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We are studying the behavior of self-breaking, high-voltage water switches for the Z refurbishment project. In Z-20, three or four water switches in parallel are charged to 4 MV in /spl sim/220 ns. The water gap between switch electrodes is 13-15 cm, and the enhancement of the positive and negative electrodes is varied to study time-evolution of the breakdown arcs, current sharing, and switch simultaneity. In addition to the standard electrical diagnostics (V,I), we are looking at one or more of the switches during the breakdown phase with two optical diagnostics: a streak camera and a fast framing camera. The streak camera has /spl sim/1-ns resolution, and the framing camera provides seven frames with >5 ns exposure times. For identical electric fields, the streamers originating on the positive electrode form earlier and move more rapidly than the streamers originating on the negative electrode. We observe four distinct phases in the closure of the water switches that depend on the macroscopic electric fields in the water: 1) No streamers propagate at E-fields below /spl sim/100 kV/cm from positive electrodes or voltages below /spl sim/140 kV/cm for negative electrodes; 2) streamers propagate with constant velocity between 100 and /spl sim/300 kV/cm; 3) above 300 kV/cm, the streamer velocities become linearly proportional to the electric field; 4) above 600 kV/cm, the velocity of streamers from the negative electrodes appears to saturate at /spl sim/100 cm//spl mu/s. The velocity of the streamers from the positive electrode continues to increase with E-field, reaching /spl sim/1% of the speed of light when the switch reaches closure.

The three-dimensional, particle-in-cell code QUICKSILVER [J. P. Quintenz et al., Lasers Part. Beams 12, 283 (1994)] is now being used to simulate the inner region of the Z accelerator [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] at Sandia National Laboratories. The simulations model electron flow and anode losses in the double post-hole convolute, which couples four radial, magnetically insulated transmission lines (MITLs) in parallel to a single MITL that drives a Z-pinch load. To efficiently handle the large range in the magnetic field, 0

We describe herein a system of self-magnetically insulated vacuum transmission lines (MITLs) that operated successfully at 20 MA, 3 MV, and 55 TW. The system delivered the electromagnetic-power pulse generated by the $Z$ accelerator to a physics-package load on over 1700 $Z$ shots. The system included four levels that were electrically in parallel. Each level consisted of a water flare, vacuum-insulator stack, vacuum flare, and 1.3-m-radius conical outer MITL. The outputs of the four outer MITLs were connected in parallel by a 7.6-cm-radius 12-post double-post-hole vacuum convolute. The convolute added the currents of the four outer MITLs, and delivered the combined current to a single 6-cm-long inner MITL. The inner MITL delivered the current to the load. The total initial inductance of the stack-MITL system was 11 nH. A 300-element transmission-line-circuit model of the system has been developed using the tl code. The model accounts for the following: (i) impedance and electrical length of each of the 300 circuit elements, (ii) electron emission from MITL-cathode surfaces wherever the electric field has previously exceeded a constant threshold value, (iii) Child-Langmuir electron loss in the MITLs before magnetic insulation is established, (iv) MITL-flow-electron loss after insulation, assuming either collisionless or collisional electron flow, (v) MITL-gap closure, (vi) energy loss to MITL conductors operated at high lineal current densities, (vii) time-dependent self-consistent inductance of an imploding $z$-pinch load, and (viii) load resistance, which is assumed to be constant. Simulations performed with the tl model demonstrate that the nominal geometric outer-MITL-system impedance that optimizes overall performance is a factor of $\ensuremath{\sim}3$ greater than the convolute-load impedance, which is consistent with an analytic model of an idealized MITL-load system. Power-flow measurements demonstrate that, until peak current, the $Z$ stack-MITL system performed as expected. tl calculations of the peak electromagnetic power at the stack, stack energy, stack voltage, outer-MITL current, and load current, as well as the pinch-implosion time, agree with measurements to within 5%. After peak current, tl calculations and measurements diverge, which appears to be due in part to the idealized pinch model assumed by tl. The results presented suggest that the design of the $Z$ accelerator's stack-MITL system, and the tl model, can serve as starting points for the design of stack-MITL systems of future superpower accelerators.

We have conducted dielectric-breakdown tests on water subject to a single unipolar pulse. The peak voltages used for the tests range from 5.8 to 6.8 MV; the effective pulse widths range from 0.60 to $1.1\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$; and the effective areas tested range from $1.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ to $3.6\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }{\mathrm{cm}}^{2}$. The tests were conducted on water-insulated coaxial capacitors. The two electrodes of each capacitor have outer and inner radii of 99 and 56 cm, respectively. Results of the tests are consistent with predictions of the water-dielectric-breakdown relation developed in [Phys. Rev. ST Accel. Beams 9, 070401 (2006)].

We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density j' � B=� 0 to be the current per unit electrode width, where B is the magnetic field at the electrode surface and � 0 is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, jB work, and the increase in the transmission line's vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current Iðt Þ¼ 0 for t< 0, and Iðt Þ/ t for t � 0; (iii) j' � 10 MA=cm; and (iv) the current-pulse width is between 50 and 300 ns. Under these con- ditions we find that, to first order, the total energy lost per unit electrode-surface area is given by Wtðt Þ¼ �tB � ðt Þþ �tB � ðtÞ, where BðtÞ is the nominal magnetic field at the surface. The quantities � , � , � , � , � , andare material constants that are determined by normalizing the expression for WtðtÞ to the results of 1D magnetohydrodynamic MACH2 simulations. For stainless-steel electrodes operated at current densities between 0.5 and 10 MA=cm, we find that � ¼ 3:36 � 10 5 , � ¼ 1=2, � ¼ 2, � ¼ 4:47 � 10 4 , � ¼ 5=4, and � ¼ 4 (in SI units). An effective time-dependent resistance, appropriate for circuit simulations of pulsed-power accelerators, is derived from WtðtÞ. Resistance-model predictions are compared to energy-loss measurements made with stainless-steel electrodes operated at peak lineal current densities as high as 12 MA=cm (and peak currents as high as 23 MA). The predictions are consistent with the measurements, to within experimental uncertainties. We also find that a previously used electrode-energy-loss model overpredicts the measurements by as much as an order of magnitude.

