Performance Scaling in Magnetized Liner Inertial Fusion Experiments.

We present experimental results from the first systematic study of performance scaling with drive parameters for a magnetoinertial fusion concept. In magnetized liner inertial fusion experiments, the burn-averaged ion temperature doubles to 3.1 keV and the primary deuterium-deuterium neutron yield increases by more than an order of magnitude to 1.1×10^{13} (2 kJ deuterium-tritium equivalent) through a simultaneous increase in the applied magnetic field (from 10.4 to 15.9 T), laser preheat energy (from 0.46 to 1.2 kJ), and current coupling (from 16 to 20 MA). Individual parametric scans of the initial magnetic field and laser preheat energy show the expected trends, demonstrating the importance of magnetic insulation and the impact of the Nernst effect for this concept. A drive-current scan shows that present experiments operate close to the point where implosion stability is a limiting factor in performance, demonstrating the need to raise fuel pressure as drive current is increased. Simulations that capture these experimental trends indicate that another order of magnitude increase in yield on the Z facility is possible with additional increases of input parameters.

Experimental demonstration of fusion-relevant conditions in magnetized liner inertial fusion.

This Letter presents results from the first fully integrated experiments testing the magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)], in which a cylinder of deuterium gas with a preimposed 10 Taxial magnetic field is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA, 100 ns rise time current on the Z facility. Despite a predicted peak implosion velocity of only 70 km = s, the fuel reaches a stagnation temperature of approximately 3 keV, with T(e) ≈ T(i), and produces up to 2 x 10(12) thermonuclear deuterium-deuterium neutrons. X-ray emission indicates a hot fuel region with full width at half maximum ranging from 60 to 120 µm over a 6 mm height and lasting approximately 2 ns. Greater than 10(10) secondary deuterium-tritium neutrons were observed, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg = cm(2).

Understanding fuel magnetization and mix using secondary nuclear reactions in magneto-inertial fusion.

Magnetizing the fuel in inertial confinement fusion relaxes ignition requirements by reducing thermal conductivity and changing the physics of burn product confinement. Diagnosing the level of fuel magnetization during burn is critical to understanding target performance in magneto-inertial fusion (MIF) implosions. In pure deuterium fusion plasma, 1.01 MeV tritons are emitted during deuterium-deuterium fusion and can undergo secondary deuterium-tritium reactions before exiting the fuel. Increasing the fuel magnetization elongates the path lengths through the fuel of some of the tritons, enhancing their probability of reaction. Based on this feature, a method to diagnose fuel magnetization using the ratio of overall deuterium-tritium to deuterium-deuterium neutron yields is developed. Analysis of anisotropies in the secondary neutron energy spectra further constrain the measurement. Secondary reactions also are shown to provide an upper bound for the volumetric fuel-pusher mix in MIF. The analysis is applied to recent MIF experiments [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] on the Z Pulsed Power Facility, indicating that significant magnetic confinement of charged burn products was achieved and suggesting a relatively low-mix environment. Both of these are essential features of future ignition-scale MIF designs.

Pressure and energy balance of stagnating plasmas in z-pinch experiments: implications to current flow at stagnation.

Detailed spectroscopic diagnostics of the stagnating plasma in two disparate z pinches allow, for the first time, the examination of the plasma properties within a 1D shock wave picture, demonstrating a good agreement with this picture. The conclusion is that for a wide range of imploding-plasma masses and current amplitudes, in experiments optimizing non-Planckian hard radiation yields, contrary to previous descriptions the stagnating plasma pressure is balanced by the implosion pressure, and the radiation energy is provided by the imploding-plasma kinetic energy, rather than by the magnetic-field pressure and magnetic-field-energy dissipation, respectively.

Hybrid CMOS detectors for high-speed X-ray imaging.

Hybrid CMOS (hCMOS) x-ray framing cameras are a new and powerful detector option for experiments in the fields of Inertial Confinement Fusion (ICF) and High Energy Density Physics (HEDP). These digital cameras capture multiple images along a single line-of-sight with a time resolution as short as 1.5 ns and with high quantum efficiency. To manage the high data rate, an image sequence is acquired in a short burst of time and subsequently read out on a much longer time scale. The technology is well suited for operating in high radiation environments, including fusion ignition experiments. Diagnostics using hCMOS cameras are now deployed in experiments on major laser and pulsed-power ICF facilities around the world. Continued advances in microelectronics technologies will enable faster and more capable detectors well into the future. This paper reviews this detector technology with a focus on application to ICF and HEDP experiments.

