MHD (MagnetoHydroDynamics) is an approximation used for studying plasmas which treats the plasma a single electrically conducting fluid permeated by a magnetic field.
Electric currents induced by the motion of charged particles affect the magnetic field, and at the same the magnetic field affects the motion itself. This interaction between motion and magnetic field is an interesting feature of MHD.
MHD is valid where typical length scales are much larger then the gyro-radius of ions and electrons (the radius of gyration of electrons around magnetic field lines, and typical time scales much longer than gyro-periods.
Here are the equations of non-ideal MHD which constitute the conservation of mass,momentum and energy, along with the induction equation which describes the evolution of the magnetic field.
The MHD equations are non-linear coupled partial differential equations, and for non-trivial situations, need to be solved numerically. The CFSA uses high order finited difference numerical codes, hybrid codes, PIc codes, Vlasov codes, and Lagrangian Remap codes for solving all manner of plasma physics problems.
My work involves the use of a lagrangian remap code