N.F. Roderick

Simulations of a Plasma Flow Switch

In a portion of the experimental program using the SHIVA Star capacitor bank at the Air Force Weapons Laboratory (AFWL), a cylindrical foil load is imploded using an inductive store and a plasma flow switch. We have performed a number of two-dimensional simulations of the switch and load using the MHD code MACH2. In addition to explaining the data from the first series of experiments, the simulations led to design modifications of the basic plasma flow switch that resulted in improved current delivery and in enhanced radiation yield. The experimental results are reported in a companion paper by Degnan et al. The key modification was closing portions of the vane structure. The switch must be sealed shut or else substantial current will flow in the diffuse gas that is ablated from the walls of the switch barrel.

Hydromagnetic Rayleigh–Taylor instability in high-velocity gas-puff implosions

Experiments using the Saturn pulsed power generator have produced high-velocity z-pinch plasma implosions with velocities over 100 cm/μs using both annular and uniform-fill gas injection initial conditions. Both types of implosion show evidence of the hydromagnetic Rayleigh–Taylor instability with the uniform-fill plasmas producing a more spatially uniform pinch. Two-dimensional magnetohydrodynamic simulations including unsteady flow of gas from a nozzle into the diode region have been used to investigate these implosions. The instability develops from the nonuniform gas flow field that forms as the gas expands from the injection nozzle. Instability growth is limited to the narrow unstable region of the current sheath. For the annular puff the unstable region breaks through the inner edge of the annulus increasing nonlinear growth as mass ejected from the bubble regions is not replenished by accretion. This higher growth leads to bubble thinning and disruption producing greater nonuniformity at pinch for ...

Enhancement of the radiation yield, in plasma flow switch experiments

The Shiva Star fast capacitor bank, an inductive store, and a plasma flow switch were used to deliver multimegaampere currents with submicrosecond rise times to cylindrical foil loads. A series of numerical simulations of the plasma flow switch/imploding load system were performed with the goal of discovering a way to boost the total power radiated by the imploding plasma as it stagnates on the axis of symmetry. The changes to the experimental design that were investigated include variations of the shape of the electrodes, size and mass of the load foil, structure of the axial view vanes, shape and mass of the switching plasma, material from which the load is constructed, the degree to which the load is bowed, and the energy of the capacitor bank. Radiation yields in the range 6-9 TW are predicted for future experiments on Shiva Star. >

Numerical modeling of nested wire arrays on the Z accelerator

Summary form only given. The Magnetohydrodynamic (MHD) Rayleigh-Taylor (RT) instability is believed to be one of the limiting factors in z-pinch performance. More specifically, for high velocity, large diameter implosions characteristic of the Z accelerator, numerical calculations suggests that this instability broadens the plasma shell and can account for experimentally measured pulsewidths greater than 6 ns. To improve pinch performance, uniform fills, tailored density profiles, tuning layers (i.e., inner load downstream of outer load), and B/sub z/ stabilization have been proposed to mitigate the RT growth. In all of these schemes, a trade-off exists between improved stability and decreased energy coupling with the machine. The simplest of these techniques to implement and optimize experimentally is the tuning layer. Numerical simulations are presented for a series of nested wire array experiments which were based on the concept of the tuning layer.

Numerical simulations of Plasma/Magnetic Field/Liner interactions in magnetized target fusion systems

Summary form only given. Magnetized target fusion (MTF) relies on magnetic field suppression of thermal transport to achieve fusion conditions at relatively low driver power. One method proposed for MTF uses an imploding liner which starts at solid density to compress a hot magnetized plasma. Analytic methods and one and two dimensional magnetohydrodynamic simulations are being used to study this plasma liner compression approach. Plasma from the liner walls represents a contaminant that can increase radiation losses and lower plasma temperatures below desired values. As part of this effort are we are investigating the generation and evolution of such plasmas. Energy input to the liner from thermal conduction and joule heating from both the magnetized plasma and the driving magnetic field are under study to determine their contributions to the production of contaminant and the interaction of these plasmas with the hot fusion plasma. Results from these ongoing calculations will be presented.

Three-dimensional hydromagnetic simulation of a high-velocity gas-puff Z-pinch

Experiments on the Sandia National Laboratories Saturn pulsed power machine have produced high-velocity Z-pinch plasma implosions of krypton gas puffs from a circular nozzle. We use the three-dimensional (3-D), time-dependent MACH3 magnetohydrodynamics code to simulate these experiments. Generally, the quality of Z-pinch implosions is degraded by hydromagnetic Rayleigh-Taylor instabilities. The images displayed in this paper illustrate the growth in time of this instability in three spatial dimensions from a modest (and realistic) initial 3-D perturbation.

