Implosion Velocity Research Articles

Autocatalytic fission–fusion microexplosions for nuclear pulse propulsion

Autocatalytic fission–fusion microexplosions, mutually amplifying fission and fusion reactions, are proposed for propulsion. Autocatalytic fission–fusion microexplosions can be realized by imploding a shell of uranium 235 (or plutonium) onto a magnetized deuterium–tritium (DT) plasma. After having reached a high temperature, the DT plasma releases fusion neutrons making fission reactions in the fissile shell increasing the implosion velocity which in turn increases the fusion reaction rate until full ignition of the DT plasma. To implode the fissile shell a small amount of high explosive and to magnetize the DT plasma a small auxiliary electric discharge are required. In comparison to nuclear bomb pulse propulsion, the energy released per pulse is much smaller and the efficiency higher. And in comparison to laser- or particle-beam-ignited fusion microexplosions, there is no need for a massive fusion ignition driver.

Hydrodynamique de l'implosion d'une cible FCI

We consider the hydrodynamic behaviour of an imploding ICF target. After recalling the requirements for thermonuclear ignition, we analyse in detail the two phases of the implosion. First, the acceleration, with its two important ignition parameters, the implosion velocity and the entropy generated in the DT. Second, the slowing down which, through electronic conduction, allows the creation of a central hot spot of sufficient mass. The method of successive shocks allows the détermination of the laser pulse shape which, by insuring an isentropic acceleration, optimises the energy delivered to the DT. We obtain the implosion velocity as a function of the initial capsule parameters and the maximum incident radiation. We clarify the hydrodynamical reason which makes the ignition threshold sensitive to the entropy generated during the acceleration. These elements constitute the basis of a global indirect drive ICF model, allowing target design optimisation.

Developments in NIF Beryllium Capsule Design

Recent beryllium capsule designs have focussed on the lower temperatures and laser powers expected before the NIF laser reaches its full capability, 192 beams, 500TW, and 1.8MJ. First, several new designs are given with peak radiation temperatures for 250 to 280 eV. A 250eV design uses 2% oxygen dopant instead of 0.9% copper. Second, a radiography study of planar joints in S200D beryllium using a Cu, Au, Ag, Al, or Au/Cu braze quantified the diffusion away from the joint. LASNEX calculations show that Cu joint perturbations grow to large enough amplitude to preclude ignition. However by allowing the copper to diffuse twice as far as in these experiments (e.g. by holding at braze temperature longer), the joint calculates to be acceptable, and the capsule gives full yield. Aluminum diffuses extremely far from the joint, almost uniformly in the sample. Third, a capsule with a high Z shell and beryllium ablator calculates to ignite. As expected its ignition threshold is lower, about 70% of the implosion velocity for a capsule like the Be330. The extra tamping of DT bum by a 6 μm tungsten shell increases the yield from 17 to 32 MJ. The capsule radiates 3 MJ of this yield as X-rays. Unfortunately the capsule is more sensitive to DT ice roughness than the Be330 design, failing at 0.6μm roughness.

Physics of one-dimensional capsule designs for the National Ignition Facility

This article describes a suite of 250, 280, and 350 eV copper-doped Be [Be(Cu)] capsule designs for the National Ignition Facility [Paisner et al., Laser Focus World 30, 75 (1994)] and compare these to previous Be(Cu) and bromine-doped CH plastic [CH(Br)] capsule designs for 300 and 330 eV drives. These capsule designs are constrained to have the same deuterium-tritium (DT) fuel mass as the 300 and 330 eV designs so that differences in yield are due to differences in capsule compression before ignition. The one-dimensional (1-D) calculations show that the fuel ρr reaches a maximum value when about 20–30 μm of ablator material is left behind, and this amount of ablator material provides the best trade-off between maximizing the fuel ρr, the implosion velocity, and the calculated clean yield. The results of this paper add optimized 1-D capsule designs that operate at drive temperatures of 250, 280, and 350 eV and they complement the established 300 eV CH(Br) ablator and the 330 eV Be(Cu) ablator designs.

