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We report the results of a series of current scaling experiments with the Z accelerator for the compact, single, 20-mm diameter, 10-mm long, tungsten-wire arrays employed for the double-ended hohlraum ICF concept [M. E. Cuneo, Plasma Phys. Controlled Fusion 48, R1 (2006)]. We measured the z -pinch peak radiated x-ray power and total radiated x-ray energy as a function of the peak current, at a constant implosion time tau_{imp}=80ns . Previous x-ray emission current scaling for these compact arrays was obtained at tau_{imp}=95ns in the work of Stygar [Phys. Rev. E 69, 046403 (2004)]. In the present study we utilized lighter single-tungsten-wire arrays. For all the measurements, the load hardware dimensions, materials, and array wire number (N=300) were kept constant and were the same as the previous study. We also kept the normalized load current spatial and temporal profiles the same for all experiments reported in this work. Two different currents, 11.2+/-0.2MA and 17.0+/-0.3MA , were driven through the wire arrays. The average peak x-ray power for these compact wire arrays increased by 26%+/-7%to158+/-26TW at 17+/-0.3MA from the 125+/-24TW obtained at a peak current of 18.8+/-0.5MA with tau_{imp}=95ns . The higher peak power of the faster implosions may possibly be attributed to a higher implosion velocity, which in turn improves the implosion stability, and/or to shorter wire ablation times, which may lead to a decrease in trailing mass and trailing current. Our results show that the scaling of the radiated x-ray peak power and total radiated x-ray energy scaling with peak drive current to be closer to quadratic than the results of Stygar We find that the x-ray peak radiated power is P_{r} proportional, variantI;{1.57+/-0.20} and the total x-ray radiated energy E_{r} proportional, variantI;{1.9+/-0.24} . We also find that the current scaling exponent of the power is sensitive to the inclusion of a single data point with a peak power at least 1.9sigma below the average. If we eliminate this particular shot from our analysis (shot 1608), the power and energy scaling becomes closer to quadratic. Namely, we find that the dependence on the peak load current of the peak x-ray radiated power and the total x-ray radiated energy become P_{r} proportional, variantI;{1.71+/-0.10} and E_{r} proportional, variantI;{2.01+/-0.21} , respectively. In this case, the power scaling exponent is different by more than 2sigma from the previously published results of Stygar Larger data sets are likely required to resolve this uncertainty and eliminate the sensitivity to statistical fluctuations in any future studies of this type. Nevertheless, with or without the inclusion of shot 1608, our results with tau_{imp}=80ns fall short of an I2 scaling of the peak x-ray radiated power by at least 2sigma . In either case, the results of our study are consistent with the heuristic wire ablation model proposed by Stygar (P_{r} proportional, variantI;{1.5}) . We also derive an empirical predictive relation that connects the power scaling exponent with certain array parameters.

New extreme ultraviolet (EUV) spectroscopic diagnostics of relatively low-temperature plasmas based on the application of an EUV spectrometer and fast EUV diodes combined with glass capillary optics is described. An advanced high resolution dispersive element sliced multilayer grating was used in the compact EUV spectrometer. For monitoring of the time history of radiation, filtered fast EUV diodes were used in the same spectral region (>13 nm) as the EUV spectrometer. The radiation from the plasma was captured by using a single inexpensive glass capillary that was transported onto the spectrometer entrance slit and EUV diode. The use of glass capillary optics allowed placement of the spectrometer and diodes behind the thick radiation shield outside the direction of a possible hard x-ray radiation beam and debris from the plasma source. The results of the testing and application of this diagnostic for a compact laser plasma source are presented. Examples of modeling with parameters of plasmas are discussed.

The study of impurities is a key component of magnetic fusion research as it is directly related to plasma properties and steady-state operation. Two of the most important low-Z impurities are carbon and oxygen. The appropriate method of diagnosing these ions in plasmas is extreme ultraviolet (EUV) spectroscopy. In this work the results of two different sets of experiments are considered, and the spectra in a spectral region from 40 to 300 A are analyzed. The first set of experiments was carried out at the Sustained Spheromak Physics Experiment at LLNL, where EUV spectra of oxygen ions were recorded. The second set of experiments was performed at the compact laser-plasma x-ray/EUV facility "Sparky" at UNR. In particular, Mylar and Teflon slabs were used as targets to produce carbon, oxygen, and fluorine ions of different ionization stages. Nonlocal thermodynamic equilibrium kinetic models of O, F, and C were applied to identify the most diagnostically important spectral features of low-Z ions between 40 to 300 A and to provide plasma parameters for both sets of experiments.

Experiment demonstrates the first direct transformation of a tungsten wire core to the plasma state by Joule heating during nanosecond electrical explosion in vacuum. Energy of approximately 130 eV/atom was deposited into the 12 microm W wire coated by 2 microm polyimide during the first approximately 10 ns. All the metal rapidly transformed to highly ionized plasma, while the surrounding polyimide coating remained primarily in a gaseous state. This coating totally suppressed corona formation. The expansion velocity of the wire was approximately 12-18 km/s, the average wire ionization at 50 ns reached approximately 67% with corresponding LTE temperature of approximately 1.2 eV . Explosion of bare W wire demonstrated earlier termination of the wire core heating due to shunting corona generation. Magnetohydrodynamic (MHD) simulation reproduces the main features of coated and uncoated W wire explosion.

