Closed-form solution for a cantilevered sectorial plate subjected to a tip concentrated force.

A closed-form solution is presented for a cantilevered sectorial plate subjected to a tip concentrated force. Since the particular solution for this problem was not found in the literature, it is derived here. Deflections from the total solution (particular plus homogeneous solutions) are compared to those from a finite element analysis and are found to be in excellent agreement, producing an error within approximately 0.08 %. Normalized closed-form deflections and slopes at the fixed support, resulting from an approximate enforcement of the boundary conditions there, deviate from zero by <0.08 %. Finally, the total closed-form solutions for a cantilevered sectorial plate subjected to independent applications of a tip concentrated force, a tip bending moment, and a tip twisting moment, are compiled.

Fusion-neutron-yield, activation measurements at the Z accelerator: design, analysis, and sensitivity.

We present a general methodology to determine the diagnostic sensitivity that is directly applicable to neutron-activation diagnostics fielded on a wide variety of neutron-producing experiments, which include inertial-confinement fusion (ICF), dense plasma focus, and ion beam-driven concepts. This approach includes a combination of several effects: (1) non-isotropic neutron emission; (2) the 1/r(2) decrease in neutron fluence in the activation material; (3) the spatially distributed neutron scattering, attenuation, and energy losses due to the fielding environment and activation material itself; and (4) temporally varying neutron emission. As an example, we describe the copper-activation diagnostic used to measure secondary deuterium-tritium fusion-neutron yields on ICF experiments conducted on the pulsed-power Z Accelerator at Sandia National Laboratories. Using this methodology along with results from absolute calibrations and Monte Carlo simulations, we find that for the diagnostic configuration on Z, the diagnostic sensitivity is 0.037% ± 17% counts/neutron per cm(2) and is ∼ 40% less sensitive than it would be in an ideal geometry due to neutron attenuation, scattering, and energy-loss effects.

Mach-Zehnder recording systems for pulsed power diagnostics.

Fiber-optic transmission and recording systems, based on Mach-Zehnder modulators, have been developed and installed at the National Ignition Facility (NIF), and are being developed for other pulsed-power facilities such as the Z accelerator at Sandia, with different requirements. We present the design and performance characteristics for the mature analog links, based on the system developed for the Gamma Reaction History diagnostic at the OMEGA laser and at NIF. For a single detector channel, two Mach-Zehnders are used to provide high dynamic range at the full recording bandwidth with no gaps in the coverage. We present laboratory and shot data to estimate upper limits on the radiation effects as they impact recorded data quality. Finally, we will assess the technology readiness level for mature and developing implementations of Mach-Zehnder links for these environments.

Progress in obtaining an absolute calibration of a total deuterium-tritium neutron yield diagnostic based on copper activation.

The 350-keV Cockroft-Walton accelerator at Sandia National laboratory's Ion Beam facility is being used to calibrate absolutely a total DT neutron yield diagnostic based on the (63)Cu(n,2n)(62)Cu(ß+) reaction. These investigations have led to first-order uncertainties approaching 5% or better. The experiments employ the associated-particle technique. Deuterons at 175 keV impinge a 2.6 µm thick erbium tritide target producing 14.1 MeV neutrons from the T(d,n)(4)He reaction. The alpha particles emitted are measured at two angles relative to the beam direction and used to infer the neutron flux on a copper sample. The induced (62)Cu activity is then measured and related to the neutron flux. This method is known as the F-factor technique. Description of the associated-particle method, copper sample geometries employed, and the present estimates of the uncertainties to the F-factor obtained are given.

Calibration of neutron-yield diagnostics in attenuating and scattering environments.

We have performed absolute calibrations of a fusion-neutron-yield copper-activation diagnostic in environments that significantly attenuate and scatter neutrons. We have measured attenuation and scattering effects and have compared the measurements to Monte Carlo simulations using the Monte Carlo N-Particle code. We find that measurements and simulations are consistent within 10%.

A novel method for modeling the neutron time of flight detector response in current mode to inertial confinement fusion experiments (invited).

A novel method for modeling the neutron time of flight (nTOF) detector response in current mode for inertial confinement fusion experiments has been applied to the on-axis nTOF detectors located in the basement of the Z-Facility. It will be shown that this method can identify sources of neutron scattering, and is useful for predicting detector responses in future experimental configurations, and for identifying potential sources of neutron scattering when experimental set-ups change. This method can also provide insight on how much broadening neutron scattering contributes to the primary signals, which is then subtracted from them. Detector time responses are deconvolved from the signals, allowing a transformation from dN/dt to dN/dE, extracting neutron spectra at each detector location; these spectra are proportional to the absolute yield.

Copper activation deuterium-tritium neutron yield measurements at the National Ignition Facility.

A DT neutron yield diagnostic based on the reactions, (63)Cu(n,2n)(62)Cu(ß(+)) and (65)Cu(n,2n)( 64) Cu(ß(+)), has been fielded at the National Ignition Facility (NIF). The induced copper activity is measured using a NaI γ-γ coincidence system. Uncertainties in the 14-MeV DT yield measurements are on the order of 7% to 8%. In addition to measuring yield, the ratio of activities induced in two, well-separated copper samples are used to measure the relative anisotropy of the fuel ρR to uncertainties as low as 5%.

X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations.

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.

X-ray imaging measurements of capsule implosions driven by a Z-pinch dynamic hohlraum.

The radiation and shock generated by impact of an annular tungsten Z-pinch plasma on a 10-mm diam 5-mg/cc CH(2) foam are diagnosed with x-ray imaging and power measurements. The radiative shock was virtually unaffected by Z-pinch plasma instabilities. The 5-ns-duration approximately 135-eV radiation field imploded a 2.1-mm-diam CH capsule. The measured radiation temperature, shock radius, and capsule radius agreed well with computer simulations, indicating understanding of the main features of a Z-pinch dynamic-hohlraum-driven capsule implosion.