Demonstration of improved laser preheat with a cryogenically cooled magnetized liner inertial fusion platform.

We report on progress implementing and testing cryogenically cooled platforms for Magnetized Liner Inertial Fusion (MagLIF) experiments. Two cryogenically cooled experimental platforms were developed: an integrated platform fielded on the Z pulsed power generator that combines magnetization, laser preheat, and pulsed-power-driven fuel compression and a laser-only platform in a separate chamber that enables measurements of the laser preheat energy using shadowgraphy measurements. The laser-only experiments suggest that ∼89% ± 10% of the incident energy is coupled to the fuel in cooled targets across the energy range tested, significantly higher than previous warm experiments that achieved at most 67% coupling and in line with simulation predictions. The laser preheat configuration was applied to a cryogenically cooled integrated experiment that used a novel cryostat configuration that cooled the MagLIF liner from both ends. The integrated experiment, z3576, coupled 2.32 ± 0.25 kJ preheat energy to the fuel, the highest to-date, demonstrated excellent temperature control and nominal current delivery, and produced one of the highest pressure stagnations as determined by a Bayesian analysis of the data.

Penetrating radiography of imploding and stagnating beryllium liners on the Z accelerator.

The implosions of initially solid beryllium liners (tubes) have been imaged with penetrating radiography through to stagnation. These novel radiographic data reveal a high degree of azimuthal correlation in the evolving magneto-Rayleigh-Taylor structure at times just prior to (and during) stagnation, providing stringent constraints on the simulation tools used by the broader high energy density physics and inertial confinement fusion communities. To emphasize this point, comparisons to 2D and 3D radiation magnetohydrodynamics simulations are also presented. Both agreement and substantial disagreement have been found, depending on how the liner's initial outer surface finish was modeled. The various models tested, and the physical implications of these models are discussed. These comparisons exemplify the importance of the experimental data obtained.

Measurements of magneto-Rayleigh-Taylor instability growth during the implosion of initially solid Al tubes driven by the 20-MA, 100-ns Z facility.

The first controlled experiments measuring the growth of the magneto-Rayleigh-Taylor instability in fast (∼100 ns) Z-pinch plasmas are reported. Sinusoidal perturbations on the surface of an initially solid Al tube (liner) with wavelengths of 25-400 µm were used to seed the instability. Radiographs with 15 µm resolution captured the evolution of the outer liner surface. Comparisons with numerical radiation magnetohydrodynamic simulations show remarkably good agreement down to 50 µm wavelengths.

Phase modulation failsafe system for multi-kJ lasers based on optical heterodyne detection.

Amplification of the transverse scattered component of stimulated Brillouin scattering (SBS) can contribute to optical damage in the large aperture optics of multi-kJ lasers. Because increased laser bandwidth from optical phase modulation (PM) can suppress SBS, high energy laser amplifiers are injected with PM light. Phase modulation distributes the single-frequency spectrum of a master oscillator laser among individual PM sidebands, so a sufficiently high modulation index ß can maintain the fluence for all spectral components below the SBS threshold. To avoid injection of single frequency light in the event of a PM failure, a high-speed PM failsafe system (PMFS) must be employed. Because PM is easily converted to AM, essentially all PM failsafes detect AM, with the one described here employing a novel configuration where optical heterodyne detection converts PM to AM, followed by passive AM power detection. Although the PMFS is currently configured for continuous monitoring, it can also detect PM for pulse durations ≥2 ns and could be modified to accommodate shorter pulses. This PMFS was deployed on the Z-Beamlet Laser (ZBL) at Sandia National Laboratories, as required by an energy upgrade to support programs at Sandia's Z Facility such as magnetized liner inertial fusion. Depending on the origin of a PM failure, the PMFS responds in as little as 7 ns. In the event of an instantaneous failure during initiation of a laser shot, this response time translates to a 30-50 ns margin of safety by blocking a pulse from leaving ZBL's regenerative amplifier, which prevents injection of single frequency light into the main amplification chain. The performance of the PMFS, without the need for operator interaction, conforms to the principles of engineered safety.

Polycapillary x-ray lenses for single-shot, laser-driven powder diffraction.