Radiative properties of high wire number tungsten arrays with implosion times up to 250 ns

High wire number, 25-mm-diameter tungsten wire arrays have been imploded on the 8-MA Saturn generator [R. B. Spielman et al., AIP Conference Proceeding 195, 3 (American Institute of Physics, Woodbury, NY 1989)], operating in a long-pulse mode. By varying the mass of the arrays from 710 to 6140 μg/cm, implosion times of 130–250 ns have been obtained with implosion velocities of 50–25 cm/μs, respectively. These Z-pinch implosions produced plasmas with millimeter diameters that radiated 600–800 kJ of x-rays, with powers of 20–49 TW; the corresponding pulsewidths were 19–7.5 ns, with risetimes ranging from 6.5 to 4.0 ns. These powers and pulsewidths are similar to those achieved with 50-ns implosion times on Saturn. Two-dimensional, radiation-magnetohydrodynamic calculations indicate that the imploding shells in these long implosion time experiments are comparable in width to those in the short-pulse cases. This can be due to lower initial perturbations. A heuristic wire array model suggests that the reduced perturbations, in the long-pulse cases, may be due to the individual wire merger occurring well before the acceleration of the shell. The experiments and modeling suggest that 150–200 ns implosion time Z-pinches could be employed for high-power, x-ray source applications.

Z pinch driven inertial confinement fusion target physics research at Sandia National Laboratories

Three hohlraum concepts are being pursued at Sandia National Laboratories (SNL) to investigate the possibility of using pulsed power driven magnetic implosions (Z pinches) to drive targets capable of fusion yields in the range 200-1000 MJ. This research is being conducted on SNL's Z facility, which is capable of driving peak currents of 20 MA in various Z pinch load configurations that produce implosion velocities as high as 7.5 × 107cm/s, X ray energies of 1-2 MJ and X ray powers of 100-250 TW. The first concept, denoted dynamic hohlraum, has achieved a temperature of 180 ± 14 eV in a configuration suitable for driving capsules. In addition, this concept has also achieved a temperature of 230 ± 18 eV in an arrangement suitable for driving an external hohlraum. The second concept, denoted static walled hohlraum, has achieved temperatures of ∼80-100 eV. Experimental investigation of the third concept, denoted Z pinch driven hohlraum, has recently begun. The article discusses each of these hohlraum concepts and provides an overview of the experiments that have been conducted on these systems to date.

One- and two-dimensional simulations of imploding metal shells

We report results of one- and two-dimensional (2D) magnetohydrodynamic simulations of imploding, cylindrical metal shells. One-dimensional simulations are used to calculate implosion velocities of heavy liners driven by 30 MA currents. Accelerated by the j×B force, 45 g aluminum/tungsten composite liners achieve velocities on the order of 13 km/s. Used to impact a tungsten target, the liner produces shock pressures of approximately 14 Mbar. The first 2D simulations of these liners are also described. These simulations have focused on two problems: (1) the interaction of the liner with the electrically conducting glide planes, and (2) the effect of realistic surface perturbations on the dynamics of the implosion. The former interaction is confined primarily to the region of the contact point between the liner and glide plane, and does not seriously affect the inner liner surface. However a 0.2 μm surface perturbation has a significant effect on the implosion dynamics.

The physics issues that determine inertial confinement fusion target gain and driver requirements: A tutorial

This paper presents a simplified, tutorial approach to determining the gains of inertial confinement fusion (ICF) targets, via a basic, zero-dimensional (“0-D”), energy “bookkeeping” of input (parametrized by ICF drivers’ coupling efficiencies to the target, and subsequent hydrodynamic efficiencies of implosion) versus output (thermonuclear burn efficiency and target fuel mass). Physics issues/constraints such as hydrodynamic instabilities, symmetry and implosion velocity requirements will be discussed for both the direct drive (driver impinging directly on the target) and indirect drive (x-ray implosion within a driver heated hohlraum) approaches to ICF. Supplementing the 0-D model with simple models for hohlraum wall energy loss (to predict coupling efficiencies) and a simple one-dimensional (1-D) model of the implosion as a spherical rocket (to predict hydrodynamic implosion efficiencies) allows gains to be predicted that compare well with the results of complex two-dimensional (2-D) radiation hydrodynamic simulations.

