Search Results (7 total)

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 38×38 square array of 10-μm-diameter pinholes in a 50-μm-thick tantalum plate. The arrays achromatically attenuate the x-ray flux by a factor of ∼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 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 (∼0.4  GJ∕shot) and inertial-fusion-energy (∼3  GJ∕shot) research. We find that (δ_a∕δ_RT)∝(m∕ℓ)^1∕4(RΓ)^−1∕2, where δ_a is the imploding-sheath thickness of a wire-ablation-dominated pinch, δ_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 Γ is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product RΓ 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∝(I∕τ_i)^3∕2RℓΦΓ, where I is the peak pinch current, τ_i is the pinch implosion time, and Φ is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when 13  MA≤I≤20  MA, 93  ns≤τ_i≤169  ns, 10  mm≤R≤20  mm, 10  mm≤ℓ≤20  mm, and 2.0  mg∕cm≤m∕ℓ≤7.3  mg∕cm. Assuming an ablation-dominated pinch and that RℓΦΓ is held constant, we find that the x-ray-power efficiency η_x≡P_r∕P_a of a coupled pinch-accelerator system is proportional to (τ_iP_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 τ_i, and the requisite accelerator energy E_a is proportional to τ_i². 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 τ_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 τ_i^0.36 and τ_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 τ_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 have conducted a series of experiments designed to measure the flashover strength of various azimuthally symmetric 45° 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° 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±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±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.

We have developed a statistical model for the flashover of a 45° 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-exp(-E_p^βt_effC/k^β), where E_p is the peak value in time of the spatially averaged electric field E(t), t_eff≡∫[E(t)/E_p]^βdt is the effective pulse width, C is the insulator circumference, k∝exp(λ/d), and β and λ 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   μs, 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  kV/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  kV/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 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∝I^1.24±0.18, the total radiated x-ray energy E_r∝I^1.73±0.18, the x-ray-power rise time τ_r∝I^0.39±0.34, and the x-ray-power pulse width τ_w∝I^0.45±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 τ_i is scaled as I^-1/3. The measured 1σ shot-to-shot fluctuations in P_r, E_r, τ_r, τ_w, and τ_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±α (where 0<~α≪1) is equal to erf(α/2σ), where σ is the 1σ fractional variation of the peak power radiated by a single pinch. Assuming α must be <~7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, σ must be <3% for the shot-success probability to be >~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 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 Θ≫1, and the electron-ion Coulomb-coupling parameter Γ/Z≪1. (Γ 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 Γ/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 Λ₁=(ln χ₁-1 / 2)+[(2Ze²/λm_ev_e1²)(ln χ₁-ln 2^4/3)], where χ₁≡2m_ev_e1λ/ħ, m_e is the electron mass, v_e1≡(7k_BT/m_e)^1/2, k_B is the Boltzmann constant, T is the temperature, λ is the screening length, ħ is Planck’s constant divided by 2π, and e is the absolute value of the electron charge. When the plasma Debye length λ_D is greater than the ion-sphere radius a, we assume λ=λ_D; otherwise we set λ=a. The B=0 conductivity is consistent with measurements when Z≳1, Θ≳2, and Γ/Z≲1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Λ₁ when Z>~1, Θ>~2, and Γ/Z<~1 is 1.9. The expression obtained for the resistivity tensor (B≠0) predicts that η_⊥/η_∥ (where η_⊥ and η_∥ 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.

Tungsten wire array implosions on the 7- to 8-MA Saturn generator have been optimized using wire number and array diameter variations to produce 75±10 TW of x rays with total energy outputs of 450±50 kJ. By increasing the number of wires in a 12.5-mm-diam array from 24 to 70 and simultaneously decreasing the individual wire diameter from 13 to 7.5 μm, the total radiated power increased from 20±3 to 40±6 TW and the x-ray pulse width decreased from 18 to 8.5 ns. In addition, a diameter scan at an implosion time of 50±5 ns showed that the pulse width has a strong dependence on collapse velocity and wire thickness. For the largest diameter load of 17.5 mm with 120 5-μm-diam wires, a 4-ns pulse width with a peak power of 75±10 TW was achieved: four times power gain over the 20-TW electrical power generated by the pulsed power system. Time-resolved pinhole photography confirms that the power enhancement with increased wire number is associated with the plasma achieving a tighter compression and better axial uniformity. For the higher-velocity implosions, we infer from two-dimensional radiation-magnetohydrodynamic calculations that the plasma becomes hotter and hence radiates at a higher brightness temperature. Zero- and two-dimensional load models coupled with a detailed circuit model have shown expected radial kinetic energies in the range of 100–200 kJ. The total radiated energy of >400 kJ in a 4–20-ns FWHM pulse exceeds the total kinetic energy by more than a factor of 2. Two-dimensional, three-temperature simulations reproduce the observed trends in powers and pulse widths by using a variable initial random density perturbation. These calculations also indicate that the radiated energy is accounted for by the total work done on the plasma by the magnetic field.