X-ray diffraction measurements to characterize phase transitions of dynamically compressed high-Z matter at Mbar pressures require both sufficient photon energy and fluence to create data with high fidelity in a single shot. Large-scale laser systems can be used to generate x-ray sources above 10 keV utilizing line radiation of mid-Z elements. However, the laser-to-x-ray energy conversion efficiency at these energies is low, and thermal x-rays or hot electrons result in unwanted background. We employ polycapillary x-ray lenses in powder x-ray diffraction measurements using solid target x-ray emission from either the Z-Beamlet long-pulse or the Z-Petawatt (ZPW) short-pulse laser systems at Sandia National Laboratories. Polycapillary lenses allow for a 100-fold fluence increase compared to a conventional pinhole aperture while simultaneously reducing the background significantly. This enables diffraction measurements up to 16 keV at the few-photon signal level as well as diffraction experiments with ZPW at full intensity.

The dilation aided single-line-of-sight x-ray camera for the National Ignition Facility: Characterization and fielding.

Crystal x-ray imaging is frequently used in inertial confinement fusion and laser-plasma interaction applications as it has advantages compared to pinhole imaging, such as higher signal throughput, better achievable spatial resolution, and chromatic selection. However, currently used x-ray detectors are only able to obtain a single time resolved image per crystal. The dilation aided single-line-of-sight x-ray camera described here was designed for the National Ignition Facility (NIF) and combines two recent diagnostic developments, the pulse dilation principle used in the dilation x-ray imager and a ns-scale multi-frame camera that uses a hold and readout circuit for each pixel. This enables multiple images to be taken from a single-line-of-sight with high spatial and temporal resolution. At the moment, the instrument can record two single-line-of-sight images with spatial and temporal resolution of 35 µm and down to 35 ps, respectively, with a planned upgrade doubling the number of images to four. Here we present the dilation aided single-line-of-sight camera for the NIF, including the x-ray characterization measurements obtained at the COMET laser, as well as the results from the initial timing shot on the NIF.

Intestinal absorption of magnesium from food and supplements.

The purpose of this study was to measure magnesium absorption over the wide range of intakes to which the intestine may be exposed from food and/or magnesium-containing medications. Net magnesium absorption was measured in normal subjects after they ingested a standard meal supplemented with 0, 10, 20, 40, and 80 mEq of magnesium acetate. Although absorption increased with each increment in intake, fractional magnesium absorption fell progressively (from 65% at the lowest to 11% at the highest intake) so that absorption as a function of intake was curvilinear. This absorption-intake relationship was almost perfectly represented by an equation containing a hyperbolic function plus a linear function. Our results are statistically compatible with a magnesium absorption process that simultaneously uses a mechanism that reaches an absorptive maximum, plus a mechanism that endlessly absorbs a defined fraction (7%) of ingested magnesium. Compared to previous studies of calcium absorption, much less magnesium that calcium was absorbed at intakes above 8 mEq/meal, apparently due to greater restriction of intestinal permeability to magnesium. We also found that magnesium from a high magnesium-containing food source, almonds, was just as bioavailable as from soluble magnesium acetate. In contrast, magnesium absorption from commercially available enteric-coated magnesium chloride was much less than from magnesium acetate, suggesting that enteric coating can impair magnesium bioavailability.

Carbohydrate malabsorption. Its measurement and its contribution to diarrhea.

The major purpose of this research was to gain insight into the effect of carbohydrate malabsorption on fecal water output. To do this we measured daily fecal output of total carbohydrate, reducing sugars, and organic acids (a product of bacterial fermentation). Normal subjects were studied in their native state and when diarrhea was induced by mechanisms that did and did not involve carbohydrate malabsorption. Patients with malabsorption syndrome were also studied. We concluded that: (a) Excretion of carbohydrate and its breakdown products can be expressed as a single number by converting organic acids to their monosaccharide equivalents. (b) Diarrhea per se causes only a trivial increase in fecal carbohydrate excretion. (c) The molar output of osmotic moieties in feces due to unabsorbed carbohydrate can be determined by adding fecal reducing sugars to organic acids and their obligated cations. This expression parallels almost exactly the effect of increasing doses of lactulose (a nonabsorbable sugar) on fecal water output; one excreted millimole obligates 3.5 g of stool water. This relationship can be used to predict the effect of carbohydrate malabsorption on stool water output in patients with diarrhea. (d) 12 of 19 patients with malabsorption syndrome due to various diseases had excessive fecal excretion of carbohydrate and its breakdown products; of the diseases that cause malabsorption syndrome, combined small and large bowel resection is most likely to result in excessive fecal excretion of carbohydrate and monosaccharide equivalents. In 6 of these 19 patients carbohydrate malabsorption appeared to be the major cause of diarrhea.

A 7.2 keV spherical x-ray crystal backlighter for two-frame, two-color backlighting at Sandia's Z Pulsed Power Facility.