We have developed a system of differential-output monitors that diagnose current and voltage in the vacuum section of a 20-MA 3-MV pulsed-power accelerator. The system includes 62 gauges: 3 current and 6 voltage monitors that are fielded on each of the accelerator's 4 vacuum-insulator stacks, 6 current monitors on each of the accelerator's 4 outer magnetically insulated transmission lines (MITLs), and 2 current monitors on the accelerator's inner MITL. The inner-MITL monitors are located 6 cm from the axis of the load. Each of the stack and outer-MITL current monitors comprises two separate $B$-dot sensors, each of which consists of four 3-mm-diameter wire loops wound in series. The two sensors are separately located within adjacent cavities machined out of a single piece of copper. The high electrical conductivity of copper minimizes penetration of magnetic flux into the cavity walls, which minimizes changes in the sensitivity of the sensors on the 100-ns time scale of the accelerator's power pulse. A model of flux penetration has been developed and is used to correct (to first order) the $B$-dot signals for the penetration that does occur. The two sensors are designed to produce signals with opposite polarities; hence, each current monitor may be regarded as a single detector with differential outputs. Common-mode-noise rejection is achieved by combining these signals in a $50\mathrm{\text{\ensuremath{-}}}\ensuremath{\Omega}$ balun. The signal cables that connect the $B$-dot monitors to the balun are chosen to provide reasonable bandwidth and acceptable levels of Compton drive in the bremsstrahlung field of the accelerator. A single $50\mathrm{\text{\ensuremath{-}}}\ensuremath{\Omega}$ cable transmits the output signal of each balun to a double-wall screen room, where the signals are attenuated, digitized ($0.5\mathrm{\text{\ensuremath{-}}}\mathrm{ns}/\mathrm{sample}$), numerically compensated for cable losses, and numerically integrated. By contrast, each inner-MITL current monitor contains only a single $B$-dot sensor. These monitors are fielded in opposite-polarity pairs. The two signals from a pair are not combined in a balun; they are instead numerically processed for common-mode-noise rejection after digitization. All the current monitors are calibrated on a 76-cm-diameter axisymmetric radial transmission line that is driven by a 10-kA current pulse. The reference current is measured by a current-viewing resistor (CVR). The stack voltage monitors are also differential-output gauges, consisting of one 1.8-cm-diameter $D$-dot sensor and one null sensor. Hence, each voltage monitor is also a differential detector with two output signals, processed as described above. The voltage monitors are calibrated in situ at 1.5 MV on dedicated accelerator shots with a short-circuit load. Faraday's law of induction is used to generate the reference voltage: currents are obtained from calibrated outer-MITL $B$-dot monitors, and inductances from the system geometry. In this way, both current and voltage measurements are traceable to a single CVR. Dependable and consistent measurements are thus obtained with this system of calibrated diagnostics. On accelerator shots that deliver 22 MA to a low-impedance $z$-pinch load, the peak lineal current densities at the stack, outer-MITL, and inner-MITL monitor locations are 0.5, 1, and $58\text{ }\text{ }\mathrm{MA}/\mathrm{m}$, respectively. On such shots the peak currents measured at these three locations agree to within 1%.

We have developed an accelerator architecture that can serve as the basis of the design of petawatt-class $z$-pinch drivers. The architecture has been applied to the design of two $z$-pinch accelerators, each of which can be contained within a 104-m-diameter cylindrical tank. One accelerator is driven by slow ($\ensuremath{\sim}1\text{ }\ensuremath{\mu}\mathrm{s}$) Marx generators, which are a mature technology but which necessitate significant pulse compression to achieve the short pulses ($\ensuremath{\ll}1\text{ }\ensuremath{\mu}\mathrm{s}$) required to drive $z$ pinches. The other is powered by linear transformer drivers (LTDs), which are less mature but produce much shorter pulses than conventional Marxes. Consequently, an LTD-driven accelerator promises to be (at a given pinch current and implosion time) more efficient and reliable. The Marx-driven accelerator produces a peak electrical power of 500 TW and includes the following components: (i) 300 Marx generators that comprise a total of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ capacitors, store 98 MJ, and erect to 5 MV; (ii) 600 water-dielectric triplate intermediate-store transmission lines, which also serve as pulse-forming lines; (iii) 600 5-MV laser-triggered gas switches; (iv) three monolithic radial-transmission-line impedance transformers, with triplate geometries and exponential impedance profiles; (v) a 6-level 5.5-m-diameter 15-MV vacuum insulator stack; (vi) six magnetically insulated vacuum transmission lines (MITLs); and (vii) a triple-post-hole vacuum convolute that adds the output currents of the six MITLs, and delivers the combined current to a $z$-pinch load. The accelerator delivers an effective peak current of 52 MA to a 10-mm-length $z$ pinch that implodes in 95 ns, and 57 MA to a pinch that implodes in 120 ns. The LTD-driven accelerator includes monolithic radial transformers and a MITL system similar to those described above, but does not include intermediate-store transmission lines, multimegavolt gas switches, or a laser trigger system. Instead, this accelerator is driven by 210 LTD modules that include a total of $1\ifmmode\times\else\texttimes\fi{}{10}^{6}$ capacitors and $5\ifmmode\times\else\texttimes\fi{}{10}^{5}$ 200-kV electrically triggered gas switches. The LTD accelerator stores 182 MJ and produces a peak electrical power of 1000 TW. The accelerator delivers an effective peak current of 68 MA to a pinch that implodes in 95 ns, and 75 MA to a pinch that implodes in 120 ns. Conceptually straightforward upgrades to these designs would deliver even higher pinch currents and faster implosions.