Quantum-mechanical calculation of Stark widths of Ne VIIn=3, Δn=0transitions

The Stark widths of the Ne VII $2s3s\ensuremath{-}2s3p$ singlet and triplet lines are calculated in the impact approximation using quantum-mechanical convergent close-coupling and Coulomb-Born-exchange approximations. It is shown that the contribution from inelastic collisions to the linewidths exceeds the elastic width contribution by about an order of magnitude. Comparison with the linewidths measured in a hot dense plasma of a gas-liner pinch indicates a significant difference which may be naturally explained by nonthermal Doppler effects from persistent implosion velocities or turbulence developed during the pinch implosion. Contributions to the linewidth from different partial waves and types of interactions are discussed as well.

Increased x-ray power generated from low-mass large-number aluminum-wire-array Z-pinch implosions

A Saturn accelerator study of annular, aluminum-wire-array, Z-pinch implosions in the calculated high-wire-number plasma-shell regime [Phys. Rev. Lett. 77, 5063 (1996)] shows that a factor of 2 decrease in pulse width and an associated doubling of the total radiated x-ray power occurs when the mass of 12 mm radius, 2 cm long array is reduced from above 1.9 mg to below 1.3 mg. The study utilized extensive time- and space-resolved measurements to characterize the implosion over the mass range 0.42–3.4 mg. Eulerian radiation-magnetohydrodynamic-code simulations in the r-z plane agree qualitatively with the measurements. They suggest that the pulse-width decrease with mass is due to the faster implosion velocity of the plasma shell relative to the growth of the shell thickness that arises from a two-stage development of the magnetic Rayleigh–Taylor instability. Over the bulk of the mass-range explored, the variation in K-shell (lines plus free-bound continuum) yield is in qualitative agreement with simple K-shell radiation-scaling models. These models indicate that the doubling of the measured K-shell yield, which also occurs for masses below 1.3 mg relative to masses above 1.9 mg, arises from increased plasma temperature.

Symmetric aluminum-wire arrays generate high-quality Z pinches at large array radii

A Saturn-accelerator study of annular, aluminum-wire array, Z-pinch implosions, in the calculated high-wire-number plasma-shell regime [Phys. Rev. Lett. 77, 5063 (1996)], shows that the radiated x-ray pulse width increases from about 4 nsec to about 7 nsec, when the radius of the array is increased from 8.75 to 20 mm at a fixed array mass of 0.6 mg. Eulerian radiation- magnetohydrodynamic code (E-RMHC) simulations in the r-z plane suggest that this pulse-width increase with radius is due to the faster growth of the shell thickness (that arises from a two-stage development in the magnetic Rayleigh–Taylor instability) relative to the increase in the shell implosion velocity. Over the array radii explored, the measured peak total x-ray power of ∼40 TW and energy of ∼325 kJ show little change outside of a ±15% shot-to-shot fluctuation and are consistent with the E-RMHC simulations. Similarly, the measured peak K-shell (lines plus continuum) power of ∼8 TW and energy of ∼70 kJ show little change with radius. The minimal change in K-shell yield is in agreement with simple K-shell radiation scaling models that assume a fixed radial compression for all initial array radii. These results suggest that the improved uniformity provided by the large number of wires in the initial array reduces the disruptive effects of the Rayleigh–Taylor instability observed in small-wire-number imploding loads.

Improved large diameter wire array implosions from increased wire array symmetry and on-axis mass participation

Aluminum wire array, Z-pinch experiments have been performed on an 8 MA generator using arrays consisting of 24, 30, and 42 wires. These experiments were designed to scan through a region of (array mass, implosion velocity) space in which greater than 30% conversion of the implosion kinetic energy into K-shell x rays was predicted to occur [Thornhill et al., Phys. Plasmas 1, 321 (1994)]. Array masses between 120 and 2050 μg/cm were used in these experiments. An analysis of the x-ray data taken using 24 wire arrays, shows a one-to-one correspondence between the observed kilo-electron-volt yields (5–64 kJ) and the fraction of initial array mass (0.3%–60%) that is radiating from the K shell. The 30 and 42 wire experiments demonstrated that tighter pinches with increased radiated powers were achieved with these larger wire number, improved symmetry arrays. In addition, increases in the implosion mass and array diameter in the 30 and 42 wire number cases resulted in increases in the radiated yield over the corresponding 24 wire shots, up to 88 kJ, which can be interpreted as due to improved coupling and thermalization of the kinetic energy. Moreover, spectroscopic analyses of the 30 and 42 wire experiments have shown that the increased wire numbers also resulted in K-shell radiating mass fractions of greater than 50%.

