Here Z, a 60 TW/5 MJ electrical accelerator located at Sandia National Laboratories, has been used to implode tungsten wire-array Z pinches. These arrays consisted of large numbers of tungsten wires (120–300) with wire diameters of 7.5 to 15 μm placed in a symmetric cylindrical array. The experiments used array diameters ranging from 1.75 to 4 cm and lengths from 1 to 2 cm. A 2 cm long, 4 cm diam tungsten array consisting of 240, 7.5 μm diam wires (4.1 mg mass) achieved an x-ray power of ∼200 TW and an x-ray energy of nearly 2 MJ. Spectral data suggest an optically thick, Planckian-like radiator below 1000 eV. One surprising experimental result was the observation that the total radiated x-ray energies and x-ray powers were nearly independent of pinch length. These data are compared with two-dimensional radiation magnetohydrodynamic code calculations.

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 ( 1 s) Marx generators, which are a mature technology but which necessitate significant pulse compression to achieve the short pulses ( 1 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 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 10 6 capacitors and 5 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 present observations for 20-MA wire-array z pinches of an extended wire ablation period of 57%+/-3% of the stagnation time of the array and non-thin-shell implosion trajectories. These experiments were performed with 20-mm-diam wire arrays used for the double- z -pinch inertial confinement fusion experiments [M. E. Cuneo, Phys. Rev. Lett. 88, 215004 (2002)] on the Z accelerator [R. B. Spielman, Phys. Plasmas 5, 2105 (1998)]. This array has the smallest wire-wire gaps typically used at 20 MA (209 microm ). The extended ablation period for this array indicates that two-dimensional (r-z) thin-shell implosion models that implicitly assume wire ablation and wire-to-wire merger into a shell on a rapid time scale compared to wire acceleration are fundamentally incorrect or incomplete for high-wire-number, massive (>2 mg/cm) , single, tungsten wire arrays. In contrast to earlier work where the wire array accelerated from its initial position at approximately 80% of the stagnation time, our results show that very late acceleration is not a universal aspect of wire array implosions. We also varied the ablation period between 46%+/-2% and 71%+/-3% of the stagnation time, for the first time, by scaling the array diameter between 40 mm (at a wire-wire gap of 524 mum ) and 12 mm (at a wire-wire gap of 209 microm ), at a constant stagnation time of 100+/-6 ns . The deviation of the wire-array trajectory from that of a thin shell scales inversely with the ablation rate per unit mass: f(m) proportional[dm(ablate)/dt]/m(array). The convergence ratio of the effective position of the current at peak x-ray power is approximately 3.6+/-0.6:1 , much less than the > or = 10:1 typically inferred from x-ray pinhole camera measurements of the brightest emitting regions on axis, at peak x-ray power. The trailing mass at the array edge early in the implosion appears to produce wings on the pinch mass profile at stagnation that reduces the rate of compression of the pinch. The observation of precursor pinch formation, trailing mass, and trailing current indicates that all the mass and current do not assemble simultaneously on axis. Precursor and trailing implosions appear to impact the efficiency of the conversion of current (driver energy) to x rays. An instability with the character of an m = 0 sausage grows rapidly on axis at stagnation, during the rise time of pinch power. Just after peak power, a mild m = 1 kink instability of the pinch occurs which is correlated with the higher compression ratio of the pinch after peak power and the decrease of the power pulse. Understanding these three-dimensional, discrete-wire implosion characteristics is critical in order to efficiently scale wire arrays to higher currents and powers for fusion applications.

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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-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-cable transmits the output signal of each balun to a double-wall screen room, where the signals are attenuated, digitized (0:5-ns=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-cmdiameter 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 differentialoutput 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 MVon 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...

We have developed a relativistic-fluid model of the flow-electron plasma in a steady-state onedimensional 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, where h 1=4 ÿ 1 1=2 ÿ lnb 2 ÿ 1 1=2 c=2 ÿ 1 and I a =I k . The relation is valid when V a * 1 MV. In the minimally insulated limit, the anode current I a;min 1:78V a =Z 0 , the electron-flow current I f;min 1:25V a =Z 0 , and the flow impedance Z f;min 0:588Z 0 . {The electronflow current I f I a ÿ I k . Following Mendel and Rosenthal [Phys. Plasmas 2, 1332 (1995)], we define the flow impedance Z f as V a =I 2 a ÿ I 2 k 1=2 .g In the well-insulated limit (i.e., when I a I a;min ), the electron-flow current I f 9V 2 a =8I a Z 2 0 and the flow impedance Z f 2Z 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 & 40 . 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;min and I f;min above the values predicted by the collisionless models, and decrease Z f;min . When I a I a;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 pulsedpower 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 lessenhanced cathode when E p 0:3300:026 eff 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 eff is the temporal width (in s) 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 eff 0:6 s. The normalized standard deviation of the differences between these measurements and the associated predictions of the relation is 12%.

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 $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.