ten orders of magnitude,1 and the calculated peak temperatures may vary from 0.1 to 100 eV. Radiation-magnetohydrodynamics and intense current are vital to a wide variety of applications including singlewire and wire-array z-pinches, magnetically insulated transmission lines,2 recyclable transmission lines,3 dense plasma foci,4 ultrahigh magnetic field generators,5 and magnetized target fusion systems.6–8 While thin wire experimental studies have been conducted for many decades,9–12 only limited experimental data for surface-heated thick metal have been available.13 Plasma formation from a metal in the “liner,” “surface-heating,” or “thick-rod” regime 共where current flow and Ohmic heating are confined to a skin layer of thickness ␦B兲 is far less certain than for thin wires even when the linear current density and surface magnetic field are an order of magnitude or more higher. Plasma formation from thick rods is uncertain, in part, because cool, underlying, high conductivity metal persists, reducing the electric field strength, cura兲

Electronic mail: [email protected].

1070-664X/2010/17共10兲/102507/11/$30.00

rent density, and Ohmic heating at the rod surface. A detailed understanding of the ohmically driven phase changes at the surface of thick metal pulsed to high magnetic field is critical to the design of practical devices. The interplay of intense magnetic field and ohmically heated conductor is a significant physical process in metallicliner-driven magnetized target fusion or “MTF” 共one approach to magnetoinertial fusion兲, where magnetized plasma is compressed by an imploding, flux conserving metallic shell or liner. During the liner implosion, the magnetic field contained in the fusion fuel 共which reduces losses associated with electron thermal conduction and can aid in alpha particle confinement14兲 is compressed to the megagauss level. During compression, eddy currents are induced in the inner wall of the liner, causing intense Ohmic heating. The liner surface will melt, then vaporize, and finally, if the rate of energy deposition exceeds that of the losses, transform to plasma.15 Plasma may initially form in a thin surface layer. Processes that depend on the electrical conductivity of both the plasma sheath and the interior conductor determine the current in the plasma, the spatial distribution of deposited electrical energy, and the expansion of the metallic plasma across magnetic field lines. The details of the diffusion process and the severity of hydrodynamic instability formation will determine the amount of liner material able to mix with and contaminate the fusion fuel.16,17 These complex phenomena determine the maximum time for which the fusion fuel will be held at high pressure before severe high-Z contamination occurs and may ultimately determine the success of an MTF system. Plasma initiation from thick metallic surfaces pulsed to ultrahigh magnetic field has recently been examined by Garanin et al.18 With detailed computations and theory that included the effects of dynamic resistivity, radiation transfer, and thermal conduction, they studied the phase state of a thick metal surface subject to intense Ohmic heating during

17, 102507-1

© 2010 American Institute of Physics

102507-2

Awe et al.

the diffusion of multimegagauss magnetic field. Conflicting basic descriptions of if, when, and how plasma forms were summarized and evaluated. One common view is that when a metal surface is ohmically heated to the vaporization temperature, a resistive metal vapor forms, which expands freely through the magnetic field, carrying little current, remaining cool, and therefore forming no plasma.19 Others argue that even for lower 共submegagauss兲 fields, high conductivity plasma forms on a thick metal surface. In this case, the majority of the current is shunted to the plasma sheath, which is ohmically heated to high temperature. In contrast to both arguments, the work of Garanin et al. suggests that the expanding vapor will ionize only for sufficiently high magnetic field. Plasma is made by Ohmic heating as the magnetic field diffuses into the material and possibly initiated by photoionization from nearby interior radiating metal of eV temperature. Plasma initially forms in a thin surface layer, is of low density, and 共since the interior metal is also a good conductor兲 carries only a small fraction of the current. The electrical energy deposition remains radially distributed and the temperature of the surface plasma remains modest. Garanin et al. concluded that plasma will form from a thick copper surface for fields in excess of about 1.5–3 MG, depending on the rise rate of the applied field. The lack of available data and the remaining theoretical uncertainties make experiments that investigate the diffusion of multimegagauss magnetic field into thick metal fundamentally important. To examine the interaction of intensely ohmically heated thick metal with ultrahigh magnetic field in a configuration relevant to MTF, metallic-liner-driven magnetic flux compression experiments have been designed and modeled.20,21 In such experiments, the dynamics and phase state of the inner liner surface would be studied. However, relevant physics issues can be examined in lower energy experiments, where the multimegagauss field is pulsed on the more diagnostically accessible surface of a thick conducting rod in the z-pinch configuration.22 In both configurations, conductors are driven with fast rising 共100 ns兲 current that flows nonuniformly in a skin layer. 共The outer wall of the liner is driven with a slow, of the order of 10 ␮s, current pulse, but the eddy currents induced in the inner liner wall rise rapidly during the later stages of compression.兲 For each configuration, ultrahigh current densities drive phase changes in the material and place megagauss magnetic field at the material-vacuum interface. Low-density surface plasma is decelerated by magnetic forces, resulting in flute mode instability growth. The pulsed-rod configuration offers several advantages. First, the rod surface is much easier to diagnose since in the case of liner-driven magnetic flux compression, the surface of interest is enveloped by the liner material and moves at supersonic velocity. Next, the multimegagauss field can be pulsed on a rod using a short-pulse, lower-current driver, whereas flux compression requires a long-pulse, ultrahigh-current driver to accelerate the massive liner to high kinetic energy. The total energy delivered to the load is therefore reduced, and the experiment is relatively nondestructive. This enables increased shot repetition rate and reduced cost per shot. Finally, the fabrication of thick rods is

Phys. Plasmas 17, 102507 共2010兲

FIG. 1. Cross sections of commonly used load hardware: 共a兲 21.0-mm-long SSR with sliding small-diameter contacts and gravitationally bound 共GRAV兲 power flow connection; 共b兲 7.0-mm-long SSR with sliding small-diameter contacts and compressed knife-edge 共KE兲 power flow connection; 共c兲 hourglass load machined from a 3-in.-diameter Al cylinder, mounted on KE hardware; and 共d兲 barbell load machined from a 6-mm-diameter Al cylinder. Barbells can be inserted into GRAV or KE hardware. Small circles denote knife-edge penetration locations.

far less challenging than that of precision liners, further reducing shot costs. The thick-rod-megagauss experiments reported here have obtained results of sufficient quality to validate R-MHD codes and to design transmission lines, MTF devices, and other high-current-density systems. Rod surfaces are pulsed to high field by the University of Nevada Reno-Nevada Terawatt Facility Zebra generator,23,24 which delivers a consistent 1.0 MA, 100 ns rise-time current pulse. Initial rod radii 共R0兲 range from 0.25 to 1.00 mm, large enough for the current to flow in a skin layer 共␦B ⬍ R0兲, yet small enough for megagauss magnetic field to be generated on the expanding rod surface. Novel load and anode-cathode configurations limit non-MHD precursor plasma formation 共Fig. 1兲. “Hourglass” and “barbell” loads 共details in Sec. II兲 transition smoothly to small radius and use buried current joints to mitigate plasma formation from nonthermal effects such as electric-field-driven electron avalanche and contact arcing.25 Furthermore, the rod radii used are sufficiently large to limit the growth of MHD instabilities until after the time of plasma formation,16,26 making one-dimensional modeling potentially relevant to at least this point in time. Measurements are made to infer or calculate the surface magnetic field 共Bs兲, time of plasma formation 共tplasma兲, surface bright-