Ignition condition and gain scaling of low temperature ignition targets

The ignition and burn dynamics of low temperature ignition (LTI) targets are investigated by means of one dimensional (1-D) coupled transport-hydrodynamics simulations, in which the stagnation dynamics is appropriately taken into account. In this scheme, ignition takes place in the central region of the fuel and then the burn wave propagates outward owing to heating of the fusion products, without the production of a strong shock wave. The ignition condition in the LTI scheme is presented in terms of the usual ρR - T criterion and of the required implosion velocity. A scaling law for the limiting energy gain is proposed. It is shown that with enough fuel confinement (high ρR), higher energy gains can be achieved than those obtained in the previous model with volume ignited, uniformly compressed targets. (The limiting gain is about 1.5 times larger than that in the `volume ignition' computations.) Without sufficient confinement, on the contrary, the bremsstrahlung loss during the stagnation phase increases rapidly, which significantly lowers the energy gain.

Self-similar implosions and explosions of radiatively cooling gaseous masses

A self-similar solution of the gas dynamics equations with heat conduction, which describes homologous contraction and expansion of gaseous masses with a free external boundary, is investigated in detail. As a primary application, implosion of deuterium–tritium (DT) fuel in inertial confinement fusion targets is considered. For strongly non-adiabatic implosions the self-similar solution predicts that the flow pattern should approach an asymptotical regime in which it ceases to depend on the initial entropy. For DT masses relevant to inertial confinement fusion (ICF) this regime begins to dominate at αUim≳6×108 cm/s, where α=p/pdeg is the fuel isentrope parameter, and Uim is its implosion velocity. The solution has also a branch which describes an asymptotical regime of explosive expansion after an ultra-fast initial heating to a strongly radiating state.

Z pinches as intense x-ray sources for high-energy density physics applications

Fast Z-pinch implosions can efficiently convert the stored electrical energy in a pulsed-power accelerator into x rays. These x rays are produced when an imploding cylindrical plasma, driven by the magnetic field pressure associated with very large axial currents, stagnates upon the cylindrical axis of symmetry. On the Saturn pulsed-power accelerator [R. B. Spielman et al., in Proceedings of the 2nd International Conference on Dense Z Pinches, Laguna Beach, CA, 1989, edited by N. R. Pereira, J. Davis, and N. Rostoker (American Institute of Physics, New York, 1989), p. 3] at Sandia National Laboratories, for example, currents of 6–8 MA with a rise time of less than 50 ns are driven through cylindrically symmetric loads, producing implosion velocities as high as 108 cm/s and x-ray energies exceeding 400 kJ. Hydromagnetic Rayleigh–Taylor instabilities and cylindrical load symmetry are critical, limiting factors in determining the assembled plasma densities and temperatures, and thus in the x-ray energies and pulse widths that can be produced on these accelerators. In recent experiments on the Saturn accelerator, these implosion nonuniformities have been minimized by using wire arrays with as many as 192 wires. Increasing the wire number produced significant improvements in the pinched plasma quality, reproducibility, and x-ray output power. X-ray pulse widths of less than 5 ns and peak powers of 75±10 TW have been achieved with arrays of 120 tungsten wires. Similar loads have recently been fielded on the Particle Beam Fusion Accelerator (PBFA II), producing x-ray energies in excess of 1.8 MJ at powers in excess of 160 TW. These intense x-ray sources offer the potential for performing many new basic physics and fusion-relevant experiments.