We have developed a diagnostic system that measures the spectrally integrated (i.e. the total) energy and power radiated by a pulsed blackbody x-ray source. The total-energy-and-power (TEP) diagnostic system is optimized for blackbody temperatures between 50 and 350 eV. The system can view apertured sources that radiate energies and powers as high as 2 MJ and 200 TW, respectively, and has been successfully tested at 0.84 MJ and 73 TW on the $Z$ pulsed-power accelerator. The TEP system consists of two pinhole arrays, two silicon-diode detectors, and two thin-film nickel bolometers. Each of the two pinhole arrays is paired with a single silicon diode. Each array consists of a $38\ifmmode\times\else\texttimes\fi{}38$ square array of 10-$\ensuremath{\mu}\mathrm{m}$-diameter pinholes in a 50-$\ensuremath{\mu}\mathrm{m}$-thick tantalum plate. The arrays achromatically attenuate the x-ray flux by a factor of $\ensuremath{\sim}1800$. The use of such arrays for the attenuation of soft x rays was first proposed by Turner and co-workers [Rev. Sci. Instrum. 70, 656 (1999)]. The attenuated flux from each array illuminates its associated diode; the diode's output current is recorded by a data-acquisition system with 0.6-ns time resolution. The arrays and diodes are located 19 and 24 m from the source, respectively. Because the diodes are designed to have an approximately flat spectral sensitivity, the output current from each diode is proportional to the x-ray power. The nickel bolometers are fielded at a slightly different angle from the array-diode combinations, and view (without pinhole attenuation) the same x-ray source. The bolometers measure the total x-ray energy radiated by the source and---on every shot---provide an in situ calibration of the array-diode combinations. Two array-diode pairs and two bolometers are fielded to reduce random uncertainties. An analytic model (which accounts for pinhole-diffraction effects) of the sensitivity of an array-diode combination is presented.

We have developed a relativistic-fluid model of the flow-electron plasma in a steady-state one-dimensional magnetically insulated transmission line (MITL). The model assumes that the electrons are collisional and, as a result, drift toward the anode. The model predicts that in the limit of fully developed collisional flow, the relation between the voltage ${V}_{a}$, anode current ${I}_{a}$, cathode current ${I}_{k}$, and geometric impedance ${Z}_{0}$ of a 1D planar MITL can be expressed as ${V}_{a}={I}_{a}{Z}_{0}h(\ensuremath{\chi})$, where $h(\ensuremath{\chi})\ensuremath{\equiv}[(\ensuremath{\chi}+1)/4(\ensuremath{\chi}\ensuremath{-}1){]}^{1/2}\ensuremath{-}\mathrm{ln} \ensuremath{\lfloor}\ensuremath{\chi}+({\ensuremath{\chi}}^{2}\ensuremath{-}1{)}^{1/2}\ensuremath{\rfloor}/2\ensuremath{\chi}(\ensuremath{\chi}\ensuremath{-}1)$ and $\ensuremath{\chi}\ensuremath{\equiv}{I}_{a}/{I}_{k}$. The relation is valid when ${V}_{a}\ensuremath{\gtrsim}1\text{ }\mathrm{MV}$. In the minimally insulated limit, the anode current ${I}_{a,\mathrm{min} }=1.78{V}_{a}/{Z}_{0}$, the electron-flow current ${I}_{f,\mathrm{min} }=1.25{V}_{a}/{Z}_{0}$, and the flow impedance ${Z}_{f,\mathrm{min} }=0.588{Z}_{0}$. {The electron-flow current ${I}_{f}\ensuremath{\equiv}{I}_{a}\ensuremath{-}{I}_{k}$. Following Mendel and Rosenthal [Phys. Plasmas 2, 1332 (1995)], we define the flow impedance ${Z}_{f}$ as ${V}_{a}/({I}_{a}^{2}\ensuremath{-}{I}_{k}^{2}{)}^{1/2}$.} In the well-insulated limit (i.e., when ${I}_{a}\ensuremath{\gg}{I}_{a,\mathrm{min} }$), the electron-flow current ${I}_{f}=9{V}_{a}^{2}/8{I}_{a}{Z}_{0}^{2}$ and the flow impedance ${Z}_{f}=2{Z}_{0}/3$. Similar results are obtained for a 1D collisional MITL with coaxial cylindrical electrodes, when the inner conductor is at a negative potential with respect to the outer, and ${Z}_{0}\ensuremath{\lesssim}40\text{ }\ensuremath{\Omega}$. We compare the predictions of the collisional model to those of several MITL models that assume the flow electrons are collisionless. We find that at given values of ${V}_{a}$ and ${Z}_{0}$, collisions can significantly increase both ${I}_{a,\mathrm{min} }$ and ${I}_{f,\mathrm{min} }$ above the values predicted by the collisionless models, and decrease ${Z}_{f,\mathrm{min} }$. When ${I}_{a}\ensuremath{\gg}{I}_{a,\mathrm{min} }$, we find that, at given values of ${V}_{a}$, ${Z}_{0}$, and ${I}_{a}$, collisions can significantly increase ${I}_{f}$ and decrease ${Z}_{f}$. Since the steady-state collisional model is valid only when the drift of electrons toward the anode has had sufficient time to establish fully developed collisional flow, and collisionless models assume there is no net electron drift toward the anode, we expect these two types of models to provide theoretical bounds on ${I}_{a}$, ${I}_{f}$, and ${Z}_{f}$.