102507-3

Experimental investigation of thermal plasma formation…

FIG. 2. Green-light brightness temperature 共TBB兲 for barbell loads of varying R0 共pulsed with closely similar current兲. Data have been averaged over several shots. The 共2009兲 average Zebra current is also plotted 共dots兲. Smaller diameter loads form plasma at a lower current and reach higher peak temperature. Peak plasma temperatures for R0 = 0.25 mm rods reach TBB = 36 eV, while peak vapor temperatures for R0 = 1.00 mm rods reach only TBB = 0.7 eV. Temperatures below 2 eV are measured with a set of photodiodes configured to allow high incident intensity in order to achieve increased signal-to-noise ratio. These diodes eventually respond nonlinearly to the large photon flux received at high temperature 共TBB ⬎ 1.6 eV兲. Higher temperatures are measured with a second set of photodiodes, which are configured to receive lower incident intensity, and maintain linear response for all temperatures measured 共but with poor signal-to-noise ratio at a low temperature兲. Circles locate where the two datasets have been joined.

ness temperature 共TBB兲, spectrum of the emitted radiation, surface-heating uniformity, radial expansion velocity, and instability growth rates. Variations in ⳵ j / ⳵t and ⳵B / ⳵t 共where j and B are the current density and magnetic field strength, respectively兲 are made by altering R0, allowing access to qualitatively different regimes. Peak surface magnetic fields range from 1.5 to 4 MG; levels which Ref. 18 suggests bracket those required for surface plasma to form. The experiment finds that for nominal magnetic field rise rates 共⳵B / ⳵t = 兵␮0 / 2␲R0其 ⫻ ⳵I / ⳵t兲 from 30 to 80 MG/ ␮s, thermal plasma will form from a thick 6061-alloy Al surface only when the magnetic field reaches a threshold level 共Bthreshold兲 of 2.2 MG. This paper is organized in the following manner. In Sec. II, an overview of the experimental design is presented. Novel load hardware configurations, with features for mitigating nonthermal plasma production, are detailed. In Sec. III, evidence from multiple independent diagnostics 关including visible and extreme ultraviolet 共EUV兲 photodiodes, visible and EUV spectrometers, gated imaging of visible emission, and laser shadowgraphy兴 is presented, which confirms that thermal plasma forms from rod surfaces for sufficiently high surface magnetic field. In Sec. IV, it is shown that a magnetic field threshold of 2.2 MG exists for the thermal formation of plasma from a 6061-alloy Al surface when pulsed with ⳵B / ⳵t nominally rising from 30 to 80 MG/ ␮s. In Sec. V, computational modeling of the experiment is discussed. Finally, Sec. VI summarizes the results.


FIG. 3. Al filtered EUV photodiode data 共solid lines兲 and TBB 共dashed lines兲 for R0 = 0.25 mm 共black兲 and R0 = 0.50 mm 共gray兲 rods. Low TBB are measured with a set of photodiodes configured to allow high incident intensity 共increasing the signal-to-noise ratio兲. These diodes eventually respond nonlinearly to the large incident photon flux at high plasma temperatures and are accurate only for TBB ⱕ 1.6 eV. Extrapolation of the TBB curves suggests that for both R0 = 0.25 mm and R0 = 0.50 rods, EUV photon flux is measurable only for TBB ⱖ 2 eV. The 共2008兲 average Zebra current is also plotted 共dots兲. As will be discussed in Sec. IV, the onset of thermal plasma is evident as an abrupt increase in ⳵TBB / ⳵t when TBB 共dashed lines兲 reaches about 0.6–0.9 eV for R0 ⱕ 0.63 mm.

II. EXPERIMENTAL DESIGN: MITIGATION OF NONTHERMAL PRECURSOR PLASMA

The thick-rod-megagauss experiments are designed to access physical parameters relevant to the Al liners used in the joint Los Alamos National Laboratory⫺Air Force Research Laboratory MTF experiment27 currently under development at the Shiva Star pulsed-power facility.28 Al rods with R0 from 0.25 to 1.00 mm are pulsed to high field by the Zebra generator, which delivers a consistent 1.0 MA current pulse. The current is measured by three differential Bdot probes, positioned in the anode plate at 0°, 120°, and 240°, and located either 13 or 17 cm from the central axis of the pinch. Individual calibration constants 共determined by Team Specialty Products Corporation, Albuquerque, NM兲 allow the time-varying current to be determined by numeric integration of raw probe data. The three current traces are then averaged to determine the shot current. Typically, the three measurements are quite similar. For example, of the 29 shots taken in 2009, the standard deviation in the peak current measured by the three probes averaged 22 kA. For the 30 shots taken in 2008 and the 29 shots taken in 2009, the average peak Zebra current reached 990 kA 共with a standard deviation ␴ = 30 kA兲 and 1050 kA 共␴ = 20 kA兲, respectively. The 2009 and 2008 average current waveforms are displayed in Figs. 2 and 3, respectively. By definition, both waveforms reach I = 500 kA at t = 100 ns. All current waveforms are time-shifted in this manner, and all data are synchronized to this well-defined time axis. The Zebra current is quite insensitive to the initial rod radius 共R0兲, as supported by detailed circuit modeling.29 Varying R0 from 0.25 to 1.00 mm causes only modest changes to the total load-vacuum-chamber inductance and, as expected, changes in the Zebra current waveform are negligible.

102507-4

Awe et al.

The large magnitude and short rise-time of the Zebra current allow access to the liner-heating regime, where megagauss field is generated on the surface of a thick conductor carrying a skin current. The Zebra current pulse rises from 100 to 900 kA in 70 ns, with a current rise rate dI / dt = 1.1⫻ 1013 A / s. The average Zebra current I共t兲, as it rises from 20 to 200 kA, has been least-squares-fitted to the exponential function, I共t兲 ⬇ I0 exp共t / ␶兲, where ␶ = 13 ns. For cold Al, this current rise corresponds to a magnetic-fieldpenetration skin depth ␦B = 0.017 mm. After some Ohmic heating, the field will penetrate into hot, resistive Al, with ␦B many times greater than that of cold Al, of the order of 0.1 mm. For a 0.5-mm-radius current channel carrying 1.0 MA, the surface field is Bs = ␮0I / 2␲R = 4.0 MG. Therefore, rods driven by Zebra with R0 of the order of 0.5 mm meet the high-field and skin-heating requirements. Due to the fast rise of the Zebra current, such rods also demonstrate onedimensional 共radially dependent兲 behavior to at least the time of plasma formation. Maintaining a stable surface through the time of plasma formation simplifies the interpretation of experimental data and allows for a more meaningful comparison with onedimensional R-MHD simulation results. At pressures associated with megagauss level field, metals are stressed well beyond their yield strength 关a 1.0 MG magnetic field creates a pressure of PB = B2 / 共2␮0兲 = 4 GPa; the yield strength of a 6061-alloy Al is 290 MPa 共Ref. 30兲兴, so the metal acts as a fluid and instabilities are developed. For a given current rise rate 共dI / dt兲 and rod radius 共R兲, there exists a maximum field strength that may be achieved before disruption of the rod.16,25 The growth time for the development of sausage 共m = 0兲 and kink 共m = 1兲 mode instabilities is on the order of R / VA, where VA is the Alfvén velocity 关VA = Bs / sqrt共␮0␳兲, where Bs is the surface magnetic field strength and ␳ is the material density兴. To estimate the penetration depth of the Alfvén wave 共␦A兲, assume that a rod of radius R is pulsed with a current source rising at constant dI / dt ⬅ I⬘ to a field strength Bs共t兲. The Alfvén velocity therefore increases linearly in time as VA共t兲 = sqrt共␮0 / ␳兲兵I⬘ / 共2␲R兲其t. The surface magnetic field reaches B at time tB = 2␲RB / 兵␮0I⬘其, at which point the Alfvén velocity is VA共tB兲 = sqrt共␮0 / ␳兲兵I⬘ / 共2␲R兲其tB. An overestimate 共since VA increases in time兲 of the Alfvén wave penetration depth at time tB is found by assuming ␦A = 兵VA共tB兲其tB = sqrt共␮0 / ␳兲兵I⬘ / 共2␲R兲其tB2. Using the density of Al at standard temperature and pressure 共␳ = 2700 kg/ m3兲 and setting Bs = 200 T 共2 MG兲, dI / dt = 1.1 ⫻ 1013 A / s 共that of the Zebra generator兲, and R = 0.5 mm, it is found that ␦A ⬍ 0.2 mm⬍ R0. For the Zebra current pulse, Al rods with R0 near 0.5 mm remain smooth to at least the time when the surface field reaches the few megagauss level. The substantial magnitude and short rise-time of the Zebra current enables megagauss field to be pulsed on the surface of a thick, smooth conductor but also introduces large electric fields. In consequence, care must be taken to avoid nonthermal plasma created by electric-field-driven electron avalanche or ultraviolet 共UV兲 photoionization from arcing electrical contacts. A quite comprehensive discussion of vacuum breakdown in high-voltage devices is presented in