Energy scaling of inertial confinement fusion targets for ignition and high gain

The dependence of the ignition threshold on the velocity vimp and compressibility of an imploding fuel mass is central to establishing the driver requirements and implosion strategy for inertial confinement fusion (ICF). Using a series of LASNEX calculations, it is found that keimp varies as nu imp- alpha beta a, where keimp is the kinetic energy in the imploding fuel at the ignition threshold, alpha =5.5+or-0.5, a=1.7+or-0.2 and vimp is the implosion velocity. Here, the compressibility parameter beta is related to the pressure P and density rho of the DT fuel by the relation P= beta p53/. These results are obtained by starting at the peak implosion velocity for a fuel shell of a high gain ICF capsule and scaling the isentrope, mass and velocity of the fuel shell. In the presence of a mix of hot and cold material at the edge of the central hot spot, it is also found that the results can be fitted by assuming that the reduced clean fuel radius for a mixed capsule requires a velocity increase of the same magnitude as that which would be required if the entire capsule had been rescaled in size by the same ratio

Time and space resolved measurements of visible-light and soft x-ray emission from foam z-pinch plasmas and implosions

We have developed a time-resolved imaging capability to make measurements of the emission profile or spot size for low density foam z-pinch targets on the Saturn accelerator. By lens-coupling visible emission from the z-pinch target to an array of fiber optics, we obtained an emission profile as a function of time with radial resolution of 200 μm. To measure the emission at temperatures greater than ≈40 eV, x rays from the source were slit-imaged or pinhole-imaged onto a scintillator. The emission was filtered to select 50–80, 200–280, and 400–450 eV x rays. Nonuniformities were observed in both visible and x-ray emissions for solid foam targets. For wire array on foam targets, on-axis x-ray emission-spot implosion velocities calculated for the three spectral regions differed from the mass-implosion velocity. We describe the diagnostics, the image-unfold process, and results from the instrument for both visible and x-ray measurements.

Pulse shaping for ignition and gain of an indirectly driven target

A detailed study of the problem of ignition of the intended indirectly driven ‘‘point design target’’ [J. Lindl, Phys. Plasmas 2, 3933 (1995)] for the U.S. National Ignition Facility is presented. First a multistep pressure pulse which ignites the target (without its ablator) is found and the effect of changing the timing of the different shocks on the target yield is analysed in detail. A radiation drive which nearly reproduces such a pressure pulse at the ablator/fuel interface is then constructed. The resulting radiation drive is similar to the one used by the U.S. workers but has a 3 percent higher peak value. An operating window of about 35 eV width is found around the optimum maximum drive temperature. Below this window the target fails because adequate implosion velocities are not achieved, while above it the main fuel is raised to high entropies resulting in low compressions, despite high implosion velocities. These calculations represent the first independent confirmation, outside the weapons laboratories, that ignition and gain can be achieved near the operating parameters for the above target.

On the gain scaling of ICF targets

A new gain model based on a adiabatic self-similar solution of the hydrodynamic equations is proposed for deuterium-tritium fusion capsules ignited by means of a thermonuclear spark at the fuel center. The model is applied to analyze gain curves that correspond to fixed values of the implosion velocity U im . It is shown that the threshold energy investment into the fuel required for ignition scales as E f,min α α 3 U im −7 for capsules with initially thin shells, i.e. when the initial aspect ratio A 0 ⪢ 1. In the opposite limit of initially thick capsule shells, the scaling of E f,min with the entropy parameter a and the implosion velocity U im, and that of the limiting fuel gain G f ∗ with E f become ill defined; nevertheless, a fair agreement with the Livermore results is observed for α values between 1 and 2, and U im ≈ 4 × 10 7 cm s −2.

Scaling laws for the ignition of deuterium—tritium shell targets

The ignition conditions of imploding shell targets are studied by means of an analytical model for the stagnation phase. The shell is considered to stagnate isentropically, except in the central region of the fuel, where the energy balance is dominated by thermal conduction and radiation losses, and the heating is dominated by compressional work and alpha-particle deposition of energy. Scaling laws for the maximum temperature of the hot spot and for the ignition conditions are found in terms of the shell implosion velocity ν 0, The scaling E B ign ∝ ν 0 −5 for the minimum driver energy required for ignition is found in the velocity range of interest.