Extended MHD Modeling of FRC Liner Compression

Summary form only given. Compression of a field reversed configuration of plasma and magnetic field by a near-solid liner is an attractive path to fusion. We have previously developed the capability to model the formation and translation of an FRC into an imploding liner that subsequently compresses the magneto-plasma to fusion conditions aided by the magnetic inhibition of the thermal conduction. The model is embodied in a single, integrated simulation of the liner and FRC using the full power of MACH2, a 2 1/2-dimensional time-dependent arbitrary-coordinate, true ALE MHD code. The lifetime of the FRC undergoing relatively violent translation and subsequent compression is critical to the performance of the experiment. It is thought that extended MHD effects, such as the Hall effect, the thermoelectric effect, and finite Larmor radius effects may enhance or reduce this lifetime. While our previous simulations have used the Chodura subgrid turbulence model for enhanced resistivity -a nonclassical effect -the physics included has been standard MHD. The Hall and thermoelectric effects, introduced through generalization of the standard MHD Ohms law, can produce toroidal field and rotation not shown by standard MHD FRC models; if sufficient bulk rotation develops, rotational interchange instability may reduce the FRC lifetime. Finite Larmor radius effects are generally diffusive, hence stabilizing, and may enhance the lifetime. We will show simulations of FRC formation and translation that include these extended MHD effects.

Modeling Liner Compression of FRCs: Obstacles and Advances

Compression of a field-reversed configuration (FRC) by an imploding solid liner is a possible path to magnetized target fusion. It is critical to the success of such experiments to perform full-up multidimensional computational simulations of them. However, there are numerous difficulties in performing those simulations. The interacting physical processes involved introduce disparate time scales. For example, the FRC itself has near-vacuum buffer-field regions that have extremely high Alfven velocity, while the implosion of the liner proceeds at a much slower pace. These strongly differing time scales impose stringent accuracy requirements. The lifetime of an FRC of sufficient density to provide interesting fusion output is on the order of 10 ms while the implosion times of liners of sufficient thickness to survive acceleration to the requisite velocity are somewhat longer than 20 ms. Hence, the FRC must be formed and translated into the liner after the liner implosion begins, so that the FRC formation fields may perturb the liner. Our previous simulations of the experiment have addressed formation separately from the liner implosion and merged the FRC into the liner simulation, preventing proper assessment of this issue. Experimental success hinges on realizing the magnetic inhibition of thermal conduction to prevent loss of plasma energy. Our previous simulations of the final stages of FRC compression have often failed because of inaccuracy in the numerical treatment of the parallel flux. The Rayleigh Taylor instability of the inner surface of the liner during final stages of compression may ultimately limit the performance of this system and must be assessed computationally. However, the modes that grow are those with crests parallel to the FRCs magnetic field, and are not present in the 2-d azimuthally symmetric simulations used for design of the FRC formation and liner implosion. We have made significant progress on these issues. First, we have performed fully integrated, simultaneous simulations of liner implosion and FRC formation on the same grid. These simulations address the generation of rotation in the FRC as well as perturbations of the liner. Second, we have developed a mixed-order numerical treatment of the anisotropic heat conduction that has proven both more robust and more accurate. The improvement has enabled us to run more simulations for design purposes. Finally, we have begun to perform 3-d simulations of the final stages of compression, beginning from the self-consistent state of the 2-d axisymmetric simulation, perturbed in a mass, energy, momentum, and flux conserving .

MTF investigations with Shiva-Star: formation and translation of an FRC into an imploding solid liner with deformable contacts

Summary form only given. Shiva Star - the U.S. Air Force Research Laboratory Directed Energy Directorates 10 MJ, ten microsecond capacitor bank - has symmetrically imploded cylindrical aluminum liners suitable for compressing MTF plasmas. An FRC target plasma has been created in experiments at Los Alamos National Laboratory. Since the FRC is driven by a rapidly rising axial magnetic field that cannot penetrate the compression liner, the FRC will need to be translated into the liner after formation and before compression. Shiva Star has been used to explore an imploding cylindrical liner with open ends that remains connected to fixed annular electrodes during the implosion by tapered ends that implode more slowly than its cylindrical center. We show two-dimensional magnetohydrodynamic simulations performed with MACH2 of formation and translation of an FRC fusion target plasma and its compression by an imploding liner with deformable contacts. Neutron yield is presented and the effects of anisotropic thermal diffusion is explored.

Long implosion experiments and simulations on the Saturn and Z machines

Summary form only given. By increasing the implosion time for Z-pinches from the canonical 100 ns to 200-300 ns, the complexity and power flow risks can be reduced for future higher current generators, assuming that the implosions still produce high energies and powers. The recent success of high wire number arrays and nested configurations have permitted load designs to be considered that could provide the necessary performance at the longer implosion times, i.e. can we challenge the conventional wisdom? At Sandia National Laboratory, two experimental campaigns (on Saturn and Z) plus two-dimensional MHD modeling have been performed to investigate the scaling of tungsten wire arrays to 150 to 250 ns implosion times.