Many experiments on Sandia National Laboratories' Z Pulsed Power Facility-a 30 MA, 100 ns rise-time, pulsed-power driver-use a monochromatic quartz crystal backlighter system at 1.865 keV (Si Heα) or 6.151 keV (Mn Heα) x-ray energy to radiograph an imploding liner (cylindrical tube) or wire array z-pinch. The x-ray source is generated by the Z-Beamlet laser, which provides two 527-nm, 1 kJ, 1-ns laser pulses. Radiographs of imploding, thick-walled beryllium liners at convergence ratios CR above 15 [CR=ri(0)/ri(t)] using the 6.151-keV backlighter system were too opaque to identify the inner radius ri of the liner with high confidence, demonstrating the need for a higher-energy x-ray radiography system. Here, we present a 7.242 keV backlighter system using a Ge(335) spherical crystal with the Co Heα resonance line. This system operates at a similar Bragg angle as the existing 1.865 keV and 6.151 keV backlighters, enhancing our capabilities for two-color, two-frame radiography without modifying the system integration at Z. The first data taken at Z include 6.2-keV and 7.2-keV two-color radiographs as well as radiographs of low-convergence (CR about 4-5), high-areal-density liner implosions.

A high-speed two-frame, 1-2 ns gated X-ray CMOS imager used as a hohlraum diagnostic on the National Ignition Facility (invited).

A novel x-ray imager, which takes time-resolved gated images along a single line-of-sight, has been successfully implemented at the National Ignition Facility (NIF). This Gated Laser Entrance Hole diagnostic, G-LEH, incorporates a high-speed multi-frame CMOS x-ray imager developed by Sandia National Laboratories to upgrade the existing Static X-ray Imager diagnostic at NIF. The new diagnostic is capable of capturing two laser-entrance-hole images per shot on its 1024 × 448 pixels photo-detector array, with integration times as short as 1.6 ns per frame. Since its implementation on NIF, the G-LEH diagnostic has successfully acquired images from various experimental campaigns, providing critical new information for understanding the hohlraum performance in inertial confinement fusion (ICF) experiments, such as the size of the laser entrance hole vs. time, the growth of the laser-heated gold plasma bubble, the change in brightness of inner beam spots due to time-varying cross beam energy transfer, and plasma instability growth near the hohlraum wall.

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.

Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA.

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.

Des-Leu angiotensin I: biosynthesis and drinking response.

The crude rat and bovine synaptosomal lysate from brain can hydrolyze angiotensin I (AI) to des-Leu angiotensin I (AI-dL) and no further. This cytosolic enzyme has a specificity for angiotensin-related sequences, R-His-Pro-Phe-His-Leu and therefore named angiotensin-related carboxypeptidase (ARC). These studies led to the biosynthesis and purification of AI-dL in order to determine if it can provoke a drinking response. This nonapeptide is a potent dipsogen when injected into the cerebroventricles of rats. The drinking response probably requires a second hydrolysis to angiotensin II (AII) since both captopril and saralasin can inhibit this response.

Lumbar-hip flexion motion. A comparative study between asymptomatic and chronic low back pain in 18- to 36-year-old men.

STUDY DESIGN: The amount of lumbar and hip flexion and the relative contribution within movement during standing forward bending was recorded on a group of asymptomatic men and a group of men with a history of chronic low back pain. OBJECTIVES: To compare the relative contribution of the hip and lumbar spine to forward bending in the two groups. SUMMARY OF BACKGROUND DATA: The hips and lumbar spine both contribute to the forward bending motion, and an aberrant pattern of contribution in one or both regions could be related to the presence of chronic low back pain. METHODS: Thirty-two white men aged 18-36 years (15 with chronic low back pain and 17 asymptomatic) were assessed using a three-dimensional motion analysis system that allowed uninterrupted forward bending. RESULTS: The men with chronic low back pain demonstrated a significant reduction in the mean total range and mean maximum lumbar flexion relative to the asymptomatic group. Mean hip flexion was not significantly different. Data analysis for 120 degrees of gross flexion revealed a subgroup of men with chronic low back pain with a significant decrease in hip flexion. CONCLUSIONS: When assessing the relative motion of the lumbar spine and hips in standing forward flexion, there was measurable difference between asymptomatic men and a group of chronic low back pain patients. In particular, two subgroups of individuals with chronic low back pain appeared; one moved relatively similarly to the asymptomatic group, whereas the other sub-group demonstrated reduced hip mobility. These findings indicate the importance of assessing the lumbar and hip flexion motion in chronic low back pain patients to determine if a movement abnormality is present.

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.