Ref. 31. In the thick-rod-megagauss experiments considered here, contact arcing from simple loads is observed to initiate plasma formation on rod surfaces far from the arc, possibly by photoionization. In contrast, high-voltage-breakdown phenomena are significantly reduced or even eliminated when using carefully configured load profiles and electrical contacts. The most commonly used hardware configurations are displayed in Fig. 1. Three different central load profiles are shown: simple-straight rod or “SSR” 关Figs. 1共a兲 and 1共b兲兴, hourglass 关Fig. 1共c兲兴, and barbell 关Fig. 1共d兲兴. These loads are mounted on two varieties of anode-cathode 共“AK”兲 hardware: gravitational 共“GRAV”兲关Fig. 1共a兲兴 or penetrating knife-edge 共“KE”兲关Figs. 1共b兲–1共d兲兴 hardware. GRAV hardware relies only on gravity for the mating of current joints, whereas KE hardware uses several machine screws to compress a large diameter stainless steel knife-edge ring through the Al oxide layer on the anode and cathode plates, decreasing the contact resistance. Hourglass loads are machined from a single piece of 3-in.-diameter Al and therefore have no contacts near the straight-cylindrical central section of the load and use KE hardware. Barbells are machined from 6-mm-diameter Al cylinders and are mated to either GRAV or KE hardware. In both hourglass and barbell loads, radial transitions are made smoothly to avoid electric field enhancement. Barbell loads, like SSR loads, have exposed electrical contacts, but contacts are made at a diameter of 6 mm, reducing the local contact resistance and current density. Moreover, the axial profile of the barbell reduces UV photoionization 共from contact arcs兲 by eliminating the direct line of sight from the contact region to the central rod section of the load. Detailed descriptions of the different load types and coupling hardware are found in Ref. 25. For carefully configured load profiles and electrical contacts, plasma initiation can predominantly be a thermal process even in Zebra’s high-electric-field environment. Simple loads, however, generate nonthermal plasma at low current from multiple locations. The time of plasma initiation is recorded with imaged, high-gain photomultiplier tubes 共PMTs兲. Arcing is observed from the small-diameter contacts of SSR loads and from the low-pressure current joints of GRAV hardware. Arcing from GRAV hardware initiates nonthermal plasma formation on the central rod surface, whereas arcs from SSR contacts appear to show only local effects. Furthermore, initial emission uniformity is examined with an Andor iStar intensified CCD camera and found to depend on the choice of load hardware. The diagnostic captures two high spatial and temporal resolution 共30 ␮m, 2 ns兲 images of the rod surface per shot. SSR loads consistently show arcing from small-diameter anode-cathode contacts and, when mounted on the GRAV hardware, highly nonuniform emission along the length of the rod. In contrast, for hourglass and barbell loads in KE hardware, there is no evidence of arcing from electrical contacts; plasma formation on rod surfaces distant from the contact is delayed and increased axial emission uniformity is observed. The tendency for larger-diameter rods to emit light at higher current is observed for loads coupled to KE hardware. This trend is not clear for loads coupled to GRAV hardware, suggesting that

102507-5


early emission results from 共electric-field-dependent兲 nonthermal processes rather than from 共current-densitydependent兲 Ohmic heating. The present article focuses on thermal plasma formation and hence on data obtained using the advanced load and anode-cathode hardware: barbell and hourglass loads mounted with penetrating knife-edge AK hardware. A companion paper 共to follow兲 will present the details of a thorough investigation on the impact that specific hardware features have on nonthermal plasma formation. The paper will include 共1兲 a detailed description of load-hardware design and construction; 共2兲 PMT measurements that show a clear connection between the time and location of plasma formation and specific load hardware features; 共3兲 images from the two-frame ICCD, which show both strong low-current emission from the small-diameter contacts of SSR loads as well as nonuniform plasma formation from rod surfaces when using GRAV hardware; 共4兲 the effect of surface smoothness on surface heating and plasma formation; and 共5兲 comments on how the low-current formation of nonthermal plasma affects the evolution and high-current dynamics of rod surfaces. III. EVIDENCE OF THERMAL PLASMA FORMATION

Surface plasma is identified and characterized by several independent measurements. First, evidence of plasma is clearly demonstrated by surface brightness temperatures 共TBB兲, obtained from visible light radiometry, which exceed 35 eV for the smallest radius rods examined. Second, a large flux of higher energy photons is measured by broadband EUV photodiodes, which are sensitive only to photon energies above 15 eV. Third, Al3+ and Al4+ Al ions are identified with time-resolved EUV spectroscopy. Fourth, flute mode instabilities form on rod surfaces as a result of the interaction of high magnetic field with surface plasma. Fifth and finally, the radial expansion of those rods that form surface plasma accelerates after peak current, whereas rods that form no plasma maintain constant velocity. Each indication of plasma is discussed in the paragraphs to follow. A. Brightness temperature from visible light radiometry

A time-resolved, lower-bound estimate of the rod surface temperature is obtained via visible light radiometry. The spectral radiation intensity 共W / 兵m2 sr nm wavelength其兲 emitted from a series of positions along the rod surface is measured with a linear array of green-filtered photodiodes. A Planckian blackbody radiates with a spectral intensity that increases monotonically with temperature, and thus, there is a unique blackbody temperature corresponding to any measured intensity. The relationship is not given simply by T4 because the spectrum changes with temperature. The relationship between intensity and temperature depends on what wavelength is observed. In this work, the temperatures reported are green-light brightness temperatures 共TBB兲. Typical results show a rapidly increasing temperature, from about 1 eV to tens of eV, after the time that plasma has formed.