We have developed an empirical electrical-breakdown relation that can be used to design large-area water-insulated pulsed-power systems. Such systems often form an integral part of multiterawatt pulsed-power accelerators, and may be incorporated in future petawatt-class machines. We find that complete dielectric failure is likely to occur in water between a significantly field-enhanced anode and a less-enhanced cathode when E_{p}τ_{eff}^{0.330±0.026}=0.135±0.009. In this expression E_{p}≡V_{p}/d is the peak value in time of the spatially averaged electric field between the anode and cathode (in MV/cm), V_{p} is the peak voltage across the electrodes, d is the distance between the anode and cathode, and τ_{eff} is the temporal width (in μs) of the voltage pulse at 63% of peak. This relation is based on 25 measurements for which 1≤V_{p}≤4.10 MV, 1.25≤d≤22 cm, and 0.011≤τ_{eff}≤0.6 μs. The normalized standard deviation of the differences between these measurements and the associated predictions of the relation is 12%.

We have developed wire-array $z$-pinch scaling relations for plasma-physics and inertial-confinement-fusion (ICF) experiments. The relations can be applied to the design of $z$-pinch accelerators for high-fusion-yield $(\ensuremath{\sim}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{GJ∕shot})$ and inertial-fusion-energy $(\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\mathrm{GJ∕shot})$ research. We find that $({\ensuremath{\delta}}_{a}∕{\ensuremath{\delta}}_{\mathrm{RT}})\ensuremath{\propto}{(m∕\ensuremath{\ell})}^{1∕4}{(R\ensuremath{\Gamma})}^{\ensuremath{-}1∕2}$, where ${\ensuremath{\delta}}_{a}$ is the imploding-sheath thickness of a wire-ablation-dominated pinch, ${\ensuremath{\delta}}_{\mathrm{RT}}$ is the sheath thickness of a Rayleigh-Taylor-dominated pinch, $m$ is the total wire-array mass, $\ensuremath{\ell}$ is the axial length of the array, $R$ is the initial array radius, and $\ensuremath{\Gamma}$ is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product $R\ensuremath{\Gamma}$ is held constant the sheath thickness is, at sufficiently large values of $m∕\ensuremath{\ell}$, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power ${P}_{r}\ensuremath{\propto}{(I∕{\ensuremath{\tau}}_{i})}^{3∕2}R\ensuremath{\ell}\ensuremath{\Phi}\ensuremath{\Gamma}$, where $I$ is the peak pinch current, ${\ensuremath{\tau}}_{i}$ is the pinch implosion time, and $\ensuremath{\Phi}$ is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when $13\phantom{\rule{0.3em}{0ex}}\mathrm{MA}\ensuremath{\leqslant}I\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{MA}$, $93\phantom{\rule{0.3em}{0ex}}\mathrm{ns}\ensuremath{\leqslant}{\ensuremath{\tau}}_{i}\ensuremath{\leqslant}169\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, $10\phantom{\rule{0.3em}{0ex}}\mathrm{mm}\ensuremath{\leqslant}R\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$, $10\phantom{\rule{0.3em}{0ex}}\mathrm{mm}\ensuremath{\leqslant}\ensuremath{\ell}\ensuremath{\leqslant}20\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$, and $2.0\phantom{\rule{0.3em}{0ex}}\mathrm{mg}∕\mathrm{cm}\ensuremath{\leqslant}m∕\ensuremath{\ell}\ensuremath{\leqslant}7.3\phantom{\rule{0.3em}{0ex}}\mathrm{mg}∕\mathrm{cm}$. Assuming an ablation-dominated pinch and that $R\ensuremath{\ell}\ensuremath{\Phi}\ensuremath{\Gamma}$ is held constant, we find that the x-ray-power efficiency ${\ensuremath{\eta}}_{x}\ensuremath{\equiv}{P}_{r}∕{P}_{a}$ of a coupled pinch-accelerator system is proportional to ${({\ensuremath{\tau}}_{i}{P}_{r}^{7∕9})}^{\ensuremath{-}1}$, where ${P}_{a}$ is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of ${P}_{r}$ are proportional to ${\ensuremath{\tau}}_{i}$, and the requisite accelerator energy ${E}_{a}$ is proportional to ${\ensuremath{\tau}}_{i}^{2}$. These results suggest that the performance of an ablation-dominated pinch, and the efficiency of a coupled pinch-accelerator system, can be improved substantially by decreasing the implosion time ${\ensuremath{\tau}}_{i}$. For an accelerator coupled to a double-pinch-driven hohlraum that drives the implosion of an ICF fuel capsule, we find that the accelerator power and energy required to achieve high-yield fusion scale as ${\ensuremath{\tau}}_{i}^{0.36}$ and ${\ensuremath{\tau}}_{i}^{1.36}$, respectively. Thus the accelerator requirements decrease as the implosion time is decreased. However, the x-ray-power and thermonuclear-yield efficiencies of such a coupled system increase with ${\ensuremath{\tau}}_{i}$. We also find that increasing the anode-cathode gap of the pinch from $2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ increases the requisite values of ${P}_{a}$ and ${E}_{a}$ by as much as a factor of 2.

Experiments on a large, high voltage pulsed insulator will be described. The goal was investigation of the effect of the self-magnetic field associated with current flow toward the load, on the insulator voltage hold-off capability. In principle, the self-magnetic field could improve insulator hold-off by deflecting electrons away from the insulator surface. However, it appears that no controlled experiments have been done to measure the effect of magnetic flashover-inhibition (MFI) on a 45-degree insulator. Most modern insulator stacks, including the one used here, have the insulators at 45 degrees to the power flow direction, often with reduced electric field at the cathode triple point. Results from the experiments presented in this paper do not show a significant beneficial effect from current flow in this situation. This paper will also show calculations on the effect of magnetic field on electrons emitted from the capacitively- coupled grading rings in the insulator stack

