Plasma: MHD; what about neutral fluids?

[MasterD]

When I have an ionized fluid (plasma) and I describe it in a continuum approach I can use the MHD equations (the continuity equation, the equation of motion, the induction equation and the energy equation).

However; I am modeling a certain model of a sunspot and there is also an unionized part (neutral part) present.

How do I model that part? Can I just drop the induction equation and set B=0 in the other equations (the continuity equation, equation of motion and the induction equation?), because the magnetic field has no influence on the neutral part and so I need 1 equation less to calculate all variables?

 

[AndyW]

it is important to consider all variables and factors in a model to accurately represent the system being studied. In this case, the inclusion of the neutral part in the model requires a different approach than simply dropping the induction equation and setting the magnetic field to zero.

The neutral part of the plasma still interacts with the ionized part, and therefore, its behavior cannot be completely disregarded. One possible approach is to include the neutral part in the continuity equation, as it also contributes to the overall density of the plasma. Additionally, the neutral part may also have its own equation of motion, which takes into account its interactions with the ionized part and any external forces.

Furthermore, the energy equation may also need to be modified to account for the energy transfer between the ionized and neutral parts of the plasma. This can be done by including terms that represent the energy exchange between the two components.

It is also important to note that the magnetic field may still have some influence on the neutral part, even if it is not directly coupled to it. Indirect effects, such as the magnetic pressure pushing on the neutral particles, should also be considered in the model.

In summary, the neutral part cannot be simply ignored or excluded from the model. It is necessary to carefully consider its interactions with the ionized part and incorporate it into the relevant equations in order to accurately model the system.

 

[sir-pinski]

When dealing with a plasma, the MHD equations are a suitable way to describe its behavior. This is because the ions and electrons in a plasma are highly charged and interact strongly with magnetic fields. The MHD equations take into account the fluid dynamics and electromagnetic effects of the plasma, making it a powerful tool for studying plasmas in a continuum approach.

However, in some cases, there may be a neutral component present in the plasma, such as in the case of a sunspot. In these situations, it is important to consider the behavior of the neutral fluid as well. The MHD equations do not take into account the dynamics of neutral fluids, as they do not interact with magnetic fields. Therefore, simply dropping the induction equation and assuming B=0 for the neutral part would not accurately represent its behavior.

To model the neutral part, additional equations would need to be included that describe its dynamics. These could include the Navier-Stokes equation for fluid motion, the continuity equation for mass conservation, and the energy equation for thermal effects. The magnetic field would not be included in these equations, as it has no influence on the neutral fluid.

In summary, while the MHD equations are suitable for describing the behavior of a plasma, additional equations must be included to accurately model the neutral component in situations where it is present. Simply dropping the induction equation and assuming B=0 would not provide an accurate representation of the system.