Recent quantum molecular dynamics simulations32 show that at temperatures between 1 and 3 eV, Al will make the transition from warm dense matter to plasma as it expands from near solid density 共2000 kg/ m3兲 to low density 共25 kg/ m3兲. This is the density-temperature regime expected near the surface of rods in the thick-rod-megagauss experiments according to numerical modeling. The fact that temperatures well above 3 eV are typically observed provides strong evidence that the surface material is multiply ionized Al plasma. The measurement of brightness permits a temperature estimate 共TBB兲 that is always less than or equal to the peak plasma temperature. The green-light brightness temperature 共TBB兲 is calculated assuming a Planckian blackbody spectrum, which is correct for an optically thick radiation source with a uniform temperature. When the optical depth of the plasma layer is less than unity, then the emission by bremsstrahlung and lines is less intense than a blackbody at the same temperature but is equal in intensity to that of a blackbody at lower temperature. So, the calculated brightness temperature is then smaller than the plasma temperature. For the conditions of the experiment, modeling results suggest that soon after plasma formation, the optical depth through the plasma layer for green light is greater than unity, and the green-light brightness temperature 共TBB兲 provides a reasonable estimate of plasma temperature. However, modeling also shows a temperature gradient, from hot at the lowest density outer edge to cold at the highest density inner edge of the plasma layer. The optical depth is generally comparable to the temperature gradient length. In such a case, the spectrum differs from a blackbody and TBB corresponds to a temperature intermediate between the hottest and coldest regions. Recent measurements of the emitted spectrum in this experiment will be reported in a future paper and compared with modeling predictions. Green-light brightness temperatures 共TBB兲 are determined from intensity measurements of a band of radiation escaping the rod surface. Surface emissions first pass through a Wratten #58 color filter 共70 nm full width at half maximum, centered at 530 nm兲, with time-resolved intensity measurements of the transmitted wavelengths made by a 38element 共only 15 elements are active兲, linear, fast photodiode array 共OSI Optoelectronics model A5C-38兲. The system magnification is chosen so that the width of the image of the rod exceeds the width of each array element from the onset of the experiment 共or after slight expansion for R0 = 0.25 mm rods兲. Therefore, the viewed emitter area is well defined and constant, and the radial expansion of the rod need not be considered in surface temperature calculations. Displayed in Fig. 2 are TBB共t兲 curves for rods with R0 of 0.25, 0.40, 0.50, and 1.00 mm. The smallest 共R0 = 0.25 mm兲 rods are the hottest, with peak TBB of 36 eV. The largest 共R0 = 1.00 mm兲 rods remain cool, with peak TBB of 0.7 eV 共the 1.00 mm curve in Fig. 2 has been multiplied by 10; temperatures below 0.4 eV cannot be distinguished from electrical noise兲. Evidence of the formation of low-density plasma from rod surfaces is also obtained in the observation that TBB greatly exceeds temperatures predicted by simple application

102507-6

Awe et al.

of the magnetic diffusion equation. The well known scaling of temperature with magnetic field derived by, for example, Herlach and Knoepfel33,34 is given by T = B2 / 共2cv␮0兲, where cv is the volumetric heat capacity. This relationship is found by solving the diffusion equation for an exponentially rising boundary condition on an isotropic, incompressible, constant-resistivity half space. These conditions are the most reasonable for the surface of the largest radius rods examined 共R0 = 1.00 mm兲, which remain relatively cool 共smallest change in resistivity兲 and begin to expand later at higher current 共smallest change in density and cv兲. Evaluating the formula T = B2 / 共2cv␮0兲 for a R0 = 1.00 mm rod expanded to R = 1.2 mm at the time of peak current, while using the solid-density volumetric heat capacity cv ⬃ 2.4⫻ 106 J / 共K m3兲 yields a calculated surface temperature of 0.4 eV. This is in fair agreement with the experimental measurement of TBB = 0.7 eV, which is higher due, in part, to the decreased Al density 共and cv兲 of the expanding edge material. Smaller radius rods begin to expand at lower current and reach high plasma temperatures. Material parameters are therefore far from those assumed for the scaling relation and the experimental temperatures greatly exceed this prediction. At the time of peak current, R0 = 0.50 mm rods have expanded to R = 0.85 mm, yielding a T = B2 / 共2cv␮0兲 temperature of 0.8 eV; a factor of 25 below the measured temperature of TBB = 20 eV. The measured temperatures correspond to the thin plasma layer on the rod surface, where the assumptions underpinning the T = B2 / 共2cv␮0兲 formula do not apply. However, simulations suggest that temperatures in the dense interior nonplasma regions of the rod do roughly follow T = B2 / 共2cv␮0兲. B. Extreme ultraviolet emission

Higher energy photons are sampled with an array of four EUV photodiodes. The photodiodes, with either Al 共200 nm兲 or Si/Zr 共100 nm/200 nm兲 directly deposited filters, distinguish between medium and high energy EUV plasma emissions. The Al filters transmit 16–73 eV photons, while the Si/Zr filters transmit 60–100 eV photons. Sub-eV Al vapor does not emit photons of such high energy; therefore, as expected, EUV emission is measurable only after TBB 共estimated from visible light radiometry兲 exceeds approximately 2 eV 共Fig. 3兲. EUV diode measurements are consistent with multi-eV temperatures. No EUV emission has been observed from R0 = 1.00 mm rods, consistent with measured sub-eV surface brightness temperatures. EUV spectra in the band from 70 to 150 eV 共18–8 nm兲 are detected by a McPherson model 310/G grazing incidence spectrometer. The spectrometer, equipped with a multistrip MCP, captures four independent spectra per shot 共6 ns gate pulses separated by 10 ns兲, which are lens relayed to a high resolution 16-bit CCD camera. Ion species are identified through comparisons with the NIST database,35 and the commercial radiative-collisional spectral modeling software PrismSPECT 共Ref. 36兲 is used to estimate plasma temperatures. For those rod surfaces that form plasma, primarily spectral lines from Al3+ and Al4+ ions 共identified through com-


FIG. 4. EUV spectra, gated near peak current, from R0 = 0.50 mm 6061alloy Al barbell loads in KE hardware 共averaged over several shots兲. Included in the plot are experimental data 共thick line兲, a PrismSPECT-calculated spectrum for 15 eV temperature 共thin line兲, and the wavelength and magnitude of Al3+ and Al4+ lines obtained from the NIST Atomic Spectra Database 共vertical dashed lines兲. Sixteen distinct spectral features are identified, most of which are composed of multiple unresolved ionic transitions. The wavelength, relative intensity, and configuration of the constituent ionic transitions are detailed in Table I. PrismSPECT calculations assume that radiation originates from a 1.0-␮m-thick layer of 5 kg/ m3 density Al plasma. The code was run with non-LTE selected and with “configuration splitting” set to “term split” and “fine structure.” The calibration accuracy was about ⫾0.015 nm.

parisons with the NIST database兲 are observed 共Fig. 4兲. Sixteen distinct spectral features are identified, most of which are composed of multiple unresolved ionic transitions. The wavelength, relative intensity, and configuration of the constituent ionic transitions are detailed in Table I. For R0 = 0.50 mm rods, near the time of peak current 共1.0 MA兲, Al3+ and Al4+ emission lines are observed with approximately equal intensity, indicating a plasma temperature of about 15 eV 共as determined from PrismSPECT calculations兲. Spectral features from other elements 共e.g., magnesium and oxygen兲, if present, were of too low intensity to be identified. Interestingly, for R0 = 0.25 mm rods, Al3+ and Al4+ emission lines 共observed at low current兲 subsequently turn into Al3+ and Al4+ absorption lines even before peak current. Absorption lines indicate that EUV light passes through cooler plasma containing Al3+ and Al4+ ions. The transition from emission to absorption spectra nearly coincides with the development of large amplitude sausage mode 共m = 0兲 instabilities. Possibly, for R0 = 0.25 mm rods, ejected plumes of plasma that cool during expansion are backlit by hotter plasma, producing the observed spectral absorption features. Further investigation is required to determine under what conditions the observed EUV absorption lines are generated. C. Surface instability growth

Surface plasma is further indicated by the development of instabilities, whose formation depends on the conductivity of the expanding material. Resistive vapor will move freely through the surrounding ultrahigh magnetic field, while lowdensity conductive plasma will interact with the field, and magnetic Rayleigh–Taylor or sausage mode instabilities will develop. The effect of the presence of surface plasma is demonstrated in Fig. 5, which displays surface structure near

102507-7



TABLE I. Identification of the spectral features labeled in Fig. 4, most of which are composed of multiple unresolved ionic transitions. The wavelength, ion species, relative intensity, and configuration of the transitions are given.

