\phi_g = 4 \pi G \rho \ ,
   \label{Eq:Poisson}\end{aligned}$$ where $G$ is the gravitational constant. Maxwell’s equations are written as, $$\begin{aligned}
   \nabla \cdot \Vec{E} = 4\pi \rho_e \ ,\end{aligned}$$ $$\begin{aligned}
   \nabla \cdot \Vec{H} = 0 \ ,
   \label{Eq:divH}\end{aligned}$$ $$\begin{aligned}
   \nabla \times \Vec{E} = 0 \ ,
   \label{Eq:rotE}\end{aligned}$$ $$\begin{aligned}
   \nabla \times \Vec{H} = 4 \pi \frac{\Vec{j}}{c} \ ,
   \label{Eq:rotH}\end{aligned}$$ where $\rho_e$ and $\Vec{E}$ are the electric charge density and the electric field, respectively. Notice that we neglect the displacement current term in Eq.(\[Eq:rotE\]) as is common in MHD approximation. The ideal MHD condition, or the generalized Ohm’s equation, can be expressed as: $$\begin{aligned}
   \Vec{E} = - \frac{\Vec{v}}{c} \times \Vec{H} \ .\end{aligned}$$ We choose two kinds of barotropic equations of state. One is the polytropic equation of state: $$\begin{aligned}
   p = K_0 \rho^{1+1/N} \ ,\end{aligned}$$ where $N$ and $K_0$ are the polytropic index and the polytropic constant, respectively. The other is the degenerated Fermi gas at zero temperature, defined as $$\begin{aligned}
p = a[x(2x^2 - 3)\sqrt{x^2 + 1} + 3 \ln(x + \sqrt{x^2 + 1}) ],\end{aligned}$$ where $$\begin{aligned}
 \rho = bx,\end{aligned}$$ $$\begin{aligned}
 a = 6.00 \times 10^{22} \hspace{10pt} \mathrm{dyn/cm}^2,\end{aligned}$$ $$\begin{aligned}
 b = 9.825 \times 10^5  \mu_e \hspace{10pt} \mathrm{g/cm}^3.\end{aligned}$$ Here $\mu_e$ is the 