Z-pinch simulations using the 5N-moment multi-fluid plasma model with Braginskii transport

The axisymmetric Z pinch is numerically investigated using the 5N-moment multi-fluid plasma model via the Washington Approximate Riemann Plasma (WARPXM) code [U. Shumlak et al., Comput. Phys. COmmun. 182, 1767 (2011)]. WARPXM, developed at the University of Washington, is a high-order-accurate finite element code that uses a discontinuous Galerkin (DG) spatial representation. The Z-pinch initial conditions satisfy a two-fluid (ion and electron) Bennett equilibrium with uniform temperature and axial velocity for each species such that $T_{i} = T_{e}$ and $u_{iz} = - u_{ez}$. The growth rates for a $m = 0$ sausage instability using the ideal 5N-moment two-fluid model can be larger than the growth rates obtained using the ideal MHD model. Due to the initially uniform temperature and axial velocity, the Braginskii viscosity stress tensor $∏ ∝ \nabla \vec{u}$ and conductive thermal heat flux $\vec{h} ∝\nabla T$ are found to only weakly suppress the $m = 0$ sausage instability. However, the frictional force related to the resistivity $\vec{R}_{\alpha \beta} ∝ \vec{J}$ induces electric fields that exhibit strong stabilizing effects by producing a radially sheared flow $∂_{r} u_{z}$. The applicability of 5N-moment multi-fluid plasma model in the high-temperature and weakly collisional fusion plasma will be discussed.