The effect of phenomenological modeling of z-pinch implosions on the scaling of k-shell emission with atomic number and mass

Recent 1-D phenomenological modeling of plasma turbulence by enhancing transport coefficients has shown that it is possible to achieve good agreement with experimental plasma conditions at stagnation, especially when compared to previous laminar flow calculations. Since this original phenomenological study focused upon only a single Physics International Inc. argon experiment, it is important to build a stronger foundation for this modeling. This is accomplished by: (1) including turbulence effects phenomenologically in the 1-D, radiation, MHD average fluid description of the turbulent flow by enhancing the resistivity Ω, viscosity υ, and heat conductivity κ transport coefficients; (2) finding a set of (κ,υ,Ω) coefficients that reasonably produces the stagnation temperatures and densities of a Physics International Inc. aluminum experiment; (3) this choice of transport coefficients is then tested for dependence on mass loading m and atomic number Z by comparing calculated implosion conditions with those found in a variety of PI aluminum and argon experiments. The authors find that the choice of enhanced transport coefficients that produces good agreement with the stagnation temperatures and densities of the single PI aluminum experiment also gives acceptable agreement for the other aluminum and argon experiments. Based on the presumption that a better representation of plasma conditions at stagnation also gives rise to more realistic K-shell yield scaling with atomic number, the minimum load mass and kinetic energy (machine energy) requirements needed to efficiently produce K-shell emission are calculated for aluminum and argon using enhanced transport calculations. These results are then extrapolated to other Z materials and compared with predictions of the original laminar flow scaling study. Implications of this work for large current machines will be presented