We have conducted a series of experiments designed to measure the flashover strength of various azimuthally symmetric $45\ifmmode^\circ\else\textdegree\fi{}$ vacuum-insulator configurations. The principal objective of the experiments was to identify a configuration with a flashover strength greater than that of the standard design, which consists of a $45\ifmmode^\circ\else\textdegree\fi{}$ polymethyl-methacrylate (PMMA) insulator between flat electrodes. The thickness $d$ and circumference $C$ of the insulators tested were held constant at 4.318 and 95.74 cm, respectively. The peak voltage applied to the insulators ranged from 0.8 to 2.2 MV. The rise time of the voltage pulse was 40--60 ns; the effective pulse width [as defined in Phys. Rev. ST Accel. Beams 7, 070401 (2004)] was on the order of 10 ns. Experiments conducted with flat aluminum electrodes demonstrate that the flashover strength of a crosslinked polystyrene (Rexolite) insulator is $(18\ifmmode\pm\else\textpm\fi{}7)%$ higher than that of PMMA. Experiments conducted with a Rexolite insulator and an anode plug, i.e., an extension of the anode into the insulator, demonstrate that a plug can increase the flashover strength by an additional $(44\ifmmode\pm\else\textpm\fi{}11)%$. The results are consistent with the Anderson model of anode-initiated flashover, and confirm previous measurements. It appears that a Rexolite insulator with an anode plug can, in principle, increase the peak electromagnetic power that can be transmitted across a vacuum interface by a factor of $[(1.18)(1.44){]}^{2}=2.9$ over that which can be achieved with the standard design.

A large-aperture (30-cm) kilojoule-class Nd:glass laser system known as Z-Beamlet has been constructed to perform x-ray radiography of high-energy-density science experiments conducted on the Z facility at Sandia National Laboratories, Albuquerque, New Mexico. The laser, operating with typical pulse durations from 0.3 to 1.5 ns, employs a sequence of successively larger multipass amplifiers to achieve up to 3-kJ energy at 1054 nm. Large-aperture frequency conversion and long-distance beam transport can provide on-target energies of up to 1.5 kJ at 527 nm.

Aluminum and stainless steel electrodes with dielectric surface layers have been tested for the avoidance of electron emission and plasma induced arcs that limit high voltage hold-off. The aluminum dielectric coating is a 50-/spl mu/m-thick hard-anodized surface layer. Tests of the layer were made with and without a chemical etch to improve bonding to the machined aluminum. The coating on stainless steel is a 1-/spl mu/m-thick chromium oxide surface layer formed during high humidity hydrogen firing. Tests were performed on 15 and 17-cm-diameter electrodes, with 1.8 to 6 mm gaps. Tests were made with a 150 to 500 kV, 160-ns-FWHM waveform, with 1-cos(/spl omega/)t) shape. The electrodes were cleaned with acetone and installed into the vacuum chamber in a filtered clean air environment with

We have developed a statistical model for the flashover of a $45\ifmmode^\circ\else\textdegree\fi{}$ vacuum-insulator interface (such as would be found in an accelerator) subject to a pulsed electric field. The model assumes that the initiation of a flashover plasma is a stochastic process, that the characteristic statistical component of the flashover delay time is much greater than the plasma formative time, and that the average rate at which flashovers occur is a power-law function of the instantaneous value of the electric field. Under these conditions, we find that the flashover probability is given by $1\ensuremath{-}\mathrm{exp}(\ensuremath{-}{E}_{p}^{\ensuremath{\beta}}{t}_{\mathrm{eff}}C/{k}^{\ensuremath{\beta}})$, where ${E}_{p}$ is the peak value in time of the spatially averaged electric field $E(t)$, ${t}_{\mathrm{eff}}\ensuremath{\equiv}\ensuremath{\int}[E(t)/{E}_{p}{]}^{\ensuremath{\beta}}dt$ is the effective pulse width, $C$ is the insulator circumference, $k\ensuremath{\propto}\mathrm{exp}(\ensuremath{\lambda}/d)$, and $\ensuremath{\beta}$ and $\ensuremath{\lambda}$ are constants. We define $E(t)$ as $V(t)/d$, where $V(t)$ is the voltage across the insulator and $d$ is the insulator thickness. Since the model assumes that flashovers occur at random azimuthal locations along the insulator, it does not apply to systems that have a significant defect, i.e., a location contaminated with debris or compromised by an imperfection at which flashovers repeatedly take place, and which prevents a random spatial distribution. The model is consistent with flashover measurements to within 7% for pulse widths between 0.5 ns and $10\text{ }\ensuremath{\mu}\mathrm{s}$, and to within a factor of 2 between 0.5 ns and 90 s (a span of over 11 orders of magnitude). For these measurements, ${E}_{p}$ ranges from 64 to $651\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$, $d$ from 0.50 to 4.32 cm, and $C$ from 4.96 to 95.74 cm. The model is significantly more accurate, and is valid over a wider range of parameters, than the J. C. Martin flashover relation that has been in use since 1971 [J. C. Martin on Pulsed Power, edited by T. H. Martin, A. H. Guenther, and M. Kristiansen (Plenum, New York, 1996)]. We have generalized the statistical model to estimate the total-flashover probability of an insulator stack (i.e., an assembly of insulator-electrode systems connected in series). The expression obtained is consistent with the measured flashover performance of a stack of five 5.72-cm-thick, 1003-cm-circumference insulators operated at 100 and $158\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$. The expression predicts that the total-flashover probability is a strong function of the ratio ${E}_{p}/k$, and that under certain conditions, the performance improves as the capacitance between the stack grading rings is increased. In addition, the expression suggests that given a fixed stack height, there exists an optimum number of insulator rings that maximizes the voltage at which the stack can be operated. The results presented can be applied to any system (or any set of systems connected in series) subject to random failures, when the characteristic statistical delay time of a failure is much greater than its formative time.