Peak 1 2 3 4 5 6

NIST wavelength 共nm兲

Ion

NIST intensity

Configuration

8.5518 8.5804 8.7651, 8.8163, 8.8369

5+ 4+ 5+

1000 350

2s2.2p4-2s2.2p3.共2Pⴱ兲.3d 2s2.2p5-2s2.2p4.共3P兲.6d

650, 1000, 750

8.8269 9.063, 9.0646, 9.0701 9.3755, 9.3855, 9.3955 9.5433

+

750 250, 100, 200 350, 200, 300

2s2.2p4-2s2.2p3.共2Dⴱ兲.3d 2s2.2p4-2s2.2p3.共2Pⴱ兲.3d 2s2.2p5-2s2.2p4.共1D兲.4d 2s2.2p5-2s2.2p4.共3P兲.4d

100 100

2s2.2p4-2s2.2p3.共2Dⴱ兲.3d 2s2.2p5-2s2.2p4.共1S兲.3d

300, 400, 150, 250, 200, 250, 200, 100, 150

2s2.2p5-2s2.2p4.共1D兲.3d

200, 600, 150, 300, 300 100 150 250 150

2s2.2p5-2s2.2p4.共3P兲.3d 2s2.2p6-2s2.2p5.共2Pⴱ具1 / 2典兲.5d 2s2.2p6-2s2.2p5.共2Pⴱ具3 / 2典兲.5d 2s2.2p6-2s2.2p5.共2Pⴱ具1 / 2典兲.4d 2s2.2p6-2s2.2p5.共2Pⴱ具3 / 2典兲.4d

900, 800 700 800, 1000, 900, 900 100 800

2s2.2p5-2s2.2p4.共1D兲.3s 2s2.2p6-2s2.2p5.共2Pⴱ兲.3d 2s2.2p5-2s2.2p4.共3P兲.3s 2s.2p6-2s . 2p5.共3Pⴱ兲.3s 2s2.2p6-2s2.2p5.共2Pⴱ兲.3s

700

2s2.2p6-2s2.2p5.共2Pⴱ兲.3s

5 4+ 4+ 5+ +

9.929 10.3805, 10.3882, 10.3992, 10.4072, 10.4122, 10.4181, 10.4362, 10.4447, 10.4496 10.7711, 10.7948, 10.8005, 10.8059, 10.8113

4

11

11.1196 11.1589 11.6464 11.6921 12.5529, 12.6068

3+ 3+ 3+ 3+ 4+

12 13 14 15 16

12.973 13.0411, 13.0847, 13.1002, 13.1438 13.5617 16.0074 16.1688

3+ 4+ 4+ 3+ 3+

7 8 9 10

4+ 4+

the time of peak current for R0 = 0.40 mm共D0 = 0.80 mm兲 and R0 = 1.00 mm共D0 = 2.00 mm兲 rods, respectively. The R0 = 0.40 mm rod forms surface plasma early in the current rise, and the surface grows highly unstable. In contrast, the R0 = 1.00 mm rod forms no surface plasma and remains smooth even after significant radial expansion. Simple linear instability analysis37 shows that for a self-pinched plasma, sausage modes grow exponentially in time, with a growth rate ␥ 共in units of s−1兲, given by ␥ = sqrt兵2T / 共MsR0兲其, where s = p / 共⳵ p / ⳵R兲. The perturbation amplitude 共A兲 will therefore grow as A共R , t兲 = A0共R兲exp共␥t兲. Time-resolved laser shadowgrams have been used to estimate instability amplitudes, and experimental growth rates have been determined. Instability amplitudes that grow ap-

proximately exponentially are observed 共Fig. 6兲 for rods with R0 = 0.25, 0.32, and 0.40 mm 共those rods that form plasma early in the current rise兲. Instabilities are seeded by initial perturbations in the rod surface. Surface smoothness varied from load to load, especially for those rods with R0 ⱕ 0.40 mm 共most of which were machined by hand兲. Extrapolation of experimental data suggests initial perturbation amplitudes at or below 30 ␮m for standard loads, in reasonable agreement with the surface roughness estimates gained from 共preshot兲 visible microscope images. Rods machined with smoother surface finish 共ultrasmooth, diamond turned LANL loads with submicron surface irregularity兲 demonstrated reduced instability amplitude 共for the same Zebra current兲 when compared to rougher loads. However, only a small number of ultrasmooth loads have been examined, so these results remain qualitative. D. Radial expansion

FIG. 5. Instability growth as indicated by laser shadowgraphy. The dashed lines indicate the initial rod diameter 共D0兲. 共a兲 R0 = 0.40 mm 共D0 = 0.80 mm兲 rod at peak current and 共b兲 R0 = 1.00 mm 共D0 = 2.00 mm兲 rod at peak current. Rods that form surface plasma are m = 0 unstable, while rods that do not form plasma show no instability growth even when carrying 1 MA of current and after significant radial expansion.

The expansion rate of a thick metal surface pulsed to ultrahigh magnetic field is a critical parameter for a variety of applications including magnetized target fusion. Rod surface expansion has been measured via multiframe laser shadowgraphy. The expansion characteristics of R0 = 0.50 mm and R0 = 1.00 mm rods are contrasted in Fig. 7. This is an interesting comparison because, as detailed previously, a variety of diagnostics show that plasma 共with a peak temperature of 20 eV兲 forms on R0 = 0.50 mm rods, but no plasma is observed for R0 = 1.00 mm rods 共which reach only 0.7 eV兲. Surface current density varies inversely with the rod circumference 共and radius兲, so R0 = 0.50 mm rod surfaces experi-

102507-8

Awe et al.

FIG. 6. 共Color online兲 Sausage mode instability growth rates, ␥共ns−1兲, for rods with R0 = 0.25, 0.32, and 0.40 mm 共which form plasma early in the experiment兲. Shadowgram rod-edge widths are plotted on a logarithmic scale. The inset on the right details the process used to determine instability amplitudes. For each shadowgram, a several-millimeter-long section of the rod is selected 共bold rectangle兲 to generate a plot profile 共the horizontal axis is shown in pixels, but is easily converted to millimeters兲. The average edge width, which grows after instabilities form, is given by 兵关共B − A兲 + 共D − C兲兴 / 2其. An edge width, growing approximately exponentially in time, is observed for R0 = 0.25, 0.32, and 0.40 mm rods 共estimated growth rates are given兲. The edge width of R0 = 1.00 mm rods, which form no plasma, shows no signs of growth.

