Insights from two-fluid modeling of linear growth and nonlinear saturation of kink and sausage modes in the Z pinch

Five-moment two-fluid modeling is used to explore linear and nonlinear behavior of Z-pinch instabilities. Key features of PIC results are reproduced, opening the possibility of whole device modeling with physical fidelity comparable to kinetic simulations. Initial conditions, based on Bennett equilibria, represent experimental observed plasma conditions in the FuZE experiment. Radially sheared axial flows of various strengths are included. Growth rates of m=0 sausage instabilities are benchmarked against results from prior Hall MHD and PIC kinetic calculations. Agreement with Hall MHD results is excellent, and growth rates decrease for normalized axial wavenumbers k_za>10, as observed in PIC modeling. A Braginskii-based transport model is used to capture the effects of viscosity and heat flux, including gyroviscosity and diamagnetic heat flows. Nonlinear saturation of the m=0 instability is also studied. Mode mixing due to moderate sheared flow yields a quasi-steady state after pinch ion inventory and thermal energy losses of approximately 30% and 10%, respectively. In addition, 3D modeling of linear and nonlinear behavior of m=1 kink instabilities will be presented. All modeling is done in the high-order discontinuous Galerkin WARPXM framework.