We have measured the x-ray power and energy radiated by a tungsten-wire-array $z$ pinch as a function of the peak pinch current and the width of the anode-cathode gap at the base of the pinch. The measurements were performed at 13- and 19-MA currents and 1-, 2-, 3-, and 4-mm gaps. The wire material, number of wires, wire-array diameter, wire-array length, wire-array-electrode design, normalized-pinch-current time history, implosion time, and diagnostic package were held constant for the experiments. To keep the implosion time constant, the mass of the array was increased as ${I}^{2}$ (i.e., the diameter of each wire was increased as $I),$ where $I$ is the peak pinch current. At 19 MA, the mass of the 300-wire 20-mm-diam 10-mm-length array was 5.9 mg. For the configuration studied, we find that to eliminate the effects of gap closure on the radiated energy, the width of the gap must be increased approximately as $I.$ For shots unaffected by gap closure, we find that the peak radiated x-ray power ${P}_{r}\ensuremath{\propto}{I}^{1.24\ifmmode\pm\else\textpm\fi{}0.18},$ the total radiated x-ray energy ${E}_{r}\ensuremath{\propto}{I}^{1.73\ifmmode\pm\else\textpm\fi{}0.18},$ the x-ray-power rise time ${\ensuremath{\tau}}_{r}\ensuremath{\propto}{I}^{0.39\ifmmode\pm\else\textpm\fi{}0.34},$ and the x-ray-power pulse width ${\ensuremath{\tau}}_{w}\ensuremath{\propto}{I}^{0.45\ifmmode\pm\else\textpm\fi{}0.17}.$ Calculations performed with a time-dependent model of an optically thick pinch at stagnation demonstrate that the internal energy and radiative opacity of the pinch are not responsible for the observed subquadratic power scaling. Heuristic wire-ablation arguments suggest that quadratic power scaling will be achieved if the implosion time ${\ensuremath{\tau}}_{i}$ is scaled as ${I}^{\ensuremath{-}1/3}.$ The measured 1\ensuremath{\sigma} shot-to-shot fluctuations in ${P}_{r},$ ${E}_{r},$ ${\ensuremath{\tau}}_{r},$ ${\ensuremath{\tau}}_{w},$ and ${\ensuremath{\tau}}_{i}$ are approximately 12%, 9%, 26%, 9%, and 2%, respectively, assuming that the fluctuations are independent of $I.$ These variations are for one-half of the pinch. If the half observed radiates in a manner that is statistically independent of the other half, the variations are a factor of ${2}^{1/2}$ less for the entire pinch. We calculate the effect that shot-to-shot fluctuations of a single pinch would have on the shot-success probability of the double-pinch inertial-confinement-fusion driver proposed by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. We find that on a given shot, the probability that two independent pinches would radiate the same peak power to within a factor of $1\ifmmode\pm\else\textpm\fi{}\ensuremath{\alpha}$ (where $0l~\ensuremath{\alpha}\ensuremath{\ll}1)$ is equal to $\mathrm{erf}(\ensuremath{\alpha}/2\ensuremath{\sigma}),$ where \ensuremath{\sigma} is the 1\ensuremath{\sigma} fractional variation of the peak power radiated by a single pinch. Assuming \ensuremath{\alpha} must be $l~7%$ to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, \ensuremath{\sigma} must be $l3%$ for the shot-success probability to be $g~90%.$ The observed ${(12/2}^{1/2})%=8.5%$ fluctuation in ${P}_{r}$ would provide adequate symmetry on 44% of the shots. We propose that three-dimensional radiative-magnetohydrodynamic simulations be performed to quantify the sensitivity of the x-ray emission to various initial conditions, and to determine whether an imploding $z$ pinch is a spatiotemporal chaotic system.

This research consisted of testing surface treatment processes for stainless steel and aluminum for the purpose of suppressing electron emission over large surface areas to improve the pulsed high voltage hold-off capabilities of these metals. Improvements to hold-off would be beneficial to the operation of the vacuum-insulator grading rings and final self-magnetically insulated transmission line on the ZR-upgrade machine and other pulsed power applications such as flash radiograph and pulsed-microwave machines. The treatments tested for stainless steel include the Z-protocol (chemical polish, HVFF, and gold coating), pulsed E-beam surface treatments by IHCE, Russia, and chromium oxide coatings. Treatments for aluminum were anodized and polymer coatings. Breakdown thresholds also were measured for a range of surface finishes and gap distances. The study found that: (1.) Electrical conditioning and solvent cleaning in a filtered air environment each improve HV hold-off 30%. (2.) Anodized coatings on aluminum give a factor of two improvement in high voltage hold-off. However, anodized aluminum loses this improvement when the damage is severe. Chromium oxide coatings on stainless steel give a 40% and 20% improvement in hold-off before and after damage from many arcs. (3.) Bare aluminum gives similar hold-off for surface roughness, R{sub a}, ranging from 0.08more » to 3.2 {micro}m. (4.) The various EBEST surfaces tested give high voltage hold-off a factor of two better than typical machined and similar to R{sub a} = 0.05 {micro}m polished stainless steel surfaces. (5.) For gaps > 2 mm the hold-off voltage increases as the square root of the gap for bare metal surfaces. This is inconsistent with the accepted model for metals that involves E-field induced electron emission from dielectric inclusions. Micro-particles accelerated across the gap during the voltage pulse give the observed voltage dependence. However the similarity in observed breakdown times for large and small gaps places a requirement that the particles be of molecular size. This makes accelerated micro-particle induced breakdown seem improbable also.« less