Radiation magnetohydrodynamic modeling is used to study the plasma formed on the surface of a cylindrical metallic load, driven by megagauss magnetic field at the 1MA Zebra generator (University of Nevada, Reno). An ionized aluminum plasma is used to represent the "core-corona" behavior in which a heterogeneous Z-pinch consists of a hot low-density corona surrounding a dense low-temperature core. The radiation dynamics model included simultaneously a self-consistent treatment of both the opaque and transparent plasma regions in a corona. For the parameters of this experiment, the boundary of the opaque plasma region emits the major radiation power with Planckian black-body spectrum in the extreme ultraviolet corresponding to an equilibrium temperature of 16 eV. The radiation heat transport significantly exceeds the electron and ion kinetic heat transport in the outer layers of the opaque plasma. Electromagnetic field energy is partly radiated (13%) and partly deposited into inner corona and core regions (87%). Surface temperature estimates are sensitive to the radiation effects, but the surface motion in response to pressure and magnetic forces is not. The general results of the present investigation are applicable to the liner compression experiments at multi-MA long-pulse current accelerators such as Atlas and Shiva Star. Also the radiation magnetohydrodynamic model discussed in the paper may be useful for understanding key effects of wire array implosion dynamics.

A method of thermodynamical calculation of thin metal wire heating during its electrical explosion is discussed. The technique is based on a calculation of Joule energy deposition taking into account the current wave form and the temperature dependence of the resistivity and heat capacity of the metal. Comparing the calculation to a set of exploding tungsten wire experiments demonstrates good agreement up to the time of melting. Good agreement is also demonstrated with resistive magnetohydrodynamics simulation. A similar thermodynamical calculation for Mo, Ti, Ni, Fe, Al, and Cu shows good agreement with experimental data. The thermodynamical technique is useful for verification of the voltage measurements in exploding wire experiments. This technique also shows good agreement with an exploding W foil experiment.

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 (approximately 0.4 GJ/shot) and inertial-fusion-energy (approximately 3 GJ/shot) research. We find that (delta(a)/delta(RT)) proportional (m/l)1/4 (Rgamma)(-1/2), where delta(a) is the imploding-sheath thickness of a wire-ablation-dominated pinch, delta(RT) is the sheath thickness of a Rayleigh-Taylor-dominated pinch, m is the total wire-array mass, l is the axial length of the array, R is the initial array radius, and gamma is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product Rgamma is held constant the sheath thickness is, at sufficiently large values of m/l, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power P(r) proportional (I/tau(i))(3/2)Rlphigamma, where I is the peak pinch current, tau(i) is the pinch implosion time, and phi is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when 13 MA < or = I < or = 20 MA, 93 ns < or = tau(i) < or = 169 ns, 10 mm < or = R < or = 20 mm, 10 mm < or = l < or = 20 mm, and 2.0 mg/cm < or = m/l < or = 7.3 mg/cm. Assuming an ablation-dominated pinch and that Rlphigamma is held constant, we find that the x-ray-power efficiency eta(x) congruent to P(r)/P(a) of a coupled pinch-accelerator system is proportional to (tau(i)P(r)(7/9 ))(-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 tau(i), and the requisite accelerator energy E(a) is proportional to tau2(i). 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 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 tau(i)0.36 and 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 tau(i). We also find that increasing the anode-cathode gap of the pinch from 2 to 4 mm increases the requisite values of P(a) and E(a) by as much as a factor of 2.

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.

Experimental and computational investigations of nanosecond electrical explosion of a thin Al wire in vacuum are presented. We have demonstrated that increasing the current rate leads to increased energy deposited before voltage collapse. The experimental evidence for synchronization of the wire expansion and light emission with voltage collapse is presented. Hydrocarbons are indicated in optical spectra and their influence on breakdown physics is discussed. The radial velocity of low-density plasma reaches a value of approximately 100 km/s. The possibility of an over-critical phase transition due to high pressure is discussed. A one-dimensional magnetohydrodynamic (MHD) simulation shows good agreement with experimental data. The MHD simulation demonstrates separation of the exploding wire into a high-density cold core and a low-density hot corona as well as fast rejection of the current from the wire core to the corona during voltage collapse. Important features of the dynamics for the wire core and corona follow from the MHD simulation and are discussed.

We present experimental evidence of corona-free electrical explosion of dielectric-coated W wire in vacuum. A fast current rise of approximately 150 A/ns and a coating of 2 microm polyimide are both needed to achieve the corona-free regime of explosion. Breakdown is absent in corona-free explosion; the wire remains resistive, and this allows anomalously high energy deposition (approximately 20 times atomization enthalpy). MHD simulations reproduce the main differences between corona and corona-free explosions. A corona-free explosion of a wire can be useful for the generation of a hot plasma column by direct energy deposition.

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 0< or =alpha<<1) 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 be < or =7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, sigma must be <3% for the shot-success probability to be > or =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.

Experimental evidence for a strong influence of the radial electric field on energy deposition into thin metal wires during their electrical explosion in vacuum is presented. Explosion of the metal wire with a positive polarity when the radial electric field "pushes" electrons into the wire results in twice as much deposited energy than with the negative polarity when the radial field "expels" electrons from the wires. Moreover, the axial structure of the deposited energy changes. This effect can be explained by the influence of radial electric field on electronic emission and on vapor breakdown along the wire surface.