A technique for verifying the input response function of neutron time-of-flight scintillation detectors using cosmic rays.

An accurate interpretation of DD or DT fusion neutron time-of-flight (nTOF) signals from current mode detectors employed at the Z-facility at Sandia National Laboratories requires that the instrument response functions (IRF's) be deconvolved from the measured nTOF signals. A calibration facility that produces detectable sub-ns radiation pulses is typically used to measure the IRF of such detectors. This work, however, reports on a simple method that utilizes cosmic radiation to measure the IRF of nTOF detectors, operated in pulse-counting mode. The characterizing metrics reported here are the throughput delay and full-width-at-half-maximum. This simple approach yields consistent IRF results with the same detectors calibrated in 2007 at a LINAC bremsstrahlung accelerator (Idaho State University). In particular, the IRF metrics from these two approaches and their dependence on the photomultipliers bias agree to within a few per cent. This information may thus be used to verify if the IRF for a given nTOF detector employed at Z has changed since its original current-mode calibration and warrants re-measurement.

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.

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.

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.

Theoretical z -pinch scaling relations for thermonuclear-fusion experiments.

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.

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.

Analytic electrical-conductivity tensor of a nondegenerate Lorentz plasma.

We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Theta>>1, and the electron-ion Coulomb-coupling parameter Gamma/Z<<1. (Gamma is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Gamma/Z and not simply the temperature, and that a quantum-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Lambda(1)=(ln chi(1)-1 / 2)+[(2Ze(2)/lambdam(e)v(2)(e1))(ln chi(1)-ln 2(4/3))], where chi(1) identical with 2m(e)v(e1)lambda/ variant Planck's over 2pi, m(e) is the electron mass, v(e1) identical with (7k(B)T/m(e))(1/2), k(B) is the Boltzmann constant, T is the temperature, lambda is the screening length, variant Planck's over 2pi is Planck's constant divided by 2pi, and e is the absolute value of the electron charge. When the plasma Debye length lambda(D) is greater than the ion-sphere radius a, we assume lambda=lambda(D); otherwise we set lambda=a. The B=0 conductivity is consistent with measurements when Z greater, similar 1, Theta greater, similar 2, and Gamma/Z less, similar 1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Lambda(1) when Z> or =1, Theta> or =2, and Gamma/Z< or =1 is 1.9. The expression obtained for the resistivity tensor (B not equal 0) predicts that eta( perpendicular )/eta( parallel ) (where eta( perpendicular ) and eta( parallel ) are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic calculations. The results are applied to an idealized 17-MA z pinch at stagnation.

A simple one-dimensional model for understanding planar dose-versus-depth profiles in mixed photon/electron fields.

A one-dimensional model is described for illustrating the perturbing effects of mixed photon/electron fields on planar dose-versus-depth profiles in low Z materials (Z < or = 20), and at moderate photon energies (0.3-10 MeV). An electron field may arise from photon interactions in filters upstream of a dose-versus-depth experiment. The effects of upstream mass, scattering of electrons out of a gap between a filter and the experiment, and differences between the incident electron energy distribution and locally produced KERMA are modeled and compared to Discrete Ordinates calculations. At transitional depths in a dose-versus-depth experiment, the distortions can be significant and obscure the profile of the photon component alone.

Five-frame, x-ray camera for charged particle, inertial confinement fusion studies.

A prototype framing x-ray camera has been developed for photographic studies of inertial confinement fusion (ICF) targets irradiated by charged particle beams. Electron images from five, independently gated, microchannel plates are transported out of the radiation field by means of a toroidal magnetic field and are permanently recorded on film. The calculated, effective exposure time is