We have measured the x-ray power and energy radiated by a tungsten-wire-array z pinch as a function of the peak pinch current and the width of the anode-cathode gap at the base of the pinch. The measurements were performed at 13- and 19-MA currents and 1-, 2-, 3-, and 4-mm gaps. The wire material, number of wires, wire-array diameter, wire-array length, wire-array-electrode design, normalized-pinch-current time history, implosion time, and diagnostic package were held constant for the experiments. To keep the implosion time constant, the mass of the array was increased as I2 (i.e., the diameter of each wire was increased as I), where I is the peak pinch current. At 19 MA, the mass of the 300-wire 20-mm-diam 10-mm-length array was 5.9 mg. For the configuration studied, we find that to eliminate the effects of gap closure on the radiated energy, the width of the gap must be increased approximately as I. For shots unaffected by gap closure, we find that the peak radiated x-ray power P(r) proportional to I1.24+/-0.18, the total radiated x-ray energy E(r) proportional to I1.73+/-0.18, the x-ray-power rise time tau(r) proportional to I0.39+/-0.34, and the x-ray-power pulse width tau(w) proportional to demonstrate that the internal energy and radiative opacity of the pinch are not responsible for the observed subquadratic power scaling. Heuristic wire-ablation arguments suggest that quadratic power scaling will be achieved if the implosion time tau(i) is scaled as I(-1/3). The measured 1sigma shot-to-shot fluctuations in P(r), E(r), tau(r), tau(w), and tau(i) are approximately 12%, 9%, 26%, 9%, and 2%, respectively, assuming that the fluctuations are independent of I. These variations are for one-half of the pinch. If the half observed radiates in a manner that is statistically independent of the other half, the variations are a factor of 2(1/2) less for the entire pinch. We calculate the effect that shot-to-shot fluctuations of a single pinch would have on the shot-success probability of the double-pinch inertial-confinement-fusion driver proposed by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. We find that on a given shot, the probability that two independent pinches would radiate the same peak power to within a factor of 1+/-alpha (where 0or =alpha1) is equal to erf(alpha/2sigma), where sigma is the 1sigma fractional variation of the peak power radiated by a single pinch. Assuming alpha must beor =7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, sigma must be3% for the shot-success probability to beor =90%. The observed (12/2(1/2))%=8.5% fluctuation in P(r) would provide adequate symmetry on 44% of the shots. We propose that three-dimensional radiative-magnetohydrodynamic simulations be performed to quantify the sensitivity of the x-ray emission to various initial conditions, and to determine whether an imploding z pinch is a spatiotemporal chaotic system.

We have demonstrated operation of a 3.35-m-diameter insulator stack at 158 kV/cm with no total-stack flashovers on five consecutive Z-accelerator shots. The stack consisted of five +45/spl deg/-profile 5.715-cm-thick crosslinked-polystyrene (Rexolite-1422) insulator rings, and four anodized-aluminum grading rings shaped to reduce the field at cathode triple junctions. The width of the voltage pulse at 89% of peak was 32 ns. We compare this result to a new empirical flashover relation developed from previous small-insulator experiments conducted with flat unanodized electrodes. The relation predicts a 50% flashover probability for a Rexolite insulator during an applied voltage pulse when E/sub max/e/sup -0.27/d/(t/sub eff/C)/sup 1/10/=224, where E/sub max/ is the peak mean electric field (kV/cm), d is the insulator thickness (cm), t/sub eff/ is the effective pulse width (/spl mu/s), and C is the insulator circumference (cm). We find the Z stack can be operated at a stress at least 19% higher than predicted. This result, together with previous experiments conducted by Vogtlin, suggest anodized electrodes with geometries that reduce the field at both anode and cathode triple junctions would improve the flashover strength of multi-stage insulator stacks.

A 3.3 m diameter cylindrical insulator stack and a set of 3 m diameter conical magnetically-insulated transmission lines (MITLs) were built for the Z accelerator. The 1.7 m tall stack operates at /spl sim/20 MA and 2.5-3.5 MV, and was instrumented with 12 current and 24 voltage monitors. The stack was designed to provide vertical stability for the MITLs and to resist radial buckling. The 22 crosslinked polystyrene insulators, 18 grading rings, 3 anode rings, and 2 cathode rings of the stack were concentrically and azimuthally aligned within /spl plusmn/0.75 mm. 2-D and 3-D static finite element analyses (FEA) were used in designing the MITLs to limit gravity deflections to less than 0.25 mm 2-D FEA dynamic analyses were done to predict motion and to help design features to restrict damage. The tapered MITLs are supported by the stack electrode rings so that the gaps at small radius are adjustable from 0 to 22 mm. The MITL anodes were instrumented with 24 current monitors and have 48 additional diagnostic locations available. The MITLs were fabricated from 304L stainless steel except the outer anode sections, which were made from 6061-T6 aluminum alloy. Fabrication procedures were developed for the large and small diameter MITL cones, as well as for the stack electrode and grading rings. The power-flow surfaces were successfully machined to within /spl plusmn/0.25 mm of the specified contours. A large, multi-trolley MITL handling system was designed to allow for removal, cleaning and replacement of the MITLs for each shot, at a shot rate of 1.5 shots/day. Additional equipment allows for cleaning of the insulators.

Sandia has developed PBFA-Z, a 20-MA driver for z-pinch experiments by replacing the water lines, insulator stack, and MITLs on PBFA II with hardware of a new design. The PBFA-Z accelerator was designed to deliver 20 MA to a 15-mg z-pinch load in 100 ns. The accelerator was modeled using circuit codes to determine the time-dependent voltage and current waveforms at the input and output of the water lines, the insulator stack, and the MITLs. The design of the vacuum insulator stack was dictated by the drive voltage, the electric field stress and grading requirements, the water line and MITL interface requirements, and the machine operations and maintenance requirements. The insulator stack consists of four separate modules, each of a different design because of different voltage drive and hardware interface requirements. The shape of the components in each module, i.e., grading rings, insulator rings, flux excluders, anode and cathode conductors, and the design of the water line and MITL interfaces, were optimized by using the electrostatic analysis codes, ELECTRO and JASON. The time-dependent performance of the insulator stacks was evaluated using IVORY, a 2-D PIC code. This paper describes the insulator stack design, presents the results of the ELECTRO and IVORY analyses, and show the results of the stack measurements.

