James H. Hammer

Ignition and high gain with ultrapowerful lasers

Ultrahigh intensity lasers can potentially be used in conjunction with conventional fusion lasers to ignite inertial confinement fusion (ICF) capsules with a total energy of a few tens of kilojoules of laser light, and can possibly lead to high gain with as little as 100 kJ. A scheme is proposed with three phases. First, a capsule is imploded as in the conventional approach to inertial fusion to assemble a high‐density fuel configuration. Second, a hole is bored through the capsule corona composed of ablated material, as the critical density is pushed close to the high‐density core of the capsule by the ponderomotive force associated with high‐intensity laser light. Finally, the fuel is ignited by suprathermal electrons, produced in the high‐intensity laser–plasma interactions, which then propagate from critical density to this high‐density core. This new scheme also drastically reduces the difficulty of the implosion, and thereby allows lower quality fabrication and less stringent beam quality and symmet...

High yield inertial confinement fusion target design for a z-pinch-driven hohlraum

Calculations are presented for a high yield inertial fusion design, employing indirect drive with a double-ended z-pinch-driven hohlraum radiation source. A high current (∼60 MA) accelerator implodes z pinches within an enclosing hohlraum. Radial spoke arrays and shine shields isolate the capsule from the pinch plasma, magnetic field, and direct x-ray shine. Our approach places minimal requirements on z-pinch uniformity and stability, usually problematic due to magneto-Rayleigh–Taylor instability. Large inhomogeneities of the pinch and spoke array may be present, but the hohlraum adequately smooths the radiation field at the capsule. Simultaneity and reproducibility of the pinch x-ray output to better than 7% are required, however, for good symmetry. Recent experiments suggest a pulse shaping technique, through implosion of a multishell z pinch. X-ray bursts are calculated and observed to occur at each shell collision. A capsule absorbing 1 MJ of x rays at a peak drive temperature of 210 eV is found to ha...

Investigations of the magnetic structure and the decay of a plasma‐gun‐generated compact torus

The results of a series of experimental measurements of compact toroidal (CT) plasmas produced by a magnetized coaxial plasma gun injecting into a flux‐conserving metallic liner are reported. The experiments were performed on the Beta II facility at Lawrence Livermore National Laboratory. The magnetic equilibria are well described by a force‐free eigenmode structure that results from an extension of Taylor’s theory of the reversed‐field pinch. Consideration of helicity conservation during relaxation of the composite plasma‐gun flux‐conserver system to the final state equilibrium yields theoretical expressions that are compared with the experiment. In particular the CT poloidal flux (ψpol) and the overall electrical efficiency for producing the CT are predicted to be functions of the plasma gun inner‐electrode flux (ψgun) and the volt‐seconds input to the gun discharge (∫∞0 V dt). Away from a cutoff at too low values of ∫∞0  V dt or too high values, ψgun ,ψpol scales linearly with the square root of the pr...

Development and characterization of a Z-pinch-driven hohlraum high-yield inertial confinement fusion target concept

Initial experiments to study the Z-pinch-driven hohlraum high-yield inertial confinement fusion (ICF) concept of Hammer, Tabak, and Porter [Hammer et al., Phys. Plasmas 6, 2129 (1999)] are described. The relationship between measured pinch power, hohlraum temperature, and secondary hohlraum coupling (“hohlraum energetics”) is well understood from zero-dimensional semianalytic, and two-dimensional view factor and radiation magnetohydrodynamics models. These experiments have shown the highest x-ray powers coupled to any Z-pinch-driven secondary hohlraum (26±5 TW), indicating the concept could scale to fusion yields of >200 MJ. A novel, single-sided power feed, double-pinch driven secondary that meets the pinch simultaneity requirements for polar radiation symmetry has also been developed. This source will permit investigation of the pinch power balance and hohlraum geometry requirements for ICF relevant secondary radiation symmetry, leading to a capsule implosion capability on the Z accelerator [Spielman et...

