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In the formulation of Elsasser’s variables $\mathbf{U} = \mathbf{v}+\mathbf{b}$ and $\mathbf{W} = \mathbf{v}-\mathbf{b}$, \begin{eqnarray} &&\partial_t \mathbf{U} = -(\mathbf{W}\cdot\nabla)\mathbf{U}-\nabla p,\ &&\partial_t \mathbf{W} = -(\mathbf{U}\cdot\nabla)\mathbf{W}-\nabla p,\ &&\nabla\cdot\mathbf{U} = \nabla\cdot\mathbf{W} = 0. \end{eqnarray}

In relativistic MHD, the magnetic field 4-vector $b_{\mu}$ and electric field $e_\mu$ in the fluid frame is defined through the 4-vector $u^{\mu}$ and EM 2-form $F_{\mu\nu}$. \(\begin{eqnarray} b^\mu &=& u_{\nu}*F^{\mu\nu}\\ e^\mu &=& u_{\nu}F^{\mu\nu} \end{eqnarray}\) where $*$ means the Hodge-dual of the 2-form.

Running FDM simulations The FDM simulations in ENZO can be run through ProblemType 30 for cosmological simulations and ProblemType 191 for non-cosmological FDM-only simulations. The key parameters for running FDM simulations are QuantumPressure which should be set to 1 to enable the evolution of Schrodinger-Poisson equation and FDMMass which sets the value of FDM particle mass in unit of $10^{-22}$ eV.