Circuit code simulations were used to predict the performance of and to assess design trade-offs for the vacuum section of PBFA-Z. PBFA-Z was designed to drive a plasma radiation source (PRS) within the PBFA-II facility by replacing its central water and vacuum sections. The insulator stack and vacuum feeds were patterned after those of the SATURN PRS configuration which has 4 separate sources combined in vacuum by a relatively small diameter double post hole convolute (DPHC). The design method for choosing the PBFA-Z MITL impedance profiles is described and represents a departure from the method used for PROTO-II and SATURN and was motivated by analysis of SATURN experimental data. Other trade studies included the effect of MITL impedance profile on anode dose along the MITL due to partial magnetic insulation at early times and during the load run-in, and the choice of load diameter and mass on the choice of MITL profiles. These simulations predicted peak load currents ranging from 16 to 23 MA and kinetic energies from 1 to 1.6 MJ for plasma radiation sources (PRS) with implosion times from 100 to 150 ns. PBFA-Z experimental data is compared with an "as built" circuit model for a wire array load with good agreement up to the time of peak load current. A significant disagreement between the data and the model then starts and increases until the time of implosion.

The authors have designed and tested a 10 nH, 1.5 m radius vacuum section for the Z accelerator. The vacuum section consists of four vacuum flares, four conical 1.3 m radius magnetically-insulated transmission lines (MITLs), a 7.6 cm radius 12-post double-post-hole convolute which connects the four outer MITLs in parallel, and a 5 cm long inner MITL which connects the output of the convolute to a z-pinch load. The authors have demonstrated they can deliver a 100 ns rise-time 20 MA current pulse to the baseline z-pinch load. They can reproduce the peak MITL current to within /spl plusmn/1.6%. Power-flow measurements indicate the vacuum section performs as expected until peak current. Afterward, measurements and simulation results diverge.

A new set of bi-plate transmission lines have been designed and installed in the water-section of PBFA-lI for the Z-pinch experiments. Thirty-six aluminum flat-plate transmission lines submerged in a water dielectric deliver a timed electrical pulse from coaxial tube sections to a ring stack section. Each of the lines are electrically isolated from each other by transit-time effects. The water-lines are configured radially at four vertical levels. Each level has nine sets of bi-plates, with a transition section that is unique to that level. Mechanically, the bi-plate sections are designed to carry both static and dynamic loads. Electrically, the lines are designed to transport electrical pulses that average 200 nanoseconds with peak voltage of 2.5 to 3.0 MV. The peak fields exceed 200 kV/cm. All line sections are a series of chromate coated aluminum plates, broken down into short, light weight sections. The design of the plates was meticulously developed using the Electro code for voltage breakdown, and NISA for mechanical analysis. Electrical losses associated with impedance mismatching and voltage breakdown were carefully reviewed. Changes in the bi-plate gap, surface shapes and electrical path discontinuities (mechanical joints) were precisely calculated to achieve maximum electrical performance and reliability. Several iterations of surface shapes and line gaps were reviewed to achieve the most desirable characteristics possible. Additional criteria required that minimal time and effort be required to remove and install the water-lines. Special hardware was developed to help meet this requirement.

Sandia National Laboratories is investigating and developing high-dose, high-brightness flash radiographic sources. We are in the process of designing; fabricating and conducting engineering tests on the next-generation magnetically immersed electron diodes. These diodes employ unique, large-bore (80–110 mm), high-field (28–45 T), cryogenically-cooled solenoid magnets to help produce an intense electron beam from a needle-like cathode “immersed” in the strong Bz field of the magnet. The diode designs and status of the engineering development are described. Later this year we plan to conduct experiments with these sources on the new Radiographic Integrated Test Stand (KITS) [1], now in operation at Sandia. In its present three-stage configuration, KITS provides a 4-MV, 150-kA, 70-ns pulse to the diode. Fully three-dimensional particle in cell LSP code [2] simulations are used to investigate relevant physics issues and the expected radiographic performance (spot size and dose) of this system. Preliminary results from these simulations are described.

ZR is a refurbished (R) version of Z aiming to improve its overall performance, reliability, precision, pulse shape tailoring and reproducibility. Z, the largest pulsed power machine at Sandia, began in December 1985 as the Particle Beam Fusion Accelerator II (PBFA II). PBFA II was modified in 1996 to a z-pinch driver by incorporating a high-current (20 MA, 2.5 MV) configuration in the inner /spl sim/ 4.5 meter section. Following its remarkable success as a z-pinch driver, PBFA II was renamed Z in 1997. Currently Z fires 170 to 180 shots a year with a peak load current of the order of 18-20 MA. The maximum z-pinch output achieved to date is 1.6 MJ, 170 TW radiated energy and power from a single 4 cm diameter, 2 cm tall array, and 215 eV temperature from a dynamic hohlraum. ZR in turn will, operating in double shift, enable 400 shots per year, deliver a peak current of 26 MA into a standard 4 m /spl times/ 2 m Z-pinch load, and should provide a total radiated X-ray energy and power of 3 MJ and 350 TW, respectively, achieve a maximum hohlraum temperature of 260 eV, and include a pulse-shaping flexibility extending from 100 s to 300 s for equation of state and isentropic compression studies. To achieve this performance ZR will incorporate substantial modifications and upgrades to Marx generator, intermediate store capacitors, gas and water switches, water transmission lines and the laser triggering system. Test beds are already in place, and the new pulsed power components are undergoing extensive evaluation. The Z refurbishment (ZR) will be operational by 2006 and cost approximately $60M.

Target diagnostics on PBFA II will include a time‐resolved x‐ray diode array, an energy‐resolved, time‐integrated x‐ray camera, and a grazing incidence spectrometer. A clean vacuum, independent of that on PBFA II, will be supplied to the detectors to maintain more reproducible calibrations. We also describe the diagnostics and outline the calculations which determined the shielding required. Based on the calculations the background due to bremsstrahlung in the least sensitive diagnostic is 12 eV/pixel. The appropriate shielding is being built to field these diagnostics.