ence higher Ohmic heating per unit volume for the same total current. They therefore melt, vaporize, and begin to expand at lower current than R0 = 1.00 mm rods do. Rods expand monotonically with no evidence of repinching, indicating that the outward thermal pressure continues to exceed the inward magnetic pinch pressure even if surface plasma forms. During the linear current rise, expansion velocities are similar for R0 = 0.50 mm and R0 = 1.00 mm rods 共3 – 4 ␮m / ns兲 even though R0 = 0.50 mm rods form hot plasma at t = 118 ns 共Fig. 3兲, while R0 = 1.00 mm rods remain cool. The expansion data lead to the conclusion that when surface plasma is present, the magnetic pinching force, although insufficient to stop the expansion of the underlying matter, pins the plasma layer against the expanding internal material. This keeps the plasma layer thin 共and ultimately causes fluting兲. The small radial extent of the plasma layer facilitates a short time interval for the diffusion of magnetic field, so probably only a small fraction of the current is shunted to the surface plasma. Surface radial expansion velocities for R0 = 0.50 mm and R0 = 1.00 mm rods, while similar during the linear current rise, are very different after peak current 共Fig. 7兲. When ⳵I / ⳵t approaches zero 共eventually becoming negative兲, the expansion speed of R0 = 0.50 mm surfaces increases severalfold to nearly 10 ␮m / ns, while the expansion speed of R0 = 1.00 mm surfaces remains constant at 3 – 4 ␮m / ns. As magnetic flux leaves the system, a plasma layer 共if present兲 ceases to be pinned against the underlying material. The hot plasma carries reduced current density and accelerates outward. Reduced pinching may allow expansion of the plasma surface at the thermal velocity, or the low-beta plasma may even be pulled outward by expanding field lines. For


FIG. 7. The change in radius 共⌬R兲 vs time as measured by laser shadowgraphy. The change in radius is defined as ⌬R共t兲 ⬅ R共t兲 − R0, where R0 is the initial rod radius determined from preshot reference shadowgrams. R0 was measured separately for each shot, and for each shadowgram channel. Confirmatory measurements were also made with a visible light microscope prior to experiments. Peak current occurs at approximately 170 ns. The effect of flux pulling out of the conductor is seen in the increased radial expansion speed of R0 = 0.50 mm rods after peak current. In contrast, the expansion of the outer material layers for R0 = 1.00 mm rods, which do not contain plasma, is unaffected by changes in ⳵I / ⳵t.

R0 = 1.00 mm rods, the absence of radial acceleration confirms that no surface plasma forms, or that if there is plasma, it is so resistive that the influence of the relative motion of magnetic field lines is not observed.

IV. MAGNETIC FIELD THRESHOLD FOR THERMAL PLASMA FORMATION

That plasma will form from a thick Al surface pulsed to sufficiently high magnetic field has been definitively confirmed. Furthermore, the initiation of thermal plasma is evident in visible light radiometry measurements as a sharp increase in ⳵TBB / ⳵t when TBB reaches 0.6–0.9 eV for rods with R0 ⱕ 0.63 mm. Initially, TBB rises slowly until reaching 0.6–0.9 eV, at which point ⳵TBB / ⳵t increases by nearly an order of magnitude 共shown for R0 = 0.25 mm and R0 = 0.50 mm rods in Fig. 3兲. The slow heating phase is attributed to diffusive energy deposition while magnetic field penetrates through resistive Al vapor; the duration of this phase grows with R0. This is expected since the Ohmic heating power density, PJ共r , t兲 = ␩共r , t兲关J共r , t兲兴2 ⬇ ␩共r , t兲 · 兵I共t兲 / 关2␲R0 · ⌬共t兲兴其2, varies inversely with R02 关⌬共t兲 is the growing thickness of the current-carrying skin layer兴. The abrupt increase in ⳵TBB / ⳵t that follows corresponds with the abrupt decrease 共greater than ten orders of magnitude兲 in resistivity associated with plasma initiation. The energy deposited by Ohmic heating 共PJ = E2 / ␩, using E = ␩J兲 increases when the resistivity falls, while the electric field E is maintained by the rising current. Assuming constant electric field strength, the Ohmic heating will increase drastically with the drop in resistivity, spurring the sharp increase in ⳵TBB / ⳵t. The observed sub-eV plasma formation temperature is consistent with calculations of the conductivity of warm dense Al at below one-tenth solid density.1 This supports determining the plasma formation time 共tthreshold兲 and magnetic field threshold 共Bthreshold兲 via the measured inflection in TBB共t兲.

102507-9


Thermal plasma forms when Bs reaches Bthreshold = 2.2 MG, quite independent of R0. As R0 decreases, melting, vaporization, and plasma formation occur earlier, and at a lower Zebra current. For the material temperature to rise, Ohmic heating must exceed energy losses associated with expansion, thermal conduction, and radiation. For each R0, the surface magnetic field and current density rise at different rates, and the material follows a different trajectory through ␳-T space. Although the material in the skin layer undergoes multiple orders-of-magnitude change in resistivity and heat capacity, the formation of plasma correlates mostly with the value of Bs, which is calculated from measured I共t兲 and R共t兲. I共tthreshold兲 is found using averaged shot currents 共see Sec. II for the details on current measurement techniques and shotto-shot reproducibility兲. The spread in data, along with timing uncertainty 共estimated at ⫾1 ns兲, results in a I共tthreshold兲 measurement uncertainty of ⫾3%. R共t兲 is deduced from two laser shadowgrams and two fast framing images per shot. Data from rods with similar R0 are combined, and R共tthreshold兲 is obtained from the resultant curve. Shot-to-shot variation in R共t兲 is typically small near the time of plasma formation; the error in R共tthreshold兲关interpreted as 1 standard deviation spread in individual R共t兲 data points兴 is estimated at ⫾30 ␮m. Rods with R0 = 0.25, 0.32, 0.40, 0.50, and 0.63 mm form plasma when Bs reaches 2.0, 2.1, 2.2, 2.3, and 2.2 MG, respectively. Based on the uncertainty in I共tthreshold兲 and R共tthreshold兲, the error in each of the above-quoted Bs values is approximately ⫾0.2 MG. Thermal plasma initiation depends strongly on Bs, but weakly on magnetic field rise rate 共nominal ⳵Bs / ⳵t = 兵␮0 / 2␲R0其 ⫻ ⳵I / ⳵t decreasing with increasing R0 from 80 to 30 MG/ ␮s兲 or on field-linecurvature effects associated with small radius. The experiment finds that the magnetic field threshold for thermal plasma formation from a thick 6061-alloy Al surface is 2.2 MG for nominal ⳵Bs / ⳵t from 80 to 30 MG/ ␮s. V. COMPUTATIONAL MODELING

The results from the thick-rod-megagauss experiments provide an extensive dataset for theoretical and computational modeling. As discussed, the range of radii examined display a wide variety of behaviors. For example, depending on the strength of the applied magnetic field, surfaces form either hot radiating plasma or cool weakly emitting vapor. Simulations must explain not only those observations related to one combination of parameters, but must additionally describe the observed trends associated with changes in R0. Fundamentally important questions include whether or not “standard” R-MHD models can predict experimental observations and whether or not non-MHD phenomena must be invoked to explain them. The basic challenges encountered when modeling these experiments have been described by Garanin et al.18 A sufficiently complete physical model must be incorporated so as to avoid physical impossibilities. For example, thermal conduction must be included to avoid infinite temperatures. The starting point for modeling the thick-rod-megagauss experiments is a MHD model that includes a continuity equation, an equation of motion 共with Lorentz force兲, Faraday’s law


