Multiple Ion Species MHD

If I have a fully ionized plasma consisting of electrons and a mixture of different positive ion species of varying masses and charges...how can I use the MHD model to describe the plasma fluid motion, taking into account the coupling between different ion species and electrons?

• Typically one uses MHD assuming bulk properties of fluid (i.e., is a quasi-neutral plasma), no? Otherwise it's Particle-in-Cell methods that I'm aware of for modeling (at least numerically) Aug 30, 2019 at 19:13
• quasi-neutral yes...PIC would be too coding intensive not to mention the amount of computation power needed...are there any analytical methods? Aug 30, 2019 at 19:25
• Well you could use two-fluid approx for the MHD, but that won't be any more work than a PIC code...it might help if you add more details to the question about what you are trying to do, as it is terribly vague (at least to me). Aug 30, 2019 at 20:05

In a theoretical description you can use the general fluid equations to describe some properties of a multi-species plasma. For all quantities depending on space $$\mathbf{x}$$ and time $$t$$, you have the equation of continuity: $$\partial_t n_\alpha + \nabla \cdot (n_\alpha \mathbf{v_\alpha}) = 0,$$ and the momentum equation: $$\partial_t \mathbf{v_\alpha} + \mathbf{v_\alpha} \cdot \nabla \mathbf{v_\alpha} = -\frac{1}{n_\alpha m_\alpha} \nabla p_\alpha + \frac{q_\alpha}{m_\alpha} \left(\mathbf{E} + \frac{1}{c} \mathbf{v_\alpha} \times \mathbf{B} \right),$$ with mass $$m$$, charge $$q$$ and isotropic pressure $$p_\alpha = n_\alpha T_\alpha$$ (all equations given in CGS units). $$\alpha$$ stands here for the particle species, e.g. $$\alpha = e^-, p^+, \dots$$. For each species you have 1 equation. In addition to that the electric and magnetic fields have to satisfy the Maxwell equations (which I don't write here).
The coupling of the species happens via the charge and current densities in the Maxwell equations. These quantities are given by: \begin{align} \rho &= \sum_\alpha q_\alpha n_\alpha, \\ \mathbf{J} &= \sum_\alpha q_\alpha n_\alpha \mathbf{v}_\alpha. \end{align}