Two‐dimensional radiation‐magnetohydrodynamic simulations of SATURN imploding Z pinches

Z‐pinch implosions driven by the SATURN device [D. D. Bloomquist et al., Proceedings of the 6th Institute of Electrical and Electronics Engineers (IEEE) Pulsed Power Conference, Arlington, VA, edited by P. J. Turchi and B. H. Bernstein (IEEE, New York, 1987), p. 310] at Sandia National Laboratory are modeled with a two‐dimensional radiation magnetohydrodynamic (MHD) code, showing strong growth of the magneto‐Rayleigh–Taylor (MRT) instability. Modeling of the linear and nonlinear development of MRT modes predicts growth of bubble‐spike structures that increase the time span of stagnation and the resulting x‐ray pulse width. Radiation is important in the pinch dynamics, keeping the sheath relatively cool during the run‐in and releasing most of the stagnation energy. The calculations give x‐ray pulse widths and magnitudes in reasonable agreement with experiments, but predict a radiating region that is too dense and radially localized at stagnation. We also consider peaked initial density profiles with consta...

A Consistent Approach to Solving the Radiation Diffusion Equation

Diffusive x-ray-driven heat waves are found in a variety of astrophysical and laboratory settings, e.g., in the heating of a hohlraum used for inertial confinement fusion, and hence are of intrinsic interest. However, accurate analytic diffusion wave (also called Marshak wave) solutions are difficult to obtain due to the strong nonlinearity of the radiation diffusion equation. The typical approach is to solve near the heat front, and by ansatz apply the solution globally. This approach works fairly well due to “steepness” of the heat front, but energy is not conserved and it does not lead to a consistent way of correcting the solution or estimating accuracy. In this work, the steepness of the front is employed through a perturbation expansion in e=β/(4+α), where the internal energy varies as Tβ and the opacity varies as T−α. The equations are solved using an iterative approach, equivalent to asymptotic methods that match outer (away from the front) and inner (near the front) solutions. Typically e<0.3. Ca...

Submegajoule liner implosion of a closed field line configuration

The adiabatic compression of a preformed closed field line configuration by an imploding liner is considered. Three configurations are discussed: the field-reversed configuration, the spheromak, and the Z-pinch. It is shown that by employing a two-dimensional compression, one can reach a breakeven condition with an energy input into the plasma as low as 100 kJ. A brief discussion of various phenomena affecting the plasma wall confinement is presented. It is shown that heat losses to the walls are modest and do not limit the plasma enhancement factor Q. The derived scaling law for Q versus the input parameters of the system shows a relatively weak dependence of Q on the input energy. 34 refs., 9 figs., 2 tabs.

Unstable continuous spectrum in magnetohydrodynamics

The continuous spectrum need not be stable for an equilibrium with flow. The case of a noncircular, rotating ϑ pinch is shown to have an unstable continuum with the instability interpreted as a parametric instability arising from coupling between the rotation frequency and the plasma wave frequencies. On the other hand, equilibria with sub‐Alfvenic flow parallel to the magnetic field in incompressible plasmas, as well as static equilibria, have a stable continuum. A formulation to determine the continuous spectrum is given in terms of characteristic surfaces for the equations and does not involve the use of any particular system of coordinates.

Experimental demonstration of compact torus compression and acceleration

Tests of compact torus (CT) compression on the RACE device [Phys. Rev. Lett. 61, 2843 (1988)] have successfully demonstrated stable compression by a factor of 2 in radius, field amplification by factors of 2–3 to 20 kG, and compressed densities exceeding 1016 cm−3. The results are in good agreement with two‐dimensional magnetohydrodynamic simulations of the CT dynamics. The CT is formed between a pair of coaxial conical conductors that serve as both a flux conserver for stable, symmetric formation and as electrodes for the compression and acceleration phases. The CT is compressed by J×B forces (poloidal current, toroidal field) when a 120 kV, 260 kJ capacitor bank is discharged across the electrodes. The CT reaches two‐fold compression to a radius of 8 cm and a length of 20–30 cm near the time of peak current, 10 μsec (many Alfven times) after the accelerator fire time, and is subsequently accelerated in a 150 cm straight coaxial section to velocities in the range 1.5–6.5×107 cm/sec. A new set of accelera...

Turbulent relaxation of compressible plasmas

Relaxation of plasmas via turbulence is treated by the use of a maximum entropy principle. The relaxed states are always stable to ideal modes. Taylor’s theory of field reversal is extended to finite pressure plasmas and given a rigorous support by using symmetries in the equations to determine preferred conservation laws. Relaxed states of field‐reversed ϑ pinches are predicted, some with self‐reversal of the magnetic field.