共using a simple Ohm’s law兲, and a material energy equation 共including thermal conduction and Ohmic heating terms兲. For completeness, the basic material equations need an equation-of-state 共EOS兲 that gives the specific material energy and pressure as functions of density and temperature. Also needed as functions of density, temperature, and, potentially, magnetic field are the transport coefficients—the thermal conductivity and the electrical resistivity. While all codes examining results from the thick-rod-megagauss experiments use this basic model, treatments of radiation differ somewhat. Also, various theoretical results are used for the treatment of material properties such as the EOS and resistivity. Because of the predominantly one-dimensional 共1D兲 behavior of the thick-rod-megagauss experiments, 1D “computer experiments” can be clearly defined. Computational considerations include whether to use a Lagrangian or Eulerian formulation, initial and boundary conditions, spatial resolution, time-step control, as well as choice of material properties and radiation models. The computational approach is very similar to that used for thin wire studies,38,39 but the computed behavior is substantially different. Lagrangian simulations that agree well with the thickrod-megagauss experiments have been reported by Garanin et al.40 A very high spatial resolution was required at the material-vacuum interface. The computations used an EOS with van der Waals 共VdW兲 loops in the pressure model. A minimum electrical conductivity was introduced and adjusted for some rod diameters in order to get plasma to form at the rod surfaces at the times observed in the experiment. Plasma also forms in the interior material at nearly the same time as on the surface because of unstable fluctuation growth introduced by the VdW EOS at the liquid-vapor transition. Eulerian simulations also find results that agree well with those from the thick-rod-megagauss experiments. Makhin41 found peak temperatures and radial expansion rates in qualitative agreement with experimental results for R0 = 0.50 mm rods. Furthermore, the existence of a magnetic field threshold and a maximum radius above which no plasma forms was reported by Angelova.42 However, the EOS and resistivity models used predicted plasma formation at a significantly later time and at a significantly higher magnetic field threshold than observations indicated. More recently, Eulerian results have been reported by Lindemuth et al.,43 which show that the choice of EOS and resistivity models has a major affect on the time of plasma formation and the peak temperature. Using an EOS that has Maxwell constructs to eliminate the VdW loops, plasma forms at the vacuum interface in very low-density material. The approximate constancy of the magnetic field at plasma formation is shown, whereas the electric field at plasma formation varies significantly. Analysis based on examining the characteristic Ohmic heating time for electric field values typical in the thick-rod-megagauss experiments shows why plasma should indeed form in the simulations, and that plasma formation is not a fictitious numerical effect. Analysis of the similarities and differences in the mechanisms of plasma formation for the various simulations is ongoing. All thick-rod simulations show that low-density ma-

102507-10


Awe et al.

terial expands outward prior to plasma formation. In contrast to thin wires, this initial expansion occurs not because the material pressure has exceeded the magnetic pressure but because the material is resistive enough that the high magnetic field can exert very little force. The nature of the expansion appears to be different for VdW and non-VdW EOSs. Whether or not the initial expansion is purely adiabatic is a subject of continuing debate. Lagrangian computations discussed briefly in Ref. 43 show that although the outward material pressure force significantly exceeds the inward magnetic force, Ohmic heating during expansion exceeds the expansion cooling. Therefore, net energy is deposited into the material, helping to carry it through the vapor dome. When the material exits the vapor dome, the Ohmic heating can lead to a rapid 共even subnanosecond兲 increase in temperature. The subsequent dynamics after plasma formation is qualitatively similar in all simulations. How the computed plasma density and temperature profiles, which show both optically thick and optically thin material, lead to the observed radiation emission is a subject of continuing study. More detailed computational results will be reported in future papers. To the extent that the simulations have reproduced and explained the experimental observations, it appears reasonable to conclude that the surface-plasma formation observed in the thick-rod-megagauss experiments is a predominantly thermal process driven by Ohmic heating. However, the explanation of the magnetic field threshold is an ongoing topic of research. The use of a lower limit on the conductivity by Garanin to trigger surface-plasma formation may be an indication that non-MHD processes, e.g., photoionization, may also be at play. This will be examined in the future.

VI. CONCLUSIONS

MTF liner physics is being effectively examined by using the 1.0 MA Zebra z-pinch to observe the effect of pulsed multi-MG field on the surface of thick Al rods. Recent experiments have evaluated rods with initial radii ranging from 1.00 to 0.25 mm, which experience nominal surface magnetic field rise rates of 30– 80 MG/ ␮s. For those rods that reach the surface magnetic field threshold for thermal plasma formation 共Bthreshold = 2.2 MG兲, evidence of surface-plasma formation is conclusive; peak temperatures exceeded 10 eV, EUV line emission from Al3+ and Al4+ ions is observed, and plasma surface instabilities are developed. When pulsed with the same current, R0 = 1.00 mm rods 共peak surface field below 2.2 MG兲 form resistive metal vapor. For these rods, no evidence of plasma is obtained; sub-eV temperatures persist, EUV emission is undetected, and surface material moves freely through the magnetic field. No instability growth or radial velocity dependence on ⳵I / ⳵t is observed. The experiment offers the first detailed study of the threshold for thermal plasma formation from a thick Al surface by pulsed magnetic fields. Measurements of phase, temperature, velocity, and ionization state as functions of surface magnetic field strength are being compared against several radiation MHD models.

ACKNOWLEDGMENTS

The quality and productivity of our research has been immeasurably aided by the contributions of our many colleagues and collaborators. We thank W. Atchison, M. Frese, V. Makhin, and S. Garanin for their computational and theoretical efforts, which have helped us to better understand the many intricacies of our experiment. We also thank R. Reinovsky, who facilitated the UNR-Megagauss Experiments Modeling Workshops and provided us with precision machined barbell loads and the use of a streak camera. We appreciate the assistance of the dedicated Zebra staff including T. Adkins, A. Astanovitskiy, S. Batie, D. Macaulay, V. Nalajala, and many others. We are also thankful to M. Angelova, J. Billing, W. Cline, J. Degnan, M. Desjarlais, A. Esaulov, R. Faehl, T. Goodrich, S. Frese, T. Haill, V. Ivanov, A. Kaul, B. Le Galloudec, D. Meredith, A. Oxner, I. Paraschiv, R. Presura, C. Rousculp, E. Ruden, D. Ryutov, and P. Turchi for technical assistance and/or useful discussions. This research was supported by the DOE under Grant Nos. DE-FG02-04ER54752, DE-FG02-06ER54892, and DEFC52-06NA27616. This work was completed while T.J.A. was employed by the Department of Physics at the University of Nevada, Reno. 1

