MACH2 Simulations Research Articles

Ar and Kr on deuterium gas-puff staged Z-pinch implosions on a 1-MA driver: Experiment and simulation

Recent experiments on the 1 MA, 100 ns Zebra driver at the Nevada Terawatt Facility at the University of Nevada, Reno, investigated the compression of a deuterium target by a high-atomic-number (Ar or Kr) gas-puff liner. Pinch stability improved with axial premagnetization of 1–2 kG observed as a decrease in magneto-Rayleigh-Taylor instability growth. Implosion dynamics and stagnation conditions were studied computationally with the radiation-MHD code MACH2 using initial conditions that approximate those in the experiment. Typical average and peak implosion velocities exceeded 300 and 400 km/s, respectively, which raised the target adiabat by shock heating as the front converges on axis, at which time the target is adiabatically compressed to stagnation. Experimental fusion yields of up to 2 × 109 for Ar liner on D target implosions were measured, while with a Kr liner yields up to 1 × 1010 were measured. Higher yields in Kr compared to Ar were also calculated in 2-D MACH2 simulations. These observations will be further tested with other radiation-MHD codes, and experiments on the 1 MA LTD-III machine at UC San Diego.

Energy loss to conductors operated at lineal current densities≤10 MA/cm: Semianalytic model, magnetohydrodynamic simulations, and experiment

We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density ${j}_{\ensuremath{\ell}}\ensuremath{\equiv}B/{\ensuremath{\mu}}_{0}$ to be the current per unit electrode width, where $B$ is the magnetic field at the electrode surface and ${\ensuremath{\mu}}_{0}$ is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, $\mathbf{j}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ work, and the increase in the transmission line's vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current $I(t)=0$ for $t<0$, and $I(t)\ensuremath{\propto}t$ for $t\ensuremath{\ge}0$; (iii) ${j}_{\ensuremath{\ell}}\ensuremath{\le}10\text{ }\text{ }\mathrm{MA}/\mathrm{cm}$; and (iv) the current-pulse width is between 50 and 300 ns. Under these conditions we find that, to first order, the total energy lost per unit electrode-surface area is given by ${W}_{t}(t)=\ensuremath{\alpha}{t}^{\ensuremath{\beta}}{B}^{\ensuremath{\gamma}}(t)+\ensuremath{\zeta}{t}^{\ensuremath{\kappa}}{B}^{\ensuremath{\lambda}}(t)$, where $B(t)$ is the nominal magnetic field at the surface. The quantities $\ensuremath{\alpha}$, $\ensuremath{\beta}$, $\ensuremath{\gamma}$, $\ensuremath{\zeta}$, $\ensuremath{\kappa}$, and $\ensuremath{\lambda}$ are material constants that are determined by normalizing the expression for ${W}_{t}(t)$ to the results of 1D magnetohydrodynamic MACH2 simulations. For stainless-steel electrodes operated at current densities between 0.5 and $10\text{ }\text{ }\mathrm{MA}/\mathrm{cm}$, we find that $\ensuremath{\alpha}=3.36\ifmmode\times\else\texttimes\fi{}{10}^{5}$, $\ensuremath{\beta}=1/2$, $\ensuremath{\gamma}=2$, $\ensuremath{\zeta}=4.47\ifmmode\times\else\texttimes\fi{}{10}^{4}$, $\ensuremath{\kappa}=5/4$, and $\ensuremath{\lambda}=4$ (in SI units). An effective time-dependent resistance, appropriate for circuit simulations of pulsed-power accelerators, is derived from ${W}_{t}(t)$. Resistance-model predictions are compared to energy-loss measurements made with stainless-steel electrodes operated at peak lineal current densities as high as $12\text{ }\text{ }\mathrm{MA}/\mathrm{cm}$ (and peak currents as high as 23 MA). The predictions are consistent with the measurements, to within experimental uncertainties. We also find that a previously used electrode-energy-loss model overpredicts the measurements by as much as an order of magnitude.

MACH2 simulations of a micro laser ablation plasma thruster

In this work the detailed physical processes occurring in the high density plasma that is ejected from the solid propellant surface in a small laser ablation thruster are simulated using MACH2. Qualitative results of the laser ablation process that leads to propellant erupting from the surface and leaving behind a crater in a solid Teflon® propellant are presented. Simulations were conducted for a 0.5 μs laser pulse (FWHM) at 935 nm with laser pulse energy ranging from 20 μJ to 2 mJ. Simulation results indicate that crater diameter and depth increase with pulse energy. The impulse bit also increases with pulse energy. Specific impulse follows the opposite trend and decreases with laser pulse energy. The simulated impulse bit for a 2 mJ, 0.5 μs laser pulse over-predicts that reported in the literature for a 2 mJ, 2 ms laser ablation thruster pulse by approximately one order of magnitude and under-predicts the specific impulse by approximately one order of magnitude.

Numerical simulation of cableguns using mach2

A radiation-driven ablation model was developed for the MHD code MACH2 to provide a numerical simulation for cableguns. Ablation from the insulator surface is driven by radiation from an optically thin gray gas in the computational domain adjacent to the insulator surface. Two parameters required for the model-specific opacity and vapor layer transmissivity-were determined from baseline experiments. Using these parameter values, numerical simulations for five additional cablegun configurations were compared with experimental measurements obtained using a two-beam laser interferometer. Equations of state models for copper-Teflon and polyethylene plasmas were calculated for use in these simulations. Comparisons were made for radial profiles of electron density, plume velocity, and plume width. Based on the results obtained in this study, it appears that MACH2 simulations can be used to provide reasonable estimates of cablegun plume properties that are difficult or impossible to obtain experimentally, such as the spatial flow details inside the cavity or the temporal distribution of mass loss.