M. P. Desjarlais, J. D. Kress, and L. A. Collins, Phys. Rev. E 66, 025401共R兲共2002兲. 2 W. A. Stygar, M. E. Cuneo, R. A. Vesey, H. C. Ives, M. G. Mazarakis, G. A. Chandler, D. L. Fehl, R. J. Leeper, M. K. Matzen, D. H. McDaniel, J. S. McGurn, J. L. McKenney, D. J. Muron, C. L. Olson, J. L. Porter, J. J. Ramirez, J. F. Seamen, C. S. Speas, R. B. Spielman, K. W. Struve, J. A. Torres, E. M. Waisman, T. C. Wagoner, and T. L. Gilliland, Phys. Rev. E 72, 026404 共2005兲. 3 S. A. Slutz, C. L. Olson, and P. Peterson, Phys. Plasmas 10, 429 共2003兲. 4 N. J. Peacock and B. A. Norton, Phys. Rev. A 11, 2142 共1975兲. 5 C. M. Fowler, R. S. Caird, and W. B. Garn, Report No. LA-5890-MS, 1975. 6 R. C. Kirkpatrick, I. R. Lindemuth, and M. S. Ward, Fusion Technol. 27, 201 共1995兲. 7 D. D. Ryutov, and R. E. Siemon, Comments Mod. Phys. 2, 185 共2001兲. 8 I. R. Lindemuth and R. E. Siemon, Am. J. Phys. 77, 407 共2009兲. 9 W. G. Chace and H. K. Moore, Exploding Wires 共Plenum, New York, 1968兲, Vol. 4. 10 S. V. Lebedev and A. I. Savvatimskii, Sov. Phys. Usp. 27, 749 共1984兲. 11 M. G. Haines, S. V. Lebedev, J. P. Chittenden, F. N. Beg, S. N. Bland, and A. E. Dangor, Phys. Plasmas 7, 1672 共2000兲. 12 D. A. Hammer and D. B. Sinars, Laser Part. Beams 19, 377 共2001兲. 13 S. A. Chaikovsky, V. I. Oreshkin, G. A. Mesyats, N. A. Ratakhin, I. M. Datsko, and B. A. Kablambaev, Phys. Plasmas 16, 042701 共2009兲. 14 I. R. Lindemuth, R. E. Reinovsky, R. E. Chrien, J. M. Christian, C. A. Ekdahl, J. H. Goforth, R. C. Haight, G. Idzorek, N. S. King, R. C. Kirkpatrick, R. E. Larson, G. L. Morgan, B. W. Olinger, H. Oona, P. T. Sheehey, J. S. Shlachter, R. C. Smith, L. R. Veeser, B. J. Warthen, S. M. Younger, V. K. Chernyshev, V. N. Mokhov, A. N. Demin, Y. N. Dolin, S. F. Garanin, V. A. Ivanov, V. P. Korchagin, O. D. Mikhailov, I. V. Morozov, S. V. Pak, E. S. Pavlovskii, N. Y. Seleznev, A. N. Skobelev, G. I. Volkov, and V. A. Yakubov, Phys. Rev. Lett. 75, 1953 共1995兲. 15 P. J. Turchi, IEEE Trans. Plasma Sci. 28, 1414 共2000兲. 16 R. E. Siemon, B. S. Bauer, T. J. Awe, M. A. Angelova, S. Fuelling, T. Goodrich, I. R. Lindemuth, V. Makhin, W. L. Atchison, R. J. Faehl, R. E. Reinovsky, P. J. Turchi, J. H. Degnan, E. L. Ruden, M. H. Frese, S. F. Garanin, and V. N. Mokhov, J. Fusion Energy 27, 235 共2008兲. 17 P. V. Subhash, S. Madhavan, and S. Chaturvedi, Phys. Plasmas 13, 072507 共2006兲. 18 S. F. Garanin, G. G. Ivanova, D. V. Karmishin, and V. N. Sofronov, J. Appl. Mech. Tech. Phys. 46, 153 共2005兲. 19 R. Z. Lyudaev, Proceedings of the 7th International Conference on MG Field Generation and Related Topics, 1997, Vol. 1, p. 86.

102507-11 20


V. Makhin, B. S. Bauer, T. J. Awe, S. Fuelling, T. Goodrich, I. R. Lindemuth, R. E. Siemon, and S. F. Garanin, J. Fusion Energy 26, 109 共2007兲. 21 S. Fuelling, T. J. Awe, B. S. Bauer, T. Goodrich, I. R. Lindemuth, V. Makhin, R. E. Siemon, W. L. Atchison, R. E. Reinovsky, and M. A. Salazar, J. Fusion Energy 26, 47 共2007兲. 22 T. J. Awe, B. S. Bauer, S. Fuelling, and R. E. Siemon, Phys. Rev. Lett. 104, 035001 共2010兲. 23 B. S. Bauer, V. L. Kantsyrev, F. Winterberg, A. S. Shlyaptseva, R. C. Mancini, H. Li, and A. Oxner, Proceedings of the 4th International Conference on Dense Z-Pinches, 1997, Vol. 409, p. 153. 24 B. S. Bauer, V. L. Kantsyrev, N. Le Galloudec, R. Presura, G. S. Sarkisov, A. S. Shlyaptseva, S. Batie, W. Brinsmead, H. Faretto, B. Le Galloudec, A. Oxner, M. Al-Shorman, D. A. Fedin, S. Hansen, I. Paraschiv, H. Zheng, D. McCrorey, J. W. Farley, J. Glassman, and J. S. De Groot, Proceedings of the 12th International Pulsed Power Conference, 1999, Vol. 2, p. 1045. 25 S. Fuelling, T. J. Awe, B. S. Bauer, T. Goodrich, A. Haboub, V. V. Ivanov, V. Makhin, A. Oxner, R. Presura, and R. E. Siemon, IEEE Trans. Plasma Sci. 36, 62 共2008兲. 26 R. B. Spielman, T. W. Hussey, D. L. Hanson, and S. F. Lopez, Proceedings of the Fifth International Conference on Megagauss Fields and Pulsed Power Systems 共Nova Science, Commack, NY, 1990兲. 27 T. P. Intrator, R. E. Siemon, and P. E. Sieck, Phys. Plasmas 15, 042505 共2008兲. 28 C. Grabowski, D. Gale, J. Parker, D. Ralph, W. Sommars, J. Degnan, M. Domonkos, E. Ruden, W. Tucker, T. Intrator, R. Renneke, P. Turchi, B. Waganaar, G. Wurden, and S. Zhang, Proceedings of the 15th International IEEE Pulsed Power Conference, 2005, Vol. 304. 29 A. S. Chuvatin, V. L. Kantsyrev, L. I. Rudakov, M. E. Cuneo, A. L. Astanovitskiy, R. Presura, A. S. Safronova, A. A. Esaulov, W. Cline, K.

Phys. Plasmas 17, 102507 共2010兲 M. Williamson, I. Shrestha, M. F. Yilmaz, G. C. Osborne, M. Weller, T. Jarrett, B. LeGalloudec, V. Nalajala, T. D. Pointon, and K. A. Mikkelsond, Proceedings of the 7th International Conference on Dense Z-Pinches, 2009, Vol. 1088, p. 253. 30 D. J. Steinberg, S. G. Cochran, and M. W. Guinan, J. Appl. Phys. 51, 1498 共1980兲. 31 M. E. Cuneo, IEEE Trans. Dielectr. Electr. Insul. 6, 469 共1999兲. 32 S. Mazevet, M. P. Desjarlais, L. A. Collins, J. D. Kress, and N. H. Magee, Phys. Rev. E 71, 016409 共2005兲. 33 F. Herlach, Rep. Prog. Phys. 31, 341 共1968兲. 34 H. Knoepfel, Pulsed High Magnetic Fields 共North-Holland, Amsterdam, 1970兲. 35 See www.nist.gov for information about the NIST Atomic Spectra Database. 36 See http://www.prism-cs.com/Software/PrismSpect/PrismSPECT.htm for for information about PrismSPECT’s spectral modeling software. 37 R. J. Goldston and P. H. Rutherford, Introduction to Plasma Physics 共IOP, London, 1995兲. 38 J. P. Chittenden, S. V. Lebedev, J. Ruiz-Camacho, F. N. Beg, S. N. Bland, C. A. Jennings, A. R. Bell, M. G. Haines, S. A. Pikuz, T. A. Shelkovenko, and D. A. Hammer, Phys. Rev. E 61, 4370 共2000兲. 39 G. S. Sarkisov, S. E. Rosenthal, K. R. Cochrane, K. W. Struve, C. Deeney, and D. H. McDaniel, Phys. Rev. E 71, 046404 共2005兲. 40 S. F. Garanin, S. D. Kuznetsov, W. L. Atchison, R. E. Reinovsky, T. J. Awe, B. S. Bauer, S. Fuelling, I. R. Lindemuth, and R. E. Siemon, IEEE Trans. Plasma Sci. 38, 1815 共2010兲. 41 V. Makhin 共private communication兲, 2008. 42 M. A. Angelova 共private communication兲, 2008. 43 I. R. Lindemuth, R. E. Siemon, B. S. Bauer, M. A. Angelova, W. L. Atchison, S. F. Garanin, and V. Makhin, Proceedings of the 17th IEEE International Pulsed Power Conference, 2